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Calculus/Choosing delta. Recall the definition of a limit: A number formula_1 is the limit of a function formula_2 as formula_3 approaches formula_4 if and only if "for all" numbers formula_5 there exists a number formula_6 such that whenever In other words, given a number formula_9 we must construct a number formula_10 such that assuming we can prove moreover, this proof must work for "all" values of :formula_5 . Note: this definition is not constructive -- it does not tell you how to "find" the limit formula_1 , only how to check whether a particular value is indeed the limit. We use the informal definition of the limit, experience with similar problems, or theorems (L'Hopital's rule, for example), to determine the value, and then can prove the correctness of this value using the formal definition. Example 1: Suppose we want to find the limit of formula_15 as formula_3 approaches formula_17 . We know that the limit formula_1 is 9+5=14, and desire to prove this. We choose formula_19 (this will be explained later). Then, since we assume we can show which is what we wanted to prove. We chose δ by working backwards from the formula we are trying to prove: formula_7 . In this case, we desire to prove given so the easiest way to prove it is by choosing formula_19 . This example, however, is too easy to adequately explain how to choose formula_10 in general. Lets try something harder: Example 2: Prove that the limit of formula_26 as formula_3 approaches formula_28 is formula_29 . We want to prove that given We choose formula_10 by working backwards. First, we need to rewrite the equation we want to prove using formula_10 instead of formula_3: formula_35 Note: we used the fact that formula_36 , which can be proven with the triangle inequality. Word of caution: the above series of equations is not a logical series of steps, and is not part of any proof, but is an informal technique used to help write the proof. We will select a value of formula_10 so that the last equation is true, and then use the last equation to prove the equations above it in turn (which is what was meant earlier by "working backwards"). Note: in the equations above, when formula_10 was substituted for formula_3 , the sign formula_40 was replaced with formula_41 . This can be done (but is not necessary) because we are not told that formula_42 , but rather formula_31 . The justification for this becomes clear when the above equations are used in backwards order in the proof. We can solve this last equation for formula_10 using the quadratic formula: Note: formula_10 is "almost always" in terms of formula_9 . A constant value of formula_10 (e.g., formula_49) will not work unless the limit is of a constant function (for instance, formula_50). Now, we have a value of formula_10 , and we can do our proof: given formula_53 Here a few more examples of choosing formula_10 ; try to figure them out before reading the explanation. Example 3: Prove that the limit of formula_55 as formula_3 approaches formula_57 is formula_58 . Explanation: Example 4: Prove that formula_59 has no limit as formula_3 approaches formula_57 . Example 5: Prove that formula_62 Solution: To do it, we'll look at two cases: formula_63 and formula_64 . The formula_63 case is easy. First let's let formula_66 . That means we want the values chosen in the domain to map to formula_67 in the range. We want a delta such that formula_68 so let's choose formula_69 . The chosen formula_10 defines the interval formula_71 in our domain. This gets mapped to formula_72 in our range, which is contained in formula_67 . Notice that formula_10 doesn't depend on formula_9 . So for formula_76, we widen the interval in the range that we are allowed to map onto, but our interval in the domain stays fixed and always maps to the same sub-interval in the range. So formula_69 works for any formula_63. Now suppose formula_79 . We want a formula_10 such that formula_81 whenever formula_82 . So let's assume formula_81 and work backwards to find a suitable formula_10: Since formula_79 , we have formula_89 . Since both numbers above are positive, we can take the (positive) square root of both extremes of the inequality: The above equation represents the distance, either negative or positive, that formula_3 can vary from 2 and still be within formula_9 of 4. We want to choose the smaller of the two extremes to construct our interval. It turns out that formula_94 for formula_79 , so choose formula_96 . As a sanity check, let's try with formula_97 . which is approximately At the extreme right of the domain, this gives and which is within 0.002 of 4.

Learning the vi Editor. This book aims to teach you how to use the vi editor, common to many Unix and Unix-like operating systems. ~ ~ "Learning_the_vi_editor" [New file]. The above text is a little example of how the vi editor's screen looks.

Learning the vi Editor/Getting acquainted. Introduction. Overview. vi is a powerful editor that is ubiquitous amongst Unix and Unix-like operating systems, but is available on many other operating systems, even on MS-DOS, Windows and the Macintosh. If not the original vi, there is usually at least a good clone available that runs on your system. Even if you use another editor you must have a passing knowledge of vi as an administrator. Sometimes vi is the only editor available when your computer crashes leaving a minimal system for you to repair. vi, pronounced like 'vee eye', was originally written by Bill Joy for BSD Unix in Berkeley in 1976 and became quickly part of many vendor-specific versions of the (at that time) original AT&T Unix. It was later directly added to AT&T's System V Unix, too. Bill Joy later went on to co-found Sun Microsystems, and became the company's Chief Scientist at that time. vi stands for "visual" and was an enormous improvement of the classic Unix editor called ed. ed is a line-editor. If you are still familiar with MS-DOS, then you may know the MS-DOS edlin editor. ed is similar, although more powerful than edlin, which doesn't mean much. vi also has a line-mode, called ex. In fact, one can argue that the program is indeed two editors in one, one editor called vi, another called ex. It is possible to switch between line and visual mode during editing. It is also possible to choose the mode during startup. However, pure usage of ex is rare. The visual mode is the prevailing mode. Although vi stands for "visual", classic vi is mainly operated via the character keys, and not via the mouse or the cursor keys. Once you are used to this, it becomes extremely convenient, because there is less movement of the hands to the cursor keys or mouse involved. vi also served as a kind of incubator for Unix's terminal control capabilities. Because of vi's need to control the terminal and the many different types of terminals at that time, the "termcap" (terminal-capabilities) database was introduced (later replaced with the more flexible "terminfo" database). vi's internal high-level screen control library was later separated, and became "curses" - the Unix standard library for CRT screen handling. Conventions. unix-command(section) Getting vi if you don't have it already. If you're running a Unix system, or a Unix-like system (for simplicity from now on we will refer to both as a "Unix system"), such as a BSD or Linux distribution, or even Mac OS X, you're sure to have vi or one of its variants on your system. If you're running Windows, you can get a version of vi called "vim" or "elvis". If you're on an older Mac OS (pre-OS X) system, you can get MacVim Classic here. Noted vi variants. As mentioned, vi has a number of variants. They have been created because vi was only available on rather expensive Unix operating systems. Although vi itself, as well as nvi, was created in Berkeley for the free BSD Unix variant, usage of BSD Unix required an original AT&T Unix license (this has later changed, see below). Original vi, for example, used code from AT&T's ed"(1)" editor. Over time, BSD replaced much of the original AT&T code up to the point where today there is no such code any more in BSD, and an original Unix license is no longer needed. As part of the effort to replace all AT&T code in BSD, Keith Bostic undertook the work to create a clone of vi that was free of AT&T code, called nvi. nvi then became BSD's standard vi instead of the original vi. Another vi clone is Elvis, which was written by Steve Kirkendal. Over time, nvi was enhanced – for example, supporting multiple windows – but originally it was not supposed to be an enhancement, 'just' a pure clone. BSD's original vi (with the ed code inside) lives on as the vi which is distributed with System V Unix, because AT&T decided a long time ago to take it from BSD and add it to the official Unix. Of course AT&T didn't have a problem with an AT&T Unix license, so they probably never replaced the ed code inside the original vi. Yet, some find nvi still to be too minimal, and so vim was born. vim (vi-i"m"proved), is another effort to extend vi's capabilities. Unlike nvi, vim goes even further to extend vi's capabilities. However some find that vim is often too much. vim comes in two variants, a text-only version, and a GUI version, the latter is called gvim. Other vi clones are the already mentioned elvis and stevie. These clones were born in the CP/M and home computer area to bring the editor to these platforms, too. Of course, they were later ported to MS-DOS and Windows. These days, however, vim seems to be the prevailing vi-clone on free/open platforms and proprietary platforms as well. "You should choose the version you feel most comfortable with" – if you have an editor you feel displeased with, it will affect your productivity. Getting around vi. Starting the editor. If you are running a Unix system, you can start up vi by typing vi at the command line. If you are running X, with a desktop like GNOME, KDE, CDE/Motif or OpenLook you may have a launcher button handy to start the editor - if you have such a setup, you can just click the icon. If you are running Windows or DOS with elvis, you can start up the Windows editor by double-clicking "winelvis.exe", or in DOS, you can start the editor by typing in "elvis" at the command line. You will be greeted with a screen similar to: ~ ~ ~ "No File" Quitting the editor. To quit for now, press the Escape key (the editor should beep), then enter the three characters and press Return: Just before you type the final the screen will look similar to ~ ~ ~ :q! is the short form of which quits the editor, without saving. You should be dropped back to your operating system (or, rather, the shell from where you started). There are other ways to quit, e.g. pressing () will save any unsaved work and quit the editor. Typing will always save, even if there are no unsaved changes, and then quit the editor. will write if there are no unsaved changes, and it will quit. and requires that you had previously provided a file name, so it will not work for the above simple example. Typing will quit if there have been no changes made; if changes have been made, vi will print a warning similar to "No write since last change". Don't worry. Many first time vi users stop at this point, and never touch vi again. If you tried to enter some text after you started, you will most likely have been greeted with a series of beeps and rather erratic behavior. Don't worry. This is perfectly normal for vi, and the editor is not broken. You will soon see why this is normal vi behaviour. Continue. Now that you know how to start the editor and quit it, let's move on to getting things done in vi: see Learning the vi Editor/Basic tasks

Learning the vi Editor/Basic tasks. Now that we know how to invoke the editor and quit it, we can get acquainted with how to "use" the editor. Alternatively, you can use the ViM tutor which comes with many modern vim distributions. It contains, essentially the same information as the text below. You can invoke the tutor by entering vimtutor at your shell. Vi is a "modal" editor. The vi editor can do two things: In the vi editor, each of these tasks is achieved by putting the editor into a particular mode of operation (normally just called a "mode"). When you wish to give vi a command, you enter "command mode", and when you want to enter text, you enter "insert mode". We'll cover how to do this below. It is important to set the correct mode before you begin writing, but this is simple to do. When you first start vi, it is automatically in command mode. Entering text. Entering text is the most basic task an editor can do! From command mode (in which the editor starts), press codice_1 to enter "insert mode", and you can begin typing. You can use the backspace key to correct mistakes you make. If you make a mistake after a few sentences, leave these errors for now, we will look at correcting them later. To leave insert mode once you're done typing, and return to command mode, press the Escape key on your keyboard (or type Control-[). Exercise. Let's have an exercise: Command mode. Command mode allows you to perform many useful tasks within vi. Moving around. Say you have been writing for some time, and have forgotten something. Pressing , "erasing" previous work is not the best solution! We would like to move around the document freely, moving the cursor. Exercise. You can repeat this exercise with your own sentences. Make sure you are proficient doing this before you continue. More on movement. Using codice_3, codice_4, codice_5, and codice_6 is ok, but vi understands more than rows and columns. These are some commands that move by text objects: Deleting things. If you have made a mistake after a few lines, for instance, pressing Backspace until you have erased the mistake and starting again isn't always the best solution. We need a method of deleting mistakes that happen in the normal course of editing. vi allows you several methods of deleting text, based on how much you want to remove. Now that you are familiar with moving around, once you've moved the cursor to where your error is: Exercise. From now on, we will omit the steps for you to start and quit the editor – you should be already familiar with those.

Waves/Waves in One Dimension. The Mathematics Of Waves. We start our discussion of waves by taking the equation for a very simple wave and describing its characteristics. The basic equation for such a wave is where formula_2 is the height of the wave at position formula_3 and time formula_4. This equation describes a fairly simple wave, but most complex waves are just sums of simpler ones. If we freeze this equation in time at formula_5, we get which looks like this: [TODO - Add a Graph] From the graph we can see that each of the three parameters has a meaning. formula_7 is the amplitude of the wave, how high it is. formula_8 is the wavelength, the distance from a part of the wave in one cycle to the same part of the wave in the next cycle. formula_9 is the phase of the wave, which shifts the wave to the left or right. The wavelength is a distance, and is usually measured in meters, millimeters or even nanometers depending on the wave. Phase is an angle, measured in radians. Now that we have mapped out the wave in space, let's instead set formula_10 and see how the wave changes over time Amplitude formula_7 and phase formula_9 remain, but the wavelength is gone and a new quantity has appeared: formula_14, which is the frequency, or how rapidly the wave moves up and down. Frequency is measured in units of inverse time: in a fixed period of time, how many times does the wave move up and down? The unit usually used for this is the hertz, or inverse second. Now let's combine these two pictures and see how the wave moves. Figure 3 is a diagram of how the wave looks when you plot it in both space and time. The straight lines are the places where the simple wave reaches a maximum, minimum, or zero (where it crosses the x axis). We can look at the zeros to determine the phase velocity of the wave. The phase velocity is how fast a part of the wave moves. We can think of it as the speed of the wave, but for more complicated waves it is only one type of speed - more on that in later sections. We can get an equation for the zeros by setting our equation to zero. You see here that we have the equation for a straight line, describing a point that is moving at velocity formula_18. This gives us the equation for the phase velocity of the wave, which is

Compiler Construction. Appendices. The following are Java code referenced in the book.

Compiler Construction/Code Generation. Code Generation. A compiler usually is designed to output an executable program that will allow the user to run your program, and to be directly run by the processor, without having an intermediary interpreter such as in the interpretation process. For your program to be run by the processor however, you will need to transform the instructions in your specific programming language into assembler code, which is then sent to an assembler tool to create object code, which is then linked together with specific libraries to create your executable code. For now, we only really need to worry about transforming the instructions into assembler code. This process is what we will deal with in this section. You will need to be well versed in the assembler language you wish to output. If you intend your programs to run on the x86 architecture, you need to be familiar with x86 assembler code, and so on. Code generation occurs after semantic analysis is done, which gives us enough information to generate more primitive concrete code. The general idea behind code generation is decompose the tree structure of the syntax tree into a sequence of instructions, whatever an instruction set is. In this stage, since we are done with the semantic program, we are not interested in the syntactic and semantic structure of programs but in the order of executions of instructions. Some sort of intermediate code is often produced before generating actual machine code. The benefits of this are However, it may be simpler for your program to output assembler code directly, but you lose the above advantages. See the next section for more techniques on this. In this chapter, we shall use the three address format to represent intermediate code. The format is useful because it is analogous to actual machine instructions in some architectures and, more importantly, allows us to easily change the execution order of instructions, which is a huge advantage over stack-based intermediate code like the byte code of Java. Although it is not a complex problem to reuse names after they have already been used, it is actually beneficial to allocate a new name every time one is needed because it allows us to form a call graph and optimize easily as we will see later. For this reason, we only briefly mention the methods to reuse names. You can find more on the optimization of allocation of names in optimization chapter. The three address code, as the name suggests, consist of three address and opcode, which tells what kind of operation is meant to be done. For example, an expression (a + b) * 3 can be transformed into: temp1 := a + b; temp2 := temp1 * 3 In the first line, temp1, a and b are addresses and + is an opcode, and the second line is similar to the first one. Unlike load-store machines, it is unnecessary to load variables to registers and store them back. You see why the three address code is easy to handle. Choosing portable, flexible and expressive instructions is critical; Not having enough instructions can complicate generated code with the combination of several instructions to achieve one operation and having too much may obviously make maintenance more daunting task. Probably the best way to do this is to examine existing machine code. It is more straightforward to transform code close to underlying machine code than abstract one. Expression. Algebraic expressions can be translated into the three address code in a very straightforward manner. This can be done rather recursively as follows: Assume two expressions left and right with an operation op-code, then the results should be: code for left code for right temp = place for left + place for right Control Structures. The general idea behind generating code for control structures is the same as coding in assembly programming. That is, an if statement, for instance, is converted into a chunk of code using conditional and unconditional jumps. Assembler language techniques. If the output of your compiler is assembly language code, it is necessary to understand the basic techniques of assembly language programming. Most programming languages do not map easily to most assembler languages, so some techniques or skills may need to be understood before attempting to write code that will output assembler code. These techniques are not intended to create highly optimized code - you will learn optimizing techniques later - but are intended to make sure you have a good understanding of how data and instructions are managed in the process of compiler construction. Managing variables. Many programs use hundreds of different variables (not counting arrays). Most computer architectures give you less than 32 registers (MIPS architecture and ARM give nearly 32 pointer registers; i386 gives only about 4 pointer registers; PIC microcontroller only has 1 pointer register). Since we can't squeeze 100 different variables into even 32 processor registers, we must use memory for storing most variables. We will start by storing practically all variables in memory. Later we will cover optimizing techniques that try to keep as many variables as possible in the processor registers. Labeling. The assembler tool that you are using may reserve the names of the mnemonics. For example, your assembler may not allow a variable named add, since this is reserved for the instruction to add. In this case, it may be important to use a "prefix" for your variable labels. Some compilers use a single underscore, but you can choose whichever you wish.

Macroeconomics/Contents. Introduction. This textbook concerns the wonderful world of macroeconomics, or economics on a very large scale, concerning national and international systems. It is primarily aimed at students in their final few years of secondary education, though it could also be used by interested students younger or older than that. Having a background knowledge of would be useful, but grasping overall concepts should not require an in depth previous knowledge. It is worth remembering that this textbook can be edited at any time, with the link at the top of this page. This is both good and bad - you yourself, having spotted a mistake or having noticed a poor definition, can correct it and should feel free to do so. The bad side is that anyone can edit it, so content may be inaccurate whilst the wikibook is in its infancy! Proposed Change. Advanced topics Further chapters later Useful Background Reading. The following links will lead you to Wikipedia, the online encyclopedia similar in style to this site. The information in these articles may go above and beyond that which you need to know for this book, though they will undoubtedly prove useful to refer back to from time to time, and are good portals to more relevant articles. The following links take you to useful websites for learning, revising or expanding your knowledge: For contributors. Any and all corrections, additions, alterations etc. are always welcome! If you wish some credit for your work, stick your name below :

Myers-Briggs Type Indicator. Welcome to the web's free, open content textbook of = Personality Type and the Myers-Briggs Type Indicator =

Myers-Briggs Type Indicator/Introduction. The Myers-Briggs Type Indicator (MBTI) is the name of a personality test designed to assess psychological type. It was developed by Katherine Briggs and her daughter Isabel Myers during World War II. The use of type follows from the theories of Carl Jung. The phrase is also sometimes used as a trademark of CPP Inc., formerly known as Consulting Psychologists Press, Inc. The trademark is owned by the Myers Briggs Type Indicator Trust, and when used as a trademark it must include a registered trademark symbol after the name: "Myers-Briggs Type Indicator®" or "MBTI®". There are a few widely used ways of interpreting the results: Jung-like methods, Keirsey-like methods, and popular psychology methods. The MBTI is popular with recruiters and managers, because studies using this assessment show clusters of different personality types in different professions. For instance, the proportion of engineers who are ../INTJ/ is higher than the 1% found in the general population. There are significant differences by sex, especially on the T vs. F distribution. Proponents of the system claim that almost all arguments between people tend to be manifestations of a type conflict (e.g., E vs. I, S vs. N, T vs. F, J vs. P). The P-J conflict is said to be the clearest: one person gets mad when the rules are broken and the other gets mad when rules are made. The Myers-Briggs Type Indicator is perhaps the world's most popular personality type description tool. Since its inception, many people have turned to the MBTI® for a deeper understanding of themselves and others. This MBTI textbook is designed to bring together general knowledge about the Myers-Briggs Type Indicator and make it available for understanding and application for individuals and groups, for personal and professional lives.

Myers-Briggs Type Indicator/Dimensions. The Myers-Briggs test describes four basic areas of personality: It is important to keep in mind that each dimension reveals a person's inborn preference with how he or she is most comfortable operating, and does not say that any person will "always" retain his preferred dimension.

Myers-Briggs Type Indicator/Types. There are sixteen "types":

Myers-Briggs Type Indicator/Temperaments. There are four temperaments: SJ, SP, NT, and NF. SJ. Sensing judgers, or traditionalists, are practical people that keep the home fires burning and businesses working. They're always aware of who owns what and which social positions are held by whom. Their quest is to run everything, and they are often good at doing so. SP. Sensing perceivers, or experiencers, are adventurous, fun-loving, observant, physically skillful, impatient, easily bored, and good with tools and art. They want to be happy and make others happy too. NT. Intuitive thinkers, or conceptualizers, are analytical, impersonal, intellectual, rather unworldly, absent-minded, and are more likely to forget appointments. They continually seek to acquire new skills and pride themselves on their skills, logic, and efficiency. NF. Intuitive feelers, or idealists, understand people and tend to be aware of people's feelings. They can be warm, sympathetic friends, but find offense in the smallest careless remark. They tend to be very skillful negotiators and good with words.

Myers-Briggs Type Indicator/Criticisms. The MBTI is not yet scientifically proven. Skeptics, including many psychologists, argue that the MBTI has not been validated by double-blind tests (in which participants accept reports written for other participants, and are asked whether or not the report suits them) and thus does not qualify as a scientific assessment. Some even demonstrate that profiles can apparently seem to fit any person by confirmation bias, ambiguity of basic terms. and the Byzantine complexity that allows any kind of behavior to fit any personality type. See this extensive skeptical treatment of the subject. A Temptation to Pigeonhole. Another argument says that, while the MBTI is useful in self-understanding, it is commonly used to pigeonhole people or for self-pigeonholing. Supporting arguments include:

Myers-Briggs Type Indicator/ISTJ. The Introverted Sensor Thinker Judger is a traditionally masculine personality type, detached, unexpressive, concrete, and not given to speculation. Working with an ISTJ. ISTJ's are detail people. You will mostly find them in technical service industries, including medical fields, accounting, police work, engineering, office managers, and so forth. They are keen sensors of their environments; tastes, smells, noise levels. They often prefer a quiet work environment, where they can concentrate and focus on the task at hand. They work slowly and methodically, and don't like to be rushed. They can be focused on keeping structure in order and feel most comfortable when everyone is doing what they are supposed to be doing. ISTJ's value their personal privacy, and like to remain professional. Due to their discreet and reserved nature, others may see them as snobbish or uptight. Often times they remain anonymous for achievements they have accomplished. They may be upset with people who don't follow the rules, honor their promises, or follow through, but may not say so publicly. Traits they may value among fellow coworkers are loyalty, friendliness, and a strong work ethic. They are usually willing to lend their help to others in need if they have time. ISTJs in relationships. ISTJ Relationships in the general sense are regarded as of high importance, and are expected to be of same value to associates.

Myers-Briggs Type Indicator/ENFP. ENFPs are outgoing and talkative types who often have many diverse friends. They are naturally irreverent, curious, good with words, creative, and even a bit artsy. They favor abstraction over detail and tend to flit from one activity to the next, deriving more pleasure from starting projects than from finishing them. ENFPs at work. ENFPs are sponges of knowledge. Curiously collecting information about life's experiences as fodder for their own stories, they live their lives much like a dramatic character in a movie, delighting in finding irony and drama in life situations wherever they go. They interpret the data they gather from people and the world in the form of inner meanings, relationships, and possibilities, often recounting their ideas to people though conversation. They love to spread the word! ENFPs, ../NF/s, are interested in many different things and this often leads them in multiple directions, therefore they are known for changing jobs and even careers frequently. ENFPs prefer to make work fun and have been known to put off work when there is a chance to have fun. ENFPs prefer environments which have little administrative or detailed work. Delegation to reliable support staff is important for success. ENFPs seek out jobs not confined by strict schedules and mundane tasks. According to Keirsey, the "Idealists" want to make the world a better place to live by helping others and are on a search for their "true self". Integrity, ideals, beliefs, and values matter to ENFPs. ENFP's practice and dream about being the best at what ever they seek to achieve. They want to KNOW everything! ENFPs generally have the following traits: * Project-oriented * Bright and capable * Warmly, genuinely interested in people; great people skills * Extremely intuitive and perceptive about people * Able to relate to people on their own level * Service-oriented; likely to put the needs of others above their own * Future-oriented * Dislike performing routine tasks * Need approval and appreciation from others * Cooperative and friendly * Creative and energetic * Well-developed verbal and written communication skills * Natural leaders, but do not like to control people * Resist being controlled by others * Can work logically and rationally - use their intuition to understand the goal and work backwards towards it * Usually able to grasp difficult concepts and theories Common careers for ENFPs are those which allow flexibility and spontaneity while serving others. This includes teaching, general practice of medicine, medical research, religious fields, entrepreneurship, missionary work, social work, community development, creative arts, acting, broadcasting, consulting, coaching, corporate training, public relations, counseling, advertising, and marketing. They enjoy working for themselves and creating new ideas to help people. The perfect job for an ENFP is one where they would give out useful information to others and they would receive several hundred dollars per hour for that service. ENFPs in relationships. Strengths ENFPs are energized by being around people. ENFPs take their relationships very seriously. ENFPs seek and demand authenticity and depth in their personal relationships, and will put forth a lot of effort into making things work out. ENFPs are generally warm, considerate, affirming, nurturing, and highly invested in the health of the relationship. ENFPs have excellent interpersonal skills, and are able to inspire and motivate others to be the best that they can be. ENFPs are generally highly valued for their genuine warmth and high ideals. ENFPs want to help, to be liked, and to be admired by other people on both an individual and a humanitarian level. ENFPs hold up their end of relationships, sometimes being victimized by less caring individuals. Weaknesses ENFPs are well aware of their weaknesses, often being their own harshest critic. Often the ENFP is reluctant to share intimate feelings unless in the company of deeply trusted relationships. Despite being extroverts, ENFPs require a great deal of alone time to center themselves. ENFPs who don’t have a positive support system may be strongly influenced by the opinions of others. ENFPs can exhibit preoccupation in their relationships, sometimes putting "all their eggs in one basket" and can tend to hyper focus on the other individual, in attempts to "fix" the other person or pull out their "real" emotions, transforming them into the perfect person. ENFP who do this are doing so because they don’t want to focus on their own interpersonal issues at hand. In this scenario, ENFPs may feel very anxious and preoccupied if the other partner is silent, non expressive, or withdrawn when coping with stress, instead of talking through things. This can deeply hurt them. Although energetic and effervescent, the ENFP can sometimes be smothering in their enthusiasm. They do not understand why someone would not be charmed by their enthusiastic display of affection and quirky jokes, because many are naturally drawn to their personality. They may try too hard to be what others want them to be, showing codependent tendencies. ENFPs are seen as disorganized by OCD types, having a short attention span, taking on too many tasks at once, lacking structure, and all over the place. Others expect the ENFP to follow societal roles and ENFP are a role unto their own. How to Behave Toward an ENFP. Give ENFPs the freedom to be flexible. Realize that churning through possibilities inspires their minds and get their creative juices flowing. Don't bog the ENFP down with too many details, especially on any subject not known to be of deep interest to him or her. Involve the ENFP in the process and try to keep things fun. When communicating with ENFPs you will find that many like to talk. Do not hesitate to interrupt and state your opinion. ENFPs enjoy speculating about ideas. They enjoy others who engage them in conversation, contribute their ideas and keep it moving in a positive direction. Overall ENFPs appreciate honesty in others, they want to know how people really feel. ENFPs are easily influenced by what other people say. It may not appear that they are listening when they are talking to you, but soon after the conversation ends they often ponder what the other person has said and incorporate those ideas into their own thinking to use the knowledge for the future. The main points to remember, ENFPs: <br> 1) Want to help and please the people they are working with, so give them frequent feedback.<br> 2) Like to hear from their significant others that they are loved and valued, (and are willing and eager to return the favor,) so let them know what you appreciate about them. <br> 3) Prefer happy and upbeat relationships, nevertheless, when conflict occurs, they usually want to engage in a dialog to work it out.<br> 4) Are one of the most freedom orientated personality types. Give them room to have some adventures on their own.<br> 5) May have a difficult time staying focused and following things through to completion. Let them know clearly what your deadlines are. ENFPs want to please other people, so let them know how important it is to you and why it is important to you.<br> 6) Prefer a participative and collegial atmosphere in which employees are included in the decision making.

Myers-Briggs Type Indicator/NF. = NF (The iNtuitive Feeler) = NFs are categorized as idealists and share the traits of dominant iNtuitive and Feeling traits. They include the ../ENFJ/, ../ENFP/, ../INFJ/, and ../INFP/. The iNtuitive side of the NF makes him or her more inclined towards the abstract and the future as opposed to the concrete present. The Feeler preference means he makes decisions based on his personal values more than on cold analytical data.

Myers-Briggs Type Indicator/Introversion. Introverts are rested and energized by solitude, and are very effective in solitary pursuits. An introvert is a person who prefers to process thoughts internally. Introverts tend to think before they speak. The word is also used informally to refer to somebody who prefers solitary activities to social ones, which is more of a behavioural than cognitive definition. Introverts tend to be seen as quiet and reserved, which is often confused with a lack of confidence by louder, more extroverted people. They often perform well in analytical roles that require intelligence or logic, but place less emphasis on social interactions and "people skills".

Myers-Briggs Type Indicator/Extraversion. Extraverts are energized by interacting with other people. They can often appear to be outgoing and may be effective in pursuits that involve interacting with other people. Extraverts tend to be sensation-seeking, spontaneous, and gregarious. They may enjoy crowds, noise, and stimulation. In a conversation, an extravert will tend to talk faster and louder than an introvert and to interrupt more frequently.

Myers-Briggs Type Indicator/Sensing. Sensors want, trust, and remember facts, and usually describe themselves as "practical". For a Sensor, intuition is untrustworthy, and might seem like mental static. Sensation, as a perceiving mode of consciousness, focuses on heightening reality. Guardians share the combination SJ, while Artisans share the combination SP.

Myers-Briggs Type Indicator/Intuitive. Intuitives prefer metaphor, analogy, and logic, and tend to reason from first principles and hunches. While Sensors pride themselves on living in the real world, Intuitives pride themselves on seeing possibilities. This can cause conflict. Intuition, as a perceiving mode of consciousness, filters experience through the unconscious mind. Intuition focuses on possibilities rather than realities. Idealists share the combination NF, while Rationals share the combination NT.

Myers-Briggs Type Indicator/Thinking. Thinkers use impersonal means of reasoning: logic and verifiable experience.

Myers-Briggs Type Indicator/Feeling. Feelers prefer personal reasoning: value judgements and emotions. Thinkers often find Feelers muddle-headed. Feelers often find Thinkers cold and inhuman.

Myers-Briggs Type Indicator/Judging. Judgers prefer to come to decisions and move on. They can feel betrayed if a decision is "reopened". They are prone to hastiness, but get things done.

Myers-Briggs Type Indicator/Perceiving. Perceivers prefer to leave their options open to perceive new possibilities and processes as long as possible. They tend to mourn opportunities lost to premature decisions. They are prone to analysis paralysis, but rarely make permanent mistakes.

Abstract Algebra/Hypercomplex numbers. The terms group theory and ring theory are refinements of algebraic understanding that developed in the era of electronics and aircraft, the 20th century. The term hypercomplex number harkens back to the age of steam. For the most part, the hypercomplex systems have been assimilated through the resolution of vision provided by groups, rings, and fields, and the term has been retired from use other than historic reference. Similarly, the field of complex numbers formula_1 has an insufficiently descriptive name, and might be better described as division binarions C according to composition algebra theory. Hypercomplex numbers grew out of William Rowan Hamilton's construction of "quaternions" in the 1840s. The legacy of his vision continues in spatial vector algebra: for vectors formula_2 and formula_3 the well-known products are These products are the severed remnants of Hamilton’s quaternion product: formula_6 In 1845 John T. Graves and Arthur Cayley described an eight-dimensional hypercomplex system now referred to as "octonions" or "Cayley numbers". They extend quaternions but associativity of multiplication is lost. James Cockle challenged the presumption of quaternions in four dimensions by presenting associative hypercomplex systems "tessarines" (1848) and "coquaternions" (1849). Hamilton had his own eight-dimensional system ("biquaternions") that were explored in his "Lectures on Quaternions" (1853), but virtually ignored in "Elements of Quaternions" (completed by his son in 1865) and in the version edited by Charles Jasper Jolly in 1899. Quaternions feature the property of "anti-commutativity" of the basis vectors i, j, k: Due to anti-commutativity, squaring a vector leaves many cancelled terms: For any such "r", the plane {"x" + "y r" : "x,y" in R} is a complex number plane, and by Euler's formula the mapping formula_12 takes the ray through "r" to a wrapping of the unit circle in that plane. The unit sphere in quaternions is composed of these circles, considering the variable "r". According to Hamilton, a unit quaternion is a "versor"; evidently every versor can be known by its parameters "a" and "r". When the anti-commutativity axiom is changed to commutativity, then two square roots of minus one, say "h" and "i", have a product "hi" with square formula_13 James Cockle’s tessarines are based on such an imaginary unit, now with plus one for its square. Cockle initiated the use of  j, j2 = +1, to represent this new imaginary unit that is "not" a square root of minus one. The tessarines are "z" = "w" + "z" j where "z, w" are in C. The real tessarines formula_14 feature a unit hyperbola, contrasting with the unit circle formula_15 Whereas the circle surrounds the origin, a hyperbola has radii in only half of the directions of the plane and requires a conjugate hyperbola to cover the other half, and even then the asymptotes, that they share, provide even more directions in the plane. In 1873 William Kingdon Clifford exploited the real tessarines to modify Hamilton's biquaternions: where Hamilton had used elements of C (division binarions) for coefficients of a biquaternion "q" = "w" + "x" i + "y" j + "z" k, Clifford used real tessarines (now called split-binarions D). Clifford’s construction illustrated a process of generating new algebras from given ones in a procedure called "tensor products": Hamilton’s biquaternions are formula_16, and the "split biquaternions" of Clifford are formula_17 Clifford was precocious, particularly in his anticipation of a geometric model of gravitation as hills and valleys in a temporal plenum. But he lived before set theory, modern logical and mathematical symbology, and before abstract algebra with its firmament of groups, rings and fields. One of the realities of light is its finite speed: a foot per nanosecond, an astronomic unit in 500 seconds, or a light year in a year. When a diagram uses any of these pairs of units as axes, the diagonals through the origin represent the locus of light, one for the left beam, one for the right. The diagonals are asymptotes to hyperbolas, such as formula_18 a real tessarine. Eventually, over decades of deliberation, physicists realized that this hyperbola was the answer to a linear-velocity problem: How can "v" + "w" be the sum of two velocities when such accumulation may run over the speed of light? The hyperbola lies between the asymptotes and will not run over the speed of light. In the real tessarine system the points of the hyperbola are formula_19 and formula_20 representing two velocities in the group formula_21 a hyperbola. The sum of two velocities is found by their product formula_22 another element of the hyperbola. After 1911, the parameter "a" was termed "rapidity". Evidently this aspect of special relativity was born of real tessarines. The electromagnetic work of Clerk-Maxell and Heinrich Hertz demanded a fitting context for theorizing with the temporal variable included. Maxwell had used Hamilton’s del operator but the quaternion algebra is unsuitable: it is implicitly a Euclidean 4-space since formula_24 the square of the Euclidean norm. In the 1890s Alexander Macfarlane advocated Space Analysis with a hypercomplex system that exchanged Hamilton's sphere of imaginary units for a sphere of Cockle's imaginary units that square to +1. He retained the anti-commutative property of quaternions so that formula_25 Then in this system of "hyperbolic quaternions", for any "r" on the sphere, formula_26 is a plane of split binarions, including unit hyperbola suitable to represent motion at any rapidity in direction r. The hyperbolic quaternions looked like an elegant model for electromechanics until it was found wanting. The problem was that the simple property of associative multiplication broke down in hyperbolic quaternions, and though it was a hypercomplex system with a useful model, loss of this property put it outside the purview of group theory, for instance. Once the axioms of a vector space were established, hypercomplex systems were included. The axioms require a commutative group of vectors, a scalar field, and rules of operations. Putting the axioms of a vector space together with those for a ring establishes the meaning of an algebra in the study of abstract algebra. For associative hypercomplex systems, Joseph Wedderburn removed all the mystery in 1907 when he showed that any such system could be represented with matrix rings over a field. For instance, 2 x 2 real matrices form an algebra M(2,R) isomorphic to coquaternions and 2 x 2 complex matrices form an algebra M(2,C) isomorphic to biquaternions. These algebras, along with R, C and tessarines form the associative composition algebras which are noted for the property About 1897 four cooperative efforts changed mathematics for the better. Giuseppe Peano began to assemble his "Formulario Mathematico", Felix Klein spearheaded the mathematical encyclopedia project, the quadrennial series of International Congresses of Mathematics was begun, and the International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics published a bibliography and annual review. Peano's effort gave mathematicians the symbolic language to compress concepts and proofs using set theory. Klein's encyclopedia upheld German as the primary medium, and the Congresses drew together all nations. The Quaternion Society was the primary arena addressing hypercomplex numbers, and was dissolved after 1913 upon the death of its president, Alexander Macfarlane.

Myers-Briggs Type Indicator/ISFJ. How to deal with an ISFJ. ISFJ's with a persistent guiding hand behind them can learn to like anything.

Myers-Briggs Type Indicator/INFJ. INFJs at work. INFJ individuals are goal-oriented. They prefer careers that are inspiring and add value to their goals. They are motivated by ideas, not money. Even though they are introverted, they are good communicators. They prefer role as psychologists, teachers, counselors, yoga instructors, social workers, etc. INFJs in relationships. INFJs tend to hold back part of themselves and like most introverts it can take them a while to become comfortable around new people. Having extraverted feeling as their auxiliary function, INFJs often feel the need for verbal affirmation and support from people close to them. Many of the INFJ's actions are dependent on the emotions or what they perceive to be the emotions of others and as result immature INFJs can neglect their own feelings and opinions when making decisions. The INFJ's focus on the emotions of others can lead to them being harmonizers or, on the other end of the same spectrum, manipulators. It can also cause them much social anxiety if they have not properly or fully developed their auxiliary function. INFJs are natural romantics who seek long-term or lifelong relationships. While they may not all believe in soulmates, they tend to put pressure on their partners in trying to achieve the perfect relationship. Some theorists have suggested that INFJs are most compatible with ENTPs (the Inventor). INFJ Sub King and Idealist Type.. =Fictional INFJs= =How to deal with an INFJ= Be honest with them. Don't try and manipulate them; they will see through it and never trust you again. INFJ's have an uncanny ability to read people's emotions, and they tend to take others emotions onto themselves. They easily make connections between things by matching up pieces of conversations and visual memories. They can appear to be psychic because of this. INFJs make up less than 1% of the population. You'll often encounter them in education, psychology and the arts.

Myers-Briggs Type Indicator/ISFP. ISFPs at work. ISFPs generally are underachievers and like low key, low stress, aesthetically beautiful work environments that are fun. They like to work by themselves or in small groups cooperatively, but may not like being the leader and they have a harsh inner critic. They are gentle people and don't like to pressure others into deadlines unless necessary. When forced into a position of power, they may feel cornered and very uncomfortable making decisions. Their favorite subjects might be music, cooking, painting, drawing, gardening, musical theatre, sculpting and helping others. They are often quite talented but often quiet about showing the world. Make work a game, and they'll work happily. Many ISFPs are attracted to fine arts, which they often have hidden talent in. ISFPs in relationships. ISFPs are kind, modest, quietly generous people. They like people and make true blue friends, however it may take a while. Their partners need to respect the ISFPs need for the privacy they need to recharge themselves. They like to spend time with people one-on-one or with a small group of two or three others who understand them. When the ISFP gets to know you on a personal, one-on-one basis, they are warm, affectionate, a little more talkative and even humorous, telling jokes to make friends laugh. They share opinions only with people they know very well. ISFPs like to make people happy with a smile and a song, slapstick comedy or light practical joking (ice cube down the back). If nothing works, they think it is their fault and withdraw. They often make friends with those they feel will protect and stand up for them, and usually have a small group of close (often very outgoing) friends. For love, they want someone patient who will be there for them and also stand up for them when they can't themselves, and whom they could speak their mind with without feeling foolish. However, they do not want someone to control them, as they value their freedom highly. They can be afraid of commitment at times. They take criticism personally, and feel at fault for people's reactions toward them. To show love, ISFPs would give you something they made themselves like a painting, some homemade cookies, a song dedicated to you or something they found that just happened to remind them of you. They like to be told how special and important they are to you, be specific and truthful. They aren't wordy people but can be eloquent and descriptive in their speech when they want to be. Fictional ISFPs. John Watson (Sherlock) Severus Snape (Harry Potter) Harry Potter (Harry Potter) Dobby (Harry Potter) Legolas (Lord Of The Rings) Touka Kirishima (Tokyo Ghoul) Eleven (Stranger Things) Jonathan Byers (Stranger Things) Arya Stark (Game Of Thrones) Princess Aurora (Sleeping Beauty) Black Panther (Black Panther) Cinna (Hunger Games) Jeremy Gilbert (Vampire Diaries) Snow White (Once Upon A Time) Shaggy Rogers (Scooby Doo) Marceline (Adventure Time) Rey (Star Wars) Zuko (Avatar: The Last Airbender) Lara Croft (Tomb Raider) Famous ISFPs. Michael Jackson (Musician) Billie Eilish (Musician) Bob Dylan (Musician) Prince Harry (Royal) Brad Pitt (Actor) Elizabeth Taylor (Actress) Ryan Gosling (Actor) Pamela Anderson (Actress) Lana Del Rey (Musician) Paul McCartney (Musician) Monica Bellucci (Actress) Avril Lavigne (Musician) Mick Jagger (Musician) David Bowie (Musician) Skrillex (Musician) John Travolta (Actor) Zac Efron (Actor) Norman Reedus (Actor)

Myers-Briggs Type Indicator/INFP. INFPs at work. INFPs love to work behind-the-scenes and support the group. If they feel they are appreciated for their hard, considerate work, they often enjoy themselves immensely. Because they are often socially unsure, many find jobs they can do from home. INFPs in relationships. INFPs are very sensitive beings, and oftentimes the social scene feels extremely repressive and painful for them. They want very much to be accepted and cared for, but sometimes they become so uncomfortable that they become very nervous and feel completely out of place. Many try to express feelings of sadness and helplessness to those close to them for support. For lovers, they often look for outgoing, strong, caring people who can help them feel a part of things and to whom they can give their love. Still they are quite independent and have strong personal values, which they tend to defend at all costs. They also have are deep loyalty and commitment to those close to them. How to deal with an INFP (MEDIATOR). Because the INFP (MEDIATOR) tends to extrovert their iNtuition (they can reveal out loud the possibilities that they are imagining when they imagine them) to the world yet at the same time introvert their Feeling decision-making (not reveal the values and processes they really hold), they can seem to others that the possibilities they suggest are really decisions. Because they say things (possibilities) they don't necessarily believe, it is crucial to verify with them if some of their statements are truly decisions or judgements. In order to help the INFP (MEDIATOR) feel good about themselves, it is necessary to tell them verbally that you care about them. They need a great deal of positive affirmation and can become very self-conscious and insecure and lost without it. Some say that they 'can't do anything right' and feel very depressed and lonely. In conflict, keep in mind that, if pressured, the INFP (MEDIATOR) may try to change the subject and escape. It is best to treat them very gently and lightly discuss the subject at hand without seeming angry or upset with them. When they feel very cornered, their usually sweet exterior rapidly changes and they begin to lash out. Do not take this behaviour harshly, for this happens only under very rare circumstances and when the INFP (MEDIATOR) feels they have no other choice. If they feel they have shared their feelings in a kind and loving environment without being criticized for them, they often feel quite content and calm.

Myers-Briggs Type Indicator/INTP. INTPs are introverts, meaning they tend to prefer relatively solitary lives. They are often uncomfortable in social gatherings, particularly large ones, which can leave them feeling somewhat drained. Although some may have many acquaintances, INTPs usually have only a few close friends, if any at all. However, this also means they tend to be nonchalant about their public image. INTPs favor iNtuition over Sensing. As such, they tend to be more introspective than attentive to their surroundings. It is common for an INTP to daydream, or simply become lost in his or her thoughts. INTPs often enjoy contemplating interesting ideas, concepts, and possibilities due to iNtuition—their curiosity drives them. However, their senses are somewhat less refined than in other types. They may overlook details (INTPs are prone to "careless errors" in math), and are not often completely attuned to what is going on around them. An INTP deep in thought can be oblivious to all sorts of things, ranging from a missed meal to a cap being stolen from his or her head. An INTP prefers Thinking over Feeling, meaning they tend to value logic over feelings. Although INTPs experience emotions as powerfully as other types, they almost always must see the logic behind them before acting on them. All decisions must have good reasons behind them, and INTPs rarely make good decisions without considerable thought. It is usually very important to an INTP to be as logically and grammatically accurate as possible. However, INTPs are somewhat inept at expressing feelings outwardly, sometimes causing misunderstandings. Sarcasm and cynicism are occasionally observed in INTPs. Since INTPs have a Perceiving preference, they don't enjoy being limited by schedules or decisions. They tend to have bursts of creative energy, which can lead to extraordinary efforts, but the energy can also be short-lived. After the energy is expired, attention may be directed elsewhere, where energy may be regenerated. In other words, INTPs may have many interests due to their preference for perceiving, and these interests may come and go, or change altogether. Being introverts, INTPs are usually very reserved. Their iNtuition allows them to rapidly understand new concepts and to pursue a wide variety of interests. Their Thinking helps them to find the logic in a situation from an objective point of view. INTPs' Perceiving causes them to be open-ended; often thinking about a task is more rewarding than executing the task. INTPs often feel like misfits and are not necessarily always appreciated. Many INTPs complain of boredom, as the real world fails to measure up to the vivid experiences of their imaginations. INTPs at work. INTPs might make good professors, computer programmers, photographers, mathematicians, attorneys, engineers, analysts, architects, and scientists, however, according to Wikipedia article, a lot of INTPs are found as "teachers of subjects such as English, social studies and art", once again breaking the norm. INTPs in relationships. INTPs face many tough hurdles in their relationships. Many INTPs do not focus on developing strong social skills, but even those who do will divert much of their energy into their solitary pursuits. Characterized best by the lonely adventurer, their adventures are rarely literal trips to the end of the earth (the territory of the SPs), but instead fantastic intellectual journeys. One study found that INTPs tend to marry other INTPs.

Myers-Briggs Type Indicator/ESTP. Famous ESTPs. Entertainment. Taylor Bohning/ Youtube star ESTPs at work. Spontaneous but organized ESTPs in relationships. Ben Heath and Charlie Puth How to deal with an ESTP. ESTP are fickle in love but when made firm to a decision can be quite the romantic

Myers-Briggs Type Indicator/ESFP. ESFPs at work and school. ESFPs see work as play. They like to whistle, drum, sing, talk or joke while they are doing work to keep what they are learning fun for them. This could cause teachers, mostly SJs, to feel that they are not paying attention. It could also be disturbing to people who like quiet when they think. ESFPs learn best when they are having fun. They also look at the person who is speaking to them as they can feel sound vibrations strongly. As they work they celebrate small accomplishments in what they are doing before moving on to the next, happy for what they have done, rather then being sad at what they still have to do. When they work with more logical things such as mathematics, they want to know how it relates to life right now. Preferring a hands-on approach, subjects like those can bore them. Their favorite subjects are ones that they have an interest in and ones that they can do things with and apply to the world around them. Music, drama, dance, competitive sports and computers are among many they like. They may also go into those areas when choosing their careers. Careers that may appeal to ESFPs are: actor, musician, stand up comedian, dancer, dance instructor, their favorite position in their sport of choice, gardener, painter, sculptor and chef. Sometimes though, it's hard for them to decide. ESFPs in relationships. ESFPs are warm, loving, generous and sympathetic. They especially like physical affection such as hugs, kisses, petting on the head, massages, snuggles, tickles, and just being held. They show their love through those ways as well as surprising friends and loved ones with gifts. They want fun, variety, spontaneity, travel and adventure in their relationships and are usually not keen on settling down. This could be because of fear of rejection, commitment or because they found someone else. They like to keep things light and happy and not get into anything deep and lasting unless they are sure and have thought it out, which could take a while. This could cause their mates to express impatience which would make the ESFPs nervous and withdraw from them. ESFPs do not do well with anxiety, and are highly sensitive. When they can't make people smile with their charming ways and their playfulness, they feel bad as though it was their fault and leave. When they are in their best mood, they are seen as bouncy, hyperactive and childlike. They go from one activity to another so they won't be bored. When feeling their worst, they are moody, likely to beat themselves up (physically and/or mentally), call themselves unintelligent, think nobody takes them seriously and feel better after a good cry. How to deal with an ESFP. Explain things clearly, Appeal to their common sense, Do something they enjoy with them, Discuss things over a break in the action and then get right back into the fun, give them lots of tlc.

Myers-Briggs Type Indicator/ENTP. Recognizing an ENTP. ENTPs are typically friendly and often charming. They usually want to be seen as clever and may try to impress others with their quick wit and incisive humor. They are curious about the world around them, and want to know how things work. However, for the ENTP, the rules of the universe are made to be broken. They like to find the loopholes and figure out how they can work the system to their advantage. This is not to say the Visionary is malicious: they simply find rules limiting, and believe there is probably a better, faster, or more interesting way to do things that hasn’t been thought of before. The ENTP is characteristically entrepreneurial and may be quick to share a new business idea or invention. They are confident and creative, and typically excited to discuss their many ingenious ideas. The ENTP’s enthusiasm for innovation is infectious, and they are often good at getting other people on board with their schemes. However, they are fundamentally “big-picture” people, and may be at a loss when it comes to recalling or describing details. They are typically more excited about exploring a concept than they are about making it reality, and can seem unreliable if they don’t follow through with their many ideas. Research on ENTP. Interesting facts about the ENTP: ENTP Personality Type Development & Functional Stack. Ne also works receptively, gathering information from without. Unlike Se, it does not gather overt information, but goes beyond or looks behind sensory data. It is what allows ENTPs to discern otherwise hidden patterns, possibilities, and potentials. Ne is constantly scanning for new connections and patterns. They often employ this receptive side of their Ne in activities like reading, watching movies, and conversing with others. Because it is an extraverted function, Ne is more divergent, extensive, and open-ended than Introverted Intuition (Ni). Ni is more intensive and convergent, conferring a greater sense of conviction and closure. Once Ni has done its work, INJs are apt to feel there is a single correct solution. Ne, by contrast, is disposed to multiplying rather than reducing the number of possible options or solutions. Only through use of their auxiliary Ti can ENTPs move toward convergence. Ne also confers open-mindedness. It helps ENTPs see truth on both sides of an issue without forming unwarranted judgments or premature conclusions. It also contributes an openness to alternative or Bohemian lifestyles, allowing ENTPs to entertain options such as vegetarianism or joining a commune. Ne also resists excessive external structuring, which can feel like an imposition to ENTPs’ sense of personal freedom and autonomy. ENTPs scoff at what they see as unnecessary or overly rigid rules, regulations, or procedures. They also dislike unchanging or sterile surroundings. When the environment is too bland or sterile, they can quickly become bored and restless. Like other NPs, ENTPs can have a love-hate relationship with their Ne. They love the fact that it helps them remain open-minded, to see the bigger picture, and to appreciate different options and perspectives. They also enjoy its attendant sense of adventure, expectancy, and wonderment toward life’s mysteries. But Ne also has its challenges. It can make it difficult for ENTPs to feel calm and satisfied, to arrive at firm conclusions, or to feel confident in their decision-making. Ti involves the application of logic and reason for the sake of understanding a given situation, system, or problem. It also works to bring structure and order to the inner world. This inner structuring grants ENTPs a good sense of inner control. When engaging their Ti, ENTPs dig into the background of their thoughts to better understand their origins and to ensure their ideas are logical. Like INTPs, they can quickly find inconsistencies or logical shortcomings in a given theory or argument. They excel at identifying exceptions or imagining scenarios in which the proposed explanation might breakdown. They find it easier to identify logical shortcomings or inconsistencies —to assert what is not true—than to confidently assert what is true. The difference between Ti in ENTPs versus INTPs is its place in the functional stack. For INTPs, it comes first, which makes them quicker to inwardly judge. INTPs then use their auxiliary Ne to open up and further explore their initial judgments. In ENTPs, the order is reversed. Rather than starting with an initial judgment or presumption like INTPs, they approach things through the fresh eyes of Intuition. They then employ their Ti to analyze and enhance the logic and structuring of their Ne perceptions. In addition to the different ordering of their functional stacks, ENTPs, as dominant Perceivers, can more easily leave things open-ended or ambiguous than INTPs can. Their Ne dominance also makes them more open to “playing” than INTPs are. I once administered a values inventory and was surprised when a couple ENTPs marked “having fun” as one of their top priorities in life. To most INTPs, whose dominant Ti compels them to take life seriously, such a response smacks of hedonism and would likely be among their lowest ranked values. ENTPs’ dominant Ne may also confer a greater interest in the arts and culture than typically seen among INTPs The difference between Ti and Fi seems largely a matter of interests and emphases. Fi types (FPs) are more concerned and skilled with moral judgments (Fi) than logical ones (Ti). They judge in terms of good and bad, love and hate, like and dislike. TPs, in contrast, start out with a need for sound logic (Ti) and are generally less concerned with matters of taste or morality upfront. They think less in terms of love and hate than reasonable and unreasonable, logical and illogical. With that said, since T and F are adjacent in ENTPs’ functional stack, it can sometimes be a bit tricky, especially early in their development, to tease out their T-F preference. We can also approach ENTPs’ Fe more theoretically. Namely, since Fe is their preferred extraverted Judging function and falls lower in their functional stack, ENTPs are less comfortable extroverting judgments (Fe) than keeping them to themselves (Ti). This can lead ENTPs, along with other Perceiving types, to habitually defer to others’ wishes rather than asserting their own. And because ENTPs have strong minds, they may grow inwardly resentful of those they see as trying to control them. Granted, they are generally more self-assertive than IPs are, but their discomfort in deploying Fe can still get kindle problems in ENTPs’ relationships. When using Ne, ENTPs can be rather oblivious to details. They may fail to effectively attend to the concrete details of daily life, such as forgetting to the bills, being careless with their diet, or not taking enough exercise. When engrossed in a creative project, however, ENTPs can look like INTJs, becoming perfectionistic and obsessive over details. As N-dominants, it can be difficult for them to accept anything less than perfection when it comes to the physical embodiment (S) of their vision or ideas (N). A most overlooked feature of Si is its perception and awareness of internal bodily sensations—the body as felt and experienced from within. But since Si is ENTPs’ inferior function, they may feel out of touch with their inner body. To compensate, they may grant too much attention to certain physical sensations, making them more susceptible to hypochondriasis or psychosomatic illnesses, in which an increased focus on bodily sensations cultivates or heightens symptoms. N and S also have a temporal element. Si concerns itself with the past, while Ne is focused on future possibilities and potentials. ENTPs’ Si can confer an interest in the details of history. They also enjoy using their Ne to explore historical meanings, interpretations, and implications. This is why many ENTPs take up politics or journalism, careers that allow them to use their knowledge of history to analyze current events and speculate about the future. ENTPs also experience tension between the traditional (Si) and the novel or unconventional (Ne). This is especially common for ENTPs in Phases I and II of their type development. To some degree, they remain attached and drawn to their childhood traditions (Si). At the same time, however, their Ne and Ti may encourage them to deconstruct and even rebel against those traditions. This can engender identity confusion in ENTPs, unsure of the degree to which they should break from their childhood traditions versus reconceiving themselves. Such struggles can leave ENTPs with questions like: Should I opt for family life or an unconventional lifestyle? Should I pursue the security of a conventional career (Si) or something more creative and potentially risky (Ne)? In considering such questions, ENTPs, need to ensure they are leading with their dominant function rather than their inferior. As N-dominants, ENTPs’ best strengths involve creatively exploring ideas, theories, and connections. To best utilize these strengths, they need to ensure they are not allowing their inferior Si to impose undue limits or boundaries on their explorations. They are generally better off using their Ne, as well as the reasoning capacities of their Ti, to hash out truth, rather than deferring to Si traditions. ENTP in the population. ENTP is one of the rarer types in the population. ENTPs make up: Popular hobbies for ENTP. Popular hobbies for them include continuing education, writing, art appreciation, playing sports, computers and video games, travel, and cultural events. What the experts say. - Isabel Briggs Myers, Gifts Differing - David Keirsey, Please Understand Me II - Otto Kroeger, Type Talk at Work ENTps at work. ENTps have straightforward expectations in the workplace, but ones that aren't always easy to meet. Strong believers in meritocracy, people with the ENTp personality type expect their ideas to be heard by those above them, expect robust debate among their peers, and demand that those they manage offer up new solutions and ideas regardless of their positions. While this isn't always how things play out in reality, ENTPs know what to look for, and can avoid those strictly hierarchical institutions that they would otherwise struggle with. ENTp Subordinates. This dynamic is clearest with ENTp subordinates, as they are comfortable challenging their managers' ideas and have a strong (and well-expressed) dislike for restrictive rules and guidelines. ENTPs back this unorthodox behavior with their keen minds and curiosity, and are as capable of adopting new methods as they are of suggesting others do so. If something can be done better, it's as simple as that, and ENTP personalities gladly take criticism, so long as it's logical and performance-oriented. The biggest challenge for ENTp subordinates is that it is often the fate of the "lower" positions to implement the details, do the dirty work and follow through on plans set out by their managers. This couldn't be further from what ENTPs prefer to spend their time on – they can't stand simple, routine work, and monotonous tasks are the stuff of nightmares. Things go over much better if managers are able to properly utilize ENTPs' preference for tackling complex challenges and diverse projects. ENTp Colleagues. It is as colleagues that ENTps prove most polarizing, as their passions for brainstorming, debate and over-analysis drive more practical, task-oriented colleagues crazy, but serve as stimulating inspiration for those who appreciate the innovation ENTps bring. Nothing bothers people with the ENTp personality type more than getting out of a meeting where everyone agreed with the first plan presented, only to hear everyone complain about how stupid the plan was ten minutes later – but they "didn't want to make waves". ENTps strive for honest, direct and objective assessments of these ideas, so much so that they often earn reputations for their insensitivity and condescension. Luckily ENTps know how to relax too, and their witty wordplay, healthy sense of humor and outgoing nature win new friends quickly and easily. Always willing to draw on their repository of knowledge, conversations with ENTp personalities are informative and entertaining, which makes it easy for them to be the go-to person for tough problems that stump more rote approaches. Peer-to-peer relationships with ENTPs aren't always easy, but it's tough to argue that they don't work. ENTp Managers While not always their goal, management is often where ENTPs are most at home, allowing them the freedom to fiddle with different approaches and come up with innovative ways to tackle new challenges without having to handle the tedious step-by-step implementation of these plans. ENTps are open-minded and flexible managers, not just granting but also expecting the same freedom of thought that they themselves enjoy. This can lead to disorder, conflicting ideas and approaches being put forward, but ENTps are also great at accurately and objectively assessing which plan is likely to be most effective. This doesn't always make friends, but being liked is less ENTps' goal than being respected and seen as intelligent and capable. And liked or no, people with this personality type hold firm ground in rational debates, making them fearsome advocates for their teams. The challenge for ENTps is focus, as they may find themselves jumping from project to project in a quest for challenge and excitement before their teams are able to wrap up the details of their existing goals and obligations. ENTps in relationships. ENTp's love to be in relationships, and are very loyal and great at managing life, but will not just be in a relationship just to be in a relationship. ENTp's like to think they are the caretakers, and will do so for the most part, but for a true relationship with them, one needs to get past the strong exterior and nourish their underlying needs, which they may never tell you. Massage is a great way to get an ENTp comfortable. They are shy at first and never feel 100% accepted in social settings, although they tend to be the belle of the ball. They are interesting to talk to, and find the best friendship in those who have good conversation. ENTp friend are active, like going for walks, playing sports, going on adventures and trips. Love and relationships can be the best or the worst for an ENTp, as love can inspire and drive them, but can also drive them insane. Not feeling accepted can make an ENTp shy away and hide. Happy mediums can and should be found in relationships. ENTp's get very invested in their work, ideas or passions. If something is bothering them, it never leaves their mind. If you've found an ENTp who gets inspired by you, hold on for a wild ride, your ENTp will be wildly successful and needs a sexy partner to come home to and escape with. Loyalty, support, emotional feedback – these are not what ENTps look for in their friendships. The last thing people with the ENTp personality type want to hear is "you're right", not unless they have absolutely earned the distinction in a heated round of intellectual debate. If they're wrong, ENTps want to be told so, and they want every detail of the faults in their logic to be laid bare, partly in their quest for oftentimes arbitrary truth, and partly just so they have to work to defend that logic with counterpoint and parry. It's often easy for ENTps to test compatibility with a potential friend – they just need to test combatability. ENTp personalities are quick-witted, and their primary means of expressing this is in the form of arguments and discussions, where they will easily spend an entire evening debating an idea they may not even believe in. These debates are never taken personally, no matter how heated they become or how striking the disagreement. Much as an athlete competes for the physical exertion and the spirit of competition itself, ENTps debate for the sake of intellectual stimulation and for the debate itself, and even in overwhelming victory or crushing defeat, it's never about dominance, only inspiration to try harder next time. Resources. Classic Video Game Characters ENTP Celebrities & Famous People

Myers-Briggs Type Indicator/ESTJ. ESTJs at work. very driven

Myers-Briggs Type Indicator/ENFJ. ENFJs at work. ENFJs tend to be people with good emotional and people skills. Often they hold strong views on religion or politics which they try to express without offending others. ENFJs usually have strong work ethics. However if others are abused they are offended. To release workplace tensions ENFJ's will sometimes employ a "over the top" style of humor. ENFJs in relationships. ENFJ's have a profound insight into the inner workings of people.

Myers-Briggs Type Indicator/ENTJ. ENTJs at work. ENTJ are 4 Characteristics that are found common in rulers, historically most Rulers have shared this type. Quick to begin planning, Direct, They constantly scope the area for logical problems to solve. It triggers their bank of 'ideas', allowing them to associate and classify objects. Mostly an intuitive creature, the raw 'idea', can be used, or it can receive further stimulus from Extraverted Sensing, and lastly. Introverted Feeling. A complicated, genius, logical, strategy, is born! They intensely bury their efforts into the goal at hand, and tirelessly work against it. Those working with them, soon recognize the ENTJ's competence and importance, and rely on it for many their issues. The ENTJ is now needed. With the deadline of a complex project at hand, they continue to pour in more effort, struggling against the clock, and seeking closure. Quick to stand up for any thing they find logical, they come off opinionated, aggressive, and highly extroverted at work. Their identity doesn't matter in the work place. Work matters. Production matters. Capital matters. Their emotions don't matter! If they push their limits, and establish a dominant role, as a person with high influence, they are "winning the fight". Promotions are looked at as 'positive re-enforcement'. 'Good job, you are so smart!' is liable to make an ENTJ feel like a little kid, which is not what you want to do. As the deadline of the project gets close, they push for any extra adrenaline they can find in them. Twenty-four hours a day is a common shift length. All in time, to finish 2 days early, in the 3 month battle. For that moment, they have the opportunity to seize the reward they deserve for their efforts! In general, they are too intense for standard, procedure-based, punch in, punch out, work styles. They would much rather take on a project, establishing an impossible goal, and obtain it, whenever he/she feels like working on it. They want to be heard, taken seriously, believed in, and trusted. However, don't ask them for their "fully detailed plans," - only they know what they truly mean. When working in a team, he/she'll tell you what you need to know, just believe them and be ready to give information upon request. natural talent: team work, tactics, political control, overpowering, conflict control, security, family maintaining, strategic planning, Leadership, Protecting interests, Securing people. ENTJ when completely develop makes other personalty type weak and people around them start to feel inferior, they appear arrogant and superior but its just their developed extroversion and developed thinking, their decisions will appear as unreasonable but they always have a reason for them and logical one because of that they get in trouble, putting aside emotions is weakness for developed ENTJ traits. ENTJs in relationships. -ENTJs have strong personalities, so they would also want to be in the company of people who have their own opinion and people who won't bring them down. How to deal with an ENTJ. - Be assertive and stand up for your ideas - Support your idea/argument with reasonable facts - Be completely objective (do not bring in personal beliefs or fear their wrath) - Be straightforward and never lie as to any ENTJ it shows a sign of weakness - Do not make them feel vulnerable or weak, they have trouble being open-hearted - When it seems they are becoming angry, simply give them time to think before they come up with a more cooperative nature - Acknowledge that they don't always assume that they are right but it's just their manner of speaking - Never betray their trust (seriously don't) or else you are a goner

Botany/Pteridology. Chapter 12 Chapter 12. Pteridology ~ The Ferns. "Pteridology" is the study of ferns—plants classified in the Division Pterophyta (or Filicophyta). Ferns do not have seeds the way trees and flowering plants do. Rather, they have spores the way mosses do. The haploid spores grow small haploid organisms, which then undergo fertilization and grow the diploid fern plant directly out of the haploid gametophyte, similar to the sporophyte stalk growing out of the moss. The larger part, what we think of as the fern, is the sporophyte. The gametophyte is a small green prothallus that the sporophyte grows out of. Ferns are still tied to an aquatic environment, in that once a spore grows into a prothallus, there must be moisture enough for the egg in the prothallus to be fertilized by swimming, flagellated fern sperm. Having a large sporophyte allows ferns to produce many more spores than a moss could- recall that each sporophyte on a moss only carried one sporangia. Producing many more propagules increased fern presence and dominance. Besides having a larger sporophyte generation, ferns have many important adaptations that increase their capabilities above the mosses. Ferns have roots, which, unlike moss rhizoids, not only anchor, but take up nutrients. Ferns are vascular plants, with lignified vascular tissues. These allow active water transport. That water transport along with the strength of the ligified cells allow ferns to be much larger than their moss ancestors. At one point, ferns and fern trees were the most advanced plant life, and grew even larger than ferns today do, with great size and variety of ferns. There were no flowering plants in the early cretaceous- the first forests of the dinosaurs were composed of fern trees. Evolution and ferns. Ferns have a big advantage over the mosses in their vascular tissue. They can grow taller, and can exist in more diverse environments. This is a trend that will continue in evolution, eventually leading to the rise of such large sporophyte generations as the great sequoia trees. But if ferns are so much more fit for survival, why are there still mosses? And if a larger sporophyte generation is more fit, why haven't sequoias become dominant enough to eliminate the ferns? While there are clear benefits to a larger sporophyte generation, in some recurring natural situations, natural selection favors mosses over ferns or ferns over trees. Spores are better at spreading by wind than many seeds are, for instance. So while in the long term, the protection of a seed allows seed plants to be dominant on the planet, in many situations the lightness and transport of a spore is still efficient in spreading ferns. There are two gena that have showed immense diversity in the division Pteridophyta.Selaginella and Equisetum have been identified to be the only gena that are heterosporous.

Engineering Thermodynamics/Second Law. Introduction. The first law is a statement of energy conservation. The rise in temperature of a substance when work is done is well known. Thus work can be completely converted to heat. However, we observe that in nature, we don't see the conversion in the other direction spontaneously. The statement of the second law is facilitated by using the concept of "heat engines". Heat engines work in a cycle and convert heat into work. A "thermal reservoir" is defined as a system which is in equilibrium and large enough so that heat transferred to and from it does not change its temperature appreciably. Heat Engine. Heat engines work between two thermal reservoirs, the low temperature reservoir and the high temperature reservoir. The performance of a heat engine is measured by its "thermal efficiency", which is defined as the ratio of work output to heat input, "i.e.", "η = W/Q1", where "W" is the net work done, and "Q1" is heat transferred from the high temperature reservoir. Heat Pumps. Heat pumps transfer heat from a low temperature reservoir to a high temperature reservoir using external work, and can be considered as reversed heat engines. Statement of the Second Law of Thermodynamics. Kelvin-Planck Statement. "It is impossible to construct a heat engine which will operate continuously and convert all the heat it draws from a reservoir into work." In other words, "It is impossible to have a heat engine which works in cycle and does work by exchanging heat with only one reservoir." Clausius Statement. "It is impossible to construct a heat pump which will transfer heat from a low temperature reservoir to a high temperature reservoir without using external work." In other words, "It is impossible for heat to flow from a low temperature (sink) to a high temperature (source) without external work." PMM2. A "perpetual motion machine of the second kind", or "PMM2" is one which converts 100% of the heat input into work while working in a cycle. A machine like this would violate the second law of thermodynamics, and would therefore be impossible to build. A PMM2 has an "ηth" of 1. Equivalence of Clausius and Kelvin-Planck Statements. Suppose we can construct a heat pump which transfers heat from a low temperature reservoir to a high temperature one without using external work. Then, we can couple it with a heat engine in such a way that the heat removed by the heat pump from the low temperature reservoir is the same as the heat rejected by the heat engine, so that the combined system is now a heat engine which converts heat to work without any external effect. This is thus in violation of the Kelvin-Planck statement of the second law. Now suppose we have a heat engine which can convert heat into work without rejecting heat anywhere else. We can combine it with a heat pump so that the work produced by the engine is used by the pump. Now the combined system is a heat pump which uses no external work, violating the Clausius statement of the second law. Thus, we see that the Clausius and Kelvin-Planck statements are equivalent, and one necessarily implies the other. Carnot Cycle. Nicholas Sadi Carnot devised a reversible cycle in 1824 called the "Carnot cycle" for an engine working between two reservoirs at different temperatures. It consists of two reversible isothermal and two reversible adiabatic processes. For a cycle 1-2-3-4, the working material Heat is transferred to the working material during 1-2 ("Q1") and heat is rejected during 3-4 ("Q2"). The thermal efficiency is thus "ηth = W/Q1". Applying first law, we have, "W = Q1 − Q2", so that "ηth = 1 − Q2/Q1". "Carnot's principle" states that The proof by contradiction of the above statements come from the second law, by considering cases where they are violated. For instance, if you had a Carnot engine which was more efficient than another one, we could use that as a heat pump (since processes in a Carnot cycle are reversible) and combine with the other engine to produce work without heat rejection, to violate the second law. A corollary of the Carnot principle is that "Q2/Q1" is purely a function of "t2" and "t1", the reservoir temperatures. Or, formula_1 Thermodynamic Temperature Scale. Lord Kelvin used Carnot's principle to establish the thermodynamic temperature scale which is independent of the working material. He considered three temperatures, "t1", "t2", and "t3", such that "t1" > "t3" > "t2". As shown in the previous section, the ratio of heat transferred only depends on the temperatures. Considering reservoirs 1 and 2: formula_1 Considering reservoirs 2 and 3: formula_3 Considering reservoirs 1 and 3: formula_4 Eliminating the heat transferred, we have the following condition for the function "φ". formula_5 Now, it is possible to choose an arbitrary temperature for 3, so it is easy to show using elementary multivariate calculus that "φ" can be represented in terms of an increasing function of temperature "ζ" as follows: formula_6 Now, we can have a one to one association of the function "ζ" with a new temperature scale called the "thermodynamic temperature scale", "T", so that formula_7 Thus we have the thermal efficiency of a Carnot engine as formula_8 The thermodynamic temperature scale is also known as the Kelvin scale, and it needs only one fixed point, as the other one is absolute zero. The concept of absolute zero will be further refined during the statement of the third law of thermodynamics. Reservoir. Reservoirs are systems of large quantity of matter which no temperature difference will occur when finite amount of heat is transferred or removed. Examples of reservoirs are atmosphere, oceans, seas etc. Clausius Theorem. "Clausius theorem" states that any reversible process can be replaced by a combination of reversible isothermal and adiabatic processes. Consider a reversible process "a-b". A series of isothermal and adiabatic processes can replace this process if the heat and work interaction in those processes is the same as that in the process "a-b". Let this process be replaced by the process "a-c-d-b", where "a-c" and "d-b" are reversible adiabatic processes, while "c-d" is a reversible isothermal process. The isothermal line is chosen such that the area "a-e-c" is the same as the area "b-e-d". Now, since the area under the "p-V" diagram is the work done for a reversible process, we have, the total work done in the cycle "a-c-d-b-a" is zero. Applying the first law, we have, the total heat transferred is also zero as the process is a cycle. Since "a-c" and "d-b" are adiabatic processes, the heat transferred in process "c-d" is the same as that in the process "a-b". Now applying first law between the states "a" and "b" along "a-b" and "a-c-d-b", we have, the work done is the same. Thus the heat and work in the process "a-b" and "a-c-d-b" are the same and any reversible process "a-b" can be replaced with a combination of isothermal and adiabatic processes, which is the Clausius theorem. A corollary of this theorem is that any reversible cycle can be replaced by a series of Carnot cycles. Suppose each of these Carnot cycles absorbs heat "dQ1i" at temperature "T1i" and rejects heat "dQ2i" at "T2i". Then, for each of these engines, we have "dQ1i/dQ2i = −T1i/T2i". The negative sign is included as the heat lost from the body has a negative value. Summing over a large number of these cycles, we have, in the limit, formula_9 This means that the quantity "dQ/T" is a property. It is given the name "entropy". Further, using Carnot's principle, for an irreversible cycle, the efficiency is less than that for the Carnot cycle, so that formula_10 formula_11 As the heat is transferred out of the system in the second process, we have, assuming the normal conventions for heat transfer, formula_12 So that, in the limit we have, formula_13 formula_14 The above inequality is called the "inequality of Clausius". Here the equality holds in the reversible case. Entropy. Entropy is the quantitative statement of the second law of thermodynamics. It is represented by the symbol "S", and is defined by formula_15 Note that as we have used the Carnot cycle, the temperature is the reservoir temperature. However, for a reversible process, the system temperature is the same as the reversible temperature. Consider a system undergoing a cycle 1-2-1, where it returns to the original state along a different path. Since entropy of the system is a property, the change in entropy of the system in 1-2 and 2-1 are numerically equal. Suppose reversible heat transfer takes place in process 1-2 and irreversible heat transfer takes place in process 2-1. Applying Clausius's inequality, it is easy to see that the heat transfer in process 2-1 "dQirr" is less than "T dS". That is, in an irreversible process the same change in entropy takes place with a lower heat transfer. As a corollary, the change in entropy in any process, "dS", is related to the heat transfer "dQ" as "dS ≥ dQ/T" For an isolated system, "dQ = 0", so that we have "dSisolated ≥ 0" This is called the "principle of increase of entropy" and is an alternative statement of the second law. Further, for the whole universe, we have "ΔS = ΔSsys + ΔSsurr > 0" For a reversible process, "ΔSsys = (Q/T)rev = −ΔSsurr" So that "ΔSuniverse = 0" for a reversible process. Since "T" and "S" are properties, you can use a "T-S" graph instead of a "p-V" graph to describe the change in the system undergoing a reversible cycle. We have, from the first law, "dQ + dW = 0". Thus the area under the "T-S" graph is the work done by the system. Further, the reversible adiabatic processes appear as vertical lines in the graph, while the reversible isothermal processes appear as horizontal lines. Entropy for an Ideal Gas. An ideal gas obeys the equation "pv = RT". According to the first law, "dQ + dW = dU" For a reversible process, according to the definition of entropy, we have "dQ = T dS" Also, the work done is the pressure volume work, so that "dW = -p dV" The change in internal energy: "dU = m cv dT" "T dS = p dV + m cv dT" Taking per unit quantities and applying ideal gas equation, "ds = R dV/v + cv dT/T" formula_16 As a general rule, all things being equal, entropy increases as, temperature increases and as pressure and concentration decreases and energy stored as internal energy has higher entropy than energy which is stored as kinetic energy. Availability. From the second law of thermodynamics, we see that we cannot convert all the heat energy to work. If we consider the aim of extracting useful work from heat, then only some of the heat energy is available to us. It was previously said that an engine working with a reversible cycle was more efficient than an irreversible engine. Now, we consider a system which interacts with a reservoir and generates work, "i.e.", we look for the maximum work that can be extracted from a system given that the surroundings are at a particular temperature. Consider a system interacting with a reservoir and doing work in the process. Suppose the system changes state from 1 to 2 while it does work. We have, according to the first law, "dQ - dW = dE", where "dE" is the change in the internal energy of the system. Since it is a property, it is the same for both the reversible and irreversible process. For an irreversible process, it was shown in a previous section that the heat transferred is less than the product of temperature and entropy change. Thus the work done in an irreversible process is lower, from first law. Availability Function. The availability function is given by "Φ", where "Φ ≡ E − T0S" where "T0" is the temperature of the reservoir with which the system interacts. The availability function gives the effectiveness of a process in producing useful work. The above definition is useful for a non-flow process. For a flow process, it is given by "Ψ ≡ H − T0S" Irreversibility. Maximum work can be obtained from a system by a reversible process. The work done in an actual process will be smaller due to the irreversibilities present. The difference is called the "irreversibility" and is defined as "I ≡ Wrev − W" From the first law, we have "W = ΔE − Q" "I = ΔE - Q - (Φ2 − Φ1)" As the system interacts with surroundings of temperature "T0", we have "ΔSsurr = Q/T0" Also, since "E − Φ = T0 ΔSsys" we have "I = T0 (ΔSsys + ΔSsurr)" Thus, "I ≥ 0" "I" represents increase in unavailable energy. Helmholtz and Gibbs Free Energies. "Helmholtz Free Energy" is defined as "F ≡ U − TS" The Helmholtz free energy is relevant for a non-flow process. For a flow process, we define the "Gibbs Free Energy" "G ≡ H − TS" The Helmholtz and Gibbs free energies have applications in finding the conditions for equilibrium.

German/Lesson 8. Lektion 8 Grammatik 8-1 ~ Colors. yellow: gelb<br> blue: blau<br> red: rot<br> black: schwarz<br> white: weiß<br> orange: orange<br> pink: pink<br> violet: lila<br> cyan: türkis<br> brown: braun<br> grey: grau<br> light-grey: hellgrau<br> dark-grey: dunkelgrau<br> Grammatik 8-2 ~ Possessive Adjectives, Pronouns, and the Genitive Case. Recall the following from Gespräch 3-1: Which translates: The sentence demonstrates two of the possessive adjectives. These are (singular) 'my', 'your', and 'his/her/its' in English and "mein", "dein", and "sein/ihr/sein" in German. Note that because these are adjectives, the word ending must reflect the case and gender of the noun being modified (see Grammatik 4-1 above). In German, the genitive case correspond to the English possessive case or to the objective case proceeded by "of" to denote possession. If the possessive is not followed by a noun, it becomes a possessive pronoun (see Pronoun Tables). The pattern in the case endings of the possessive adjectives is that seen in Lektion 4 for the word "ein". We can generalize these endings as in the following table, where we can express plural endings because other so-called ein-words do have plurals: The small group of words that take these endings (in addition to "ein") includes the possessive adjectives and "kein" ("not any" or "no" in the sense of none).

Real Analysis. Introduction. The subject of real analysis is concerned with studying the behavior and properties of functions, sequences, and sets on the real number line, which we denote as the mathematically familiar formula_1. Concepts that we wish to examine through real analysis include properties like Limits, Continuity, Derivatives (rates of change), and Integration (amount of change over an extension of the parameteral variable). Many of these ideas are, on a conceptual or practical level, dealt with at lower levels of mathematics, including a regular First-Year Calculus course, and so, to the uninitiated reader, the subject of Real Analysis may seem rather senseless and trivial. However, Real Analysis is at a depth, complexity, and arguably beauty, that it is because under the surface of everyday mathematics, there is an assurance of correctness, that we call rigor, that permeates the whole of mathematics. Thus, Real Analysis can, to some degree, be viewed as a development of a rigorous, well-proven framework to support the intuitive ideas that we frequently take for granted. Real Analysis is a very straightforward subject, in that it is simply a nearly linear development of mathematical ideas you have come across throughout your story of mathematics. However, instead of relying on sometimes uncertain intuition (which we have all felt when we were solving a problem we did not understand), we will anchor it to a rigorous set of mathematical theorems. Throughout this book, we will begin to see that we do not need intuition to understand mathematics - we need a manual. The overarching thesis of this book is how to define the real numbers axiomatically. How would that work? This book will read in this manner: we set down the properties which we think define the real numbers. We then prove from these properties - and these properties only - that the real numbers behave in the way which we have always imagined them to behave. We will then rework all our elementary theorems and facts we collected over our mathematical lives so that it all comes together, almost as if it always has been true before we analyzed it; that it was in fact rigorous all along - except that now we will know how it came to be. Do not believe that once you have completed this book, mathematics is over. In other fields of academic study, there are glimpses of a strange realm of mathematics increasingly brought to the forefront of standard thought. After understanding this book, mathematics will now seem as though it is incomplete and lacking in concepts that maybe you have wondered before. In this book, we will provide glimpses of something more to mathematics than the real numbers and real analysis. After all, the mathematics we talk about here always seems to only involve one variable in a sea of numbers and operations and comparisons. Note: A table of the math symbols used below and their definitions is available in the Appendix. A select list of chapters curated from other books are listed below. They should help develop your mathematical rigor that is a necessary mode of thought you will need in this book as well as in higher mathematics. The real numbers. This part of the book formalizes the various types of numbers we use in mathematics, up to the real numbers. This part focuses on the axiomatic properties (what we have defined to be true for the sake of analysis) of not just the numbers themselves but the arithmetic operations and the inequality comparators as well. Functions, Trigonometry, and Graphical Analysis. This part of the book formalizes the definition and usage of graphs, functions, as well as trigonometry. The most curious aspect of this section is its usage of graphics as a method of proof for certain properties, such as trigonometry. These methods of proof are mostly frowned upon (due to the inaccuracy and lack of rigorous definition when it comes to graphical proofs), but they are essential to derive the trigonometric relationships, as the analytical definition of the trigonometric functions will make using trigonometry too difficult—especially if they are described early on. The following chapters will rigorously define the trigonometric functions. They should only be read after you have a good understanding of derivatives, integrals, and inverse functions. Sequences and series. This part of the book formalizes sequences of numbers bound by arithmetic, set, or logical relationships. This part focuses on concepts such as mathematical induction and the properties associated with sets that are enumerable with natural numbers as well as a limit set of integers. Metric Spaces. This part of the book formalizes the concept of distance in mathematics, and provides an introduction to the analysis of metric space. Basic Topology of formula_8. This part of the book formalizes the concept of intervals in mathematics, and provides an introduction to topology. Limits and Continuity. This part of the book formalizes the concept of limits and continuity and how they form a logical relationship between elementary and higher mathematics. This part focuses on the epsilon-delta definition, how proofs following epsilon-delta operate on, and the implications of limits. It also discusses other topics such as continuity, a special case of limits. Differentiation. This part of the book formalizes differentiation and how they are used to describe the nature of functions. This part focuses on proving how derivatives study the nature of change of a function and how derivatives can provide properties to functions. Integration. This part of the book formalizes integration and how imagining what area means can yield many different forms of integration. This part focuses on proving how derivatives study the nature of change of a function and how derivatives can provide properties to functions. Appendices. Here, you will find a list of unsorted chapters. Some of them listed here are highly advanced topics, while others are tools to aid you on your mathematical journey. Since this is the last heading for the wikibook, the necessary book endings are also located here.

Macroeconomics/Macroeconomic Variables. Macroeconomic Variables. ∑E = ∑O = ∑Y That element of a factor () which is of the level of income. E.g. the level of consumption you need to even when you have no income. That element of a factor () which is influenced by the level of Y. E.g. the level of income the receives from tax (personal income). As the income level increases → so does government tax . Example:. Investment (I), is defined as the of new which add to the stock of . Capital goods are those produced not to satisfy consumer wants directly but for increasing the level of production in the future. Capital consists of items such as factories, machinery and railways.

XML - Managing Data Exchange/Contributors. The following people have recorded their contribution to the development of this book. Active Contributors. The following Wikibookians are actively editing this Wikibook, as of January 28, 2007. All participants in the project are welcome to add their name, email address, contribution, and affiliation to the following list. Please keep the list in alphabetical order, based on last name. Previous Contributors. The following Wikibookians have contributed to this Wikibook before January 2007. These include students from the University of Georgia who began writing this book for a course in Advanced Data Management, as part of a Master's degree in Internet Technology.

General Chemistry/Energy changes in chemical reactions. Exothermic and Endothermic Reactions. The release of energy in chemical reactions occurs when the reactants have higher chemical energy than the products. The chemical energy in a substance is a type of potential energy stored within the substance. This stored chemical potential energy is the "heat content" or enthalpy of the substance. If the enthalpy decreases during a chemical reaction, a corresponding amount of energy must be released to the surroundings. Conversely, if the enthalpy increases during a reaction, a corresponding amount of energy must be absorbed from the surroundings. This is simply the Law of Conservation of Energy. absorbtion reactions is when a chemical reaction releases more energy than it absorbs and you can also see them die on the inside. reletion reactions is when a chemical reaction absorbs more energy than it releases. You are already familiar with enthalpy: melting ice is endothermic and freezing water is exothermic. Because reactions release or absorb energy, they affect the temperature of their surroundings. Exothermic reactions heat up their surroundings while endothermic reactions cool them down. The study of enthalpy, along with many other energy-related topics, is covered in the Thermodynamics Unit. Activation Energy. Think about the combustion of methane. It releases enough heat energy to cause a fire. However, the reaction does not occur automatically. When methane and oxygen are mixed, an explosion does not instantly occur. First, the methane must be ignited, usually with a lighter or matchstick. This reveals something about reactions: they will not occur unless a certain amount of activation energy is added first. In this sense, all reactions absorb energy before they begin, but the exothermic reactions release even more energy. This can be explained with a graph of potential energy: This graph shows an exothermic reaction because the products are at a lower energy than the reactants (so heat has been released). Before that can happen, the energy must actually "increase". The amount of energy added before the reaction can complete is the activation energy, symbolized Ea.

Macroeconomics/Macroeconomic Objectives. Macroeconomic objectives. Broadly, the objective of macroeconomic policies is to maximize the level of national income, providing economic growth to raise the utility and standard of living of participants in the economy. There are also a number of secondary objectives which are held to lead to the maximization of income over the long run. While there are variations between the objectives of different national and international entities, most follow the ones detailed below:

Macroeconomics/Economic Activity. 'Economic activity' is a very broad term, and can be measured in a number of ways. In general, it means the level of activity, the number of transactions, the value of those transactions and the overall output or goods and services produced within an economy. Measures of Economic Activity. Gross Domestic Product. The most commonly used statistic is " (GDP)". GDP is the total money value of all the "final" goods and services produced in an economy in a given year. However, there are difficulties associated with using GDP, such as inflation - the money value of an economy's products will increase even if there is no real growth, as inflation reduces the value (or purchasing power) of money. So, GDP is often adjusted for inflation, the result being called real GDP. For example, if the GDP of an economy in 2004 is 1 trillion, and the next year is 1.1 trillion, the change in GDP is 10%. However, if inflation rate is 5% then the change in "real GDP" is somewhat less than that. Shortcomings of GDP. GDP is "not" a perfect measure. The following points are some examples of shortcomings of GDP. Terms used in measuring economic activity. Net. → NET = GROSS - rate of DEPRECIATION National. → NATIONAL = DOMESTIC + NET INCOME FROM OVERSEAS Factor cost. → FACTOR COST = MARKET PRICES - (INDIRECT TAXES + SUBSIDIES)

Macroeconomics/Macroeconomic Equilibrium. Macroeconomic Equilibrium. is the situation where there is no tendency for change. The can be in equilibrium at any level of economic activity that is a high level () or a low level (). Due to the size of many modern economies, equilibrium is a very temporary state, as changing variables affect the economy. Macroeconomic Equilibrium can be shown through the C.F.M. using: Savings + taxation + imports = investment + government spending + exports This can be understood as savings approximately equal to investment, government spending to taxation, and similarly imports to exports, at least over the long run. It means that, at equilibrium, injections into the income stream equal the leakages from the income stream. Total expenditure = total output = total income It is easier to remember if you just think that they are really different ways of measuring the same thing, which is the flow of factors through the economy, which can be demonstrated with the CFM. A change in the and will cause a new equilibrium to be established where total income (∑Y), total output (∑O), and total expenditures (∑E) will again equate but at either a higher or lower level than the original equilibrium. Leakages do not have to equal injections e.g. imports constitute a leakage from the importing country's economy, but an injection to the exporting countries economy. So looking at the world economy it is zero sum game, where Leakages = Injections, but looking at any one country's economy this need not be the case.

Macroeconomics/Savings and Investment. Role of Savings and Investment. There are two views of the topic titled Savings and Investment. One is considered to apply to real physical macroeconomic activity, the "Keynesian", or National Accounts view. The other is considered to apply to money and banking, the "Monetarist" view. They primarily differ slightly in definitions of terms, which consequently lead to different discussions about very different subject matter. The two views actually are different subject areas, making it the historical debate difficult to collate, let alone reconcile. Keynesians start with accounting definitions, where Savings is equal to Investment, by construction, and tend to emphasize the nonproductive (zero sum) nature of all vehicles by which savings eventually ends up as capital. Monetarists tend to focus on technical distinctions of how savings is transformed from money balances, eventually into capital, and emphasize the value of those vehicles in selecting which capital to invest in. In a Keynesian sense, savings is whatever is left over after income is spent on consumption of goods and services, investment is what is spent on goods and services that are not 'consumed', but are durable. Since Income = Output, Savings = Investment for the total world's economy (or for a hypothetical 'closed' economy with zero foreign trade). In a Monetarist sense, savings is the total rate at which units of account exceed expenditures, and are accumulated as unit of account (e.g. dollar) balances with financial intermediaries. Or sometimes hoarded as currency. Investment is the rate at which financial intermediaries and others expend on items intended to end up as capital that directly creates value, i.e. physical capital, durable goods, human capital, etc. In general, savings does not equal investment, but differs slightly at all times, the differences constituting a behavioral relationship, rather than an accounting one, as in the Keynesian view. The two views are just looking at very different things. The most commonly referred meaning of the phrase "Savings and Investment" is in first year college economics, where Keynesian and neoclassical macroeconomics are taught, and national accounts, (i.e. the identity Y = C + I + G) is explained. Saving is what households (i.e. participants in the consumption account) do. The level of saving in the economy depends on a number of factors (incomplete list): These factors affect the marginal propensity to save (MPS) - the greater this MPS, the more saving households will do as a proportion of each additional increment of income. The 2 Forms of Investment. a) b) Note on so-called "fiscal" policy, i.e. marginal discretionary government spending: a) Planned Injections (J) and Planned Withdrawals(W) b) Savings and investment flows most likely to change economic activity

Macroeconomics/Consumption. =Consumption= The Importance of Consumption Every time you purchase food at the drive-thru or pull out your debit or credit card to buy something, you are adding to consumption. Consumption is one of the bigger concepts in economics and is extremely important because it helps determine the growth and success of the economy. Businesses can open up and offer all kinds of great products, but if we don't purchase or consume their products, they won't stay in business very long! If they don't stay in business, many of us won't have jobs or the income to buy goods and services. Consumption can be defined in different ways, but is best described as the final purchase of goods and services by individuals. The purchase of a new pair of shoes, a hamburger at the fast food restaurant or services, like getting your house cleaned, are all examples of consumption. It is also often referred to as consumer spending. Many topics in economics explore how the income of families and individuals affects consumption and spending habits. Note:. Saving (S) is not part of A.E. due to it being a leakage, (we analyse it because it helps us determine consumption and impacts on Y levels). The savings function (S = Y - C) can be derived from the consumption function (c.f.).

Macroeconomics/Investment. =Investment= Factors Affecting Investment:. Determinants. The level of investment in the economy is determined by:

Active Server Pages. How this book is organized. This book is organized into "modules". Each module should take you about one hour to complete. Modules are organized as follows: Later modules build upon earlier modules, so we encourage you to read them in sequence.

Lucid Dreaming/Reality Checks/Reading. Presentation. With the reading reality check, you read some text, look away, and see if you can remember the text. Then, you check if it has changed when you turn back. Do this twice. You can also actively try to change the text (note that changing text in a Wikibook is not necessarily evidence you are dreaming though!). For example, consider this paragraph. Try to remember its text. Then reload the page. If you realise that the text is now missing, you know that you are dreaming. This reality check works because the mind has no external input to base the text upon. Note you will usually have no problems reading text in a dream. It is remembering the text which is hard.

Korean/Alphabet. Introduction. The Korean alphabet, known commonly as "Hangul" in English but as "Hangeul" in the official standard Romanization rule (한글, "great script"), is considered one of the most efficient and logical writing systems in the world. While most modern alphabets evolved from earlier hieroglyphics or ideographs, 한글 ("Hangeul") was created specifically to make it easy to read and write the Korean language. Although the characters of 한글 ("Hangeul") may appear to be ideograms like the traditional "Hanja" (한자, 漢字), they really form an alphabet. Each block character represents one syllable and is made up of individual "jamo" (자모), much like the letters in the Latin alphabet. 한글 ("Hangeul") is easy to learn because it has only 24 basic "jamo". Consonants. Below are the consonant (자음) letters of the Korean alphabet. You don't need to memorize them yet because individual lessons will cover each letter in detail. For now, just be aware that the Korean alphabet has ten basic consonants and nine variations on them: Notice that some consonants have two different pronunciations (e.g. ㄱ pronounced as /g/ or /k/ depending on context). Some of the alternative sounds in pronunciation of the basic consonant letters are their sound value as the final jamos when they are not altered by the initial jamo of the next syllabic character. ㅅ ㅈ ㅊ ㅎ has [t] sound as the final. Also, some are "aspirated" and some are "tense". Those details and more are explained in ../Essential Pronunciation Rules/. Vowels. There are 21 letters used to represent vowels: six basic vowels, nine combinations of those six basic vowels (which originally were all pronounced as diphthongs), and six vowels with an extra short dash representing the initial "y" [j] sound. End of introduction. To learn how to read, write, and pronounce each Korean letter, proceed to the Read, Write, and Pronounce Korean course.

General Chemistry/Chemistries of Various Elements. <includeonly> Chemistries of the Various Elements. </includeonly>

General Chemistry/Compounds and Bonding. <includeonly> Compounds and Bonding. </includeonly>

Tcl Programming. Tcl (Tool Command Language) is a dynamic programming/scripting language based on concepts of Lisp, C, and Unix shells. It can be used interactively, or by running scripts (programs) which can use a package system for structuring, hence allowing to do much with little code. Tcl is available for Linux, Windows, Mac OS X, as well as other platforms, as open-source software under BSD-like license, or as pre-built binaries. This book also discusses the GUI toolkit Tk in considerable extent, even though it's not in the title. For most users, Tcl/Tk form a single conceptual entity. Chapters. __NOEDITSECTION__

Active Server Pages/Your first page. Content. ASP is delimited with "<%" and "%>" <br> within these delimiters is your custom code that is executed in the server. Here is a small fragment of an ASP code (it outputs "My First ASP" on your browser): <% Response.Write "My First ASP" Or you could put the text into a pre-defined variable: <% Dim MyText MyText = "My First ASP Page" Response.Write MyText Here is a way to separate your code from your page layout. <%@LANGUAGE="VBSCRIPT" CODEPAGE="1252"%> Dim MyText MyText = "My First ASP" <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <title>My First ASP</title> </head> <body> <%=(MyText)%> </body> </html>

Japanese/Grammar/Counters. Most Japanese nouns do not have plural forms. Instead, when indicating a specific number or amount of a noun, the noun is followed by a counter (助数詞, じょすうし). There are a large number of these counters, each referring to a particular kind of thing to count. For example when referring to four books: Counters can also be used in adverbial or nominal manner. "There are four books there" can be either of the following: For the most part, two numbering systems are used: the numbers derived from Chinese (いち, に, さん, etc.) and the native Japanese counting words (ひとつ, ふたつ, みっつ, etc.). Common counters. Some of the most common & basic counters: Living beings. 匹 is often used for animals generally, but in more careful use it is restricted to small animals, such as cats and dogs. Large animals notably include horses, cattle, and elephants, as well as whales and dolphins. Some kinds of animals have two or more counters. For example, "3 butterflies" can be translated into 3羽 or 3匹.

Lucid Dreaming/Reality Checks/Nose. Presentation. With the nose reality check, you close one eye, and try to see your nose. If you can't, then you're dreaming. See for a discussion of this reality check's effectiveness.

Latin/Lesson 5-Perfect Indicative. Latin Perfect Active Tense. The perfect tense is used for action that has already been completed. English has two corresponding constructions: present perfect and simple past. The present perfect uses the present of "to have" plus the past participle. ("I have sailed to Athens twice." "These women have spoken the truth.") The simple past is a separate verb form that indicates a completed action. ("I came, I saw, I conquered.") Another related form, which uses "did" as an auxiliary, is used for emphasis, negation or interrogation. ("I did see you at the Forum, didn't I?") In Latin, the perfect indicative is equivalent to all of these. The perfect endings: (1) There is an alternative third person plural ending, "-ēre", used mainly in poetry. For example, "amāvēre" = "amāvērunt". Although these endings apply to all Latin verbs, each verb's stem changes differently in the perfect tense. To find the stem, use the third principal part, which is the first person singular perfect active indicative form of that verb. Example. Singular: Plural: Basically, the Perfect indicative active is the perfect tense under a flash name. Rules for Finding the Perfect Stem. The perfect stem can often be guessed by knowing the verb's first person singular and infinitive. Here are some rules that perfect stems often follow.

Scouting/BSA/Mammal Study Merit Badge. 1. Explain the meaning of animal, invertebrate, vertebrate, and Mammal. Animal-a living organism that feeds on organic matter, typically having specialized sense organs and nervous system and able to respond rapidly to stimuli. Ibvertebrate-an animal lacking a backbone, such as an arthropod, mollusk, annelid, coelenterate, etc. The invertebrates constitute an artificial division of the animal kingdom, comprising 95 percent of animal species and about 30 different phyla. an animal lacking a backbone, such as an arthropod, mollusk, annelid, coelenterate, etc. The invertebrates constitute an artificial division of the animal kingdom, comprising 95 percent of animal species and about 30 different phyla. Vertebrate- an animal of a large group distinguished by the possession of a backbone or spinal column, including mammals, birds, reptiles, amphibians, and fishes. Mammal- warm-blooded vertebrate animal of a class that is distinguished by the possession of hair or fur, the secretion of milk by females for the nourishment of the young, and (typically) the birth of live young. Name three characteristics that distinguish mammals from all other animals. Have hair at some part of their life, Give birth to live young, and warm-blooded 2. Explain how the animal kingdom is classified. Lion Kingdom: The lion is an animal because it eats other organisms for sustenance. Therefore, it is in the Kingdom Animalia. Phylum: The lion has a spinal cord, and it is thus in the Phylum Chordata. Class: The lion has hair and mammary glands, and gives birth to live young. This makes it a mammal, and a member of the Class Mammalia. Order: The lion is a member of the Order Carnivora because it shares specific characteristics of skull and teeth shape (and not because it is a carnivore). Family: The lion is a cat, and is thus a part of the Family Felidae (Note: all families of mammals end in -idae). Genus: The lion has special characteristics that allow it to roar, and is therefore a member of the Genus Panthera. Species: The lion is the species leo of the genus Panthera. The scientific name of a species is both terms combined (e.g. Panthera leo, sometimes abbreviated P. leo). Explain where mammals fit in the classification of animals. Kingdom: Animalia, class: Mammalia. Classify three mammals from phylum through species. Mammal 1 The domestic dog form of the gray wolf, a member of the Canidae family of the order Carnivora. Mammal 2 The cat (Felis catus), also known as the domestic cat or housecat to distinguish it from other felines and felids, is a small furry domesticated carnivorous mammal that is valued by humans for its companionship and for its ability to hunt household pests. Cats have been associated with humans for at least 9,500 years. Mammal 3 The fox is a common name for many species of omnivorous mammals belonging to the Canidae family. Foxes are small to medium-sized canids (slightly smaller than the median-sized domestic dog), characterized by possessing a long narrow snout, and a bushy tail (or brush). 3. Do ONE of the following: a. Spend 3 hours in each of two different kinds of natural habitats or at a different elevation. List the different mammal species and individual members that you identified by sight or sign. b. Spend 3 hours on each of 5 days on at least a 25- acre area (about the size of 3 1/2 football fields). List the mammal species you identified by sight or sign. c. From study and reading, write a simple history of one non-game mammal that lives in your area. Redtail hawk Tell how this mammal lived before its habitat was affected in any way by humans. The red tail hawk had an easier time finding food. It had a huge amount of space and many places to build a nest. And the population used to be bigger. Tell how it reproduces, Hawk pairs fly in large circles to attract each other so they can lay eggs together. what it eats, Hawks eat mice, squirrels, rabbits, etc. It is a carnivore. and its natural habitat. Its natural habitat is the wild. Trees, bushes, etc. Describe its dependency upon plants, It builds nests in trees and bushes. upon other animals (including humans), It eats other animals. and how they depend upon it. For food Tell how it is helpful or harmful to humankind. Hawks are helpful because they kill mice and we use them for hunting and food. 4. Do ONE of the following: a. Under the guidance of a nature center or natural history museum, make two study skins of rats or mice. Skin 1: Skin 2: Tell the uses of study skins and mounted specimens respectively. b. Take good pictures of two kinds of mammals in the wild. Record light conditions, film used, exposure, and other factors, including notes on the activities of the pictured animals. Photo 1 Mammal: Dog Charlie Photo 2 Mammal: Kyle (my brother) Light conditions: Bright Light conditions: Average Film Used: Digital Film Used: Digital Exposure: Exposure: Animal’s Activities: Sleeping on swing Animal’s Activities: Sitting in a chair Other factors: Flash off Other factors: Flash off c. Write a life history of a native game mammal that lives in your area, covering the points outlined in requirement 3C. List sources for this information Native Game Animal: White-tailed deer Tell how this mammal lived before its habitat was affected in any way by man. The White-Tailed Deer lived in most forests in the U.S. It was also more populated before it was hunted. Tell how it reproduces, Males are sexually active in the second year and females in their first fall. what it eats, Graze, northern white cede, red maple, hemlock, mountain ash, acorns, beechnuts, and fruits. and its natural habitat. Brush openings, crop fields, wood lots, and wetlands. Describe its dependency upon plants, It eats trees and plants and also uses them as shelter and cover. upon other animals (including man), Man thins out the population and man plants crops that they eat. and how they depend upon it. So they don’t overpopulate or starve. Tell how it is helpful or harmful to man: We thin the populated and we feed them. d. Make a bait and tracking pit. Report what mammals and other animals came to the bait. e. Visit a natural history museum. Report on how specimens are prepared and cataloged. Explain the purposes of museums. Museums show history and how people before us lived. f. Write a report of 500 words on a book about a mammal species. g. Trace two possible food chains of carnivorous mammals from soil through four stages to the mammal. Possible food chain 1: Soil: Stage 1: Stage 2 Stage 3 Stage 4 Possible food chain 2: Soil: Stage 1: Stage 2 Stage 3 Stage 4 5. Working with your counselor, select and carry out one project that will influence the numbers of one or more mammals. Requirement 2. Animals (and other organisms, like plants) are classified for several reasons. First of all, the sheer number of species of animals in the world is quite large, and many are un-named or confusingly-named (for example, several different vegetables are called "). Thus, a Swedish scientist named Linnaeus created a system to classify organisms based on recognizable traits and used an old, extinct language (Latin) to refer to organisms. He chose because it was rigid in spelling and pronunciation, and so it would enable simple communication between scientists who spoke different languages or dialects. The modern system of organism-classifying is derived from Linnaeus' system. The science of classifying organisms is called ". The exact methods of classifying organisms can change as scientists discover new characteristics that separate and unite organisms. For example, science used to classify all organisms into two kingdoms (a "kingdom" is the largest basic unit of classification), plants, and animals. This was based on a simple formulation -- anything which devoured other organisms was an animal, and anything that did not, was a plant. Eventually, however, scientists decided that this system did not adequately describe reality, and the Fungi were added as a third kingdom. Later still, three kingdoms have been added for various kinds of microscopic organisms like bacteria. There are seven basic levels of classification. They can be remembered using the "King Philip Came Over For Great Soup" (the first letter of each word is the first letter of the unit of classification, in order). An example classification for the lion The above process weeds out successively less similar organisms, so very similar animals like panthers and cheetahs, have the same classification until near the end. Requirement 3. "Spend 3 hours in each of two different kinds of natural habitats or at different elevations. List the different mammal species and individual members that you identified by sight or sign. Tell why all mammals do not live in the same kind of habitat." "Spend 3 hours on each of 5 days on at least a 25-acre area. List the mammal species you identified by sight or sign." When making these observations, it is best to prepare. Think about what kinds of mammals might be living in the habitat, and how you could see or otherwise find evidence of them. You may be able to find tracks in the ground, or dens or dams, or other physical evidence of mammals. Mammals do not all live in the same habitat because each species is uniquely adapted for one . For example, in a forest, squirrels perform a necessary function, spreading acorns, and thus ensuring that trees' offspring can spread far from the parent plant; squirrels also provide sustenance for predators, such as snakes. No other organism fits into the squirrel's niche, and the squirrel can not function well in any other niche. All species in the forest have a unique niche; mammals that do not have such a niche do not live there -- for example, lions are well-adapted for their role on the savannas, but are not well-suited for a temperate forest. "From study and reading, write a simple history of one nongame mammal that lives in your area. Tell how this mammal lived before its habitat was affected in any way by man. Tell how it reproduces, what it eats, what eats it, and its natural habitat. Describe its dependency upon plants, upon other animals (including man), and how they depend upon it. Tell how it is helpful or harmful to man." A game mammal is one that is widely hunted, such as deer. Most mammals are not game mammals. For help in choosing a mammal, see . Requirement 4. "Under the guidance of a nature center or natural history museum, make two study skins of rats or mice. Tell the uses of study skins and mounted specimens respectively." "Take good pictures of two kinds of mammals in the wild. Record light conditions, film used, exposure, and other factors, including notes on the activities of the pictured animals." "Write a life history of a native game mammal that lives in your area, covering the points outlined in requirement 3c. List sources for this information." "Make and bait a tracking pit. Report what mammals and other animals came to the bait." "Visit a natural history museum. Report on how specimens are prepared and cataloged. Explain the purposes of museums." "Write a report of 500 words on a book about a mammal species." Some classic books about mammal species include: "Trace two possible food chains of carnivorous mammals from soil through four stages to the mammal." A is a hierarchy of organisms which devour each other. Energy can be traced through a food chain, beginning with its source, plants. The first step in a food chain is always a plant (for example, ), which creates energy using sunlight (see ). The algae are then eaten by small microscopic organisms called , who are in turn eaten by a . The squid is eaten by a seal, and the by an . The energy produced by the algae can be traced to the orca. Requirement 5. "Work with your counselor, select and carry out one project that will influence the numbers of one or more mammals."

Scouting/BSA/Home Repairs Merit Badge. "1. Discuss general precautions related to home repairs. Name at least 10 safe practices that every home repairer should exercise." "2. Under the supervision of your merit badge counselor complete any four of the following:" a. How-to:Maintain or recondition a garden tool and show that you know how to clean up, store it and other tools b. How-to:Install insulation in an attic, wall, or crawl space c. How-to:Caulk cracks or joints open to the weather d. How-to:Waterproof a basement e. How-to:Repair a break in a cement or asphalt surface f. How-to:Repair the screen in a window or door g. How-to:Replace a pane of glass h. How-to:Solder a broken wire or metal object "3. Under the supervision of your merit badge counselor complete any three of the following:" a. How-to:Install or build equipment for storing tools b. How-to:Build a workbench c. How-to:Repair a piece of furniture d. How-to:Paint or varnish a piece of furniture, a door, or trim on a house and clean the brush e. How-to:Repair a sagging door or gate f. How-to:Repair a loose step g. How-to:Repair a fence "4. Under the supervision of your merit badge counselor complete any two of the following:" a. How-to:Locate a main switch box and know how to replace a fuse or reset a circuit breaker b. How-to:Repair an electric cord, plug, or lamp socket c. How-to:Install a single-pole light swich d. How-to:Replace an electrical wall outlet "5. Under the supervision of your merit badge counselor complete any two of the following:" a. How-to:Clear a clogged drain or trap b. How-to:Fix a leaky water faucet c. How-to:Repair a flush toilet d. How-to:Repair a leaky hose or connector e. How-to:Clean or replace a sprinkler head "6. Under the supervision of your merit badge counselor complete any three of the following:" a. How-to:Paint a wall or ceiling. Clean equipment b. How-to:Repair or replace damaged tile or linoleum c. How-to:Install drapery or curtain rods and hang drapes or curtains d. How-to:Replace window blind cords e. How-to:Repair or replace a window sash cord f. How-to:Reinforce a picture frame g. How-to:Mend an object made of china, glass, or pottery

Introduction to Philosophy/Philosophy of Science. < Introduction to Philosophy There are two different meanings of the term "philosophy of science": the first one is about the scientific method and it is the one meant in this article; the second one is about some philosophical questions that are answered by scientific discoveries. In recent decades physics have changed our concept of reality and biology changed our concept of life, philosophy of science in this meaning is treated in A scientific perspective of philosophy. There are subdisciplines of philosophy of science which take a philosophical look at issues arising from specific scientific disciplines: for instance, philosophy of biology looks at the meaning of concepts used in evolutionary biology, while the philosophy of social sciences looks at topics like what a 'theory' is in a field like economics or sociology. Karl Popper. The founding father of this field is widely considered to be Karl Popper, writing at the beginning of the 20th century. The idea that one was necessary stemmed from observation of the Freudian claims on the Oedipus complex, essentially Freud's theory cannot be proven wrong by any means. Whilst this might sound like a positive aspect of the theory, it means that there are also no tests to verify the claims the theory makes. Popper's proposed means of putting this right was to apply the principle of falsificationism to any one theory. To be scientific the scientist in question has to try to prove his theory wrong, or at the very least put forwards tests that can be shown to be either correct or incorrect. This led to the problem of when a theory can be known to be truly scientific and as such a correct interpretation of the natural world. Popper's answer to the criticism was that each test corroborated the theory further. This to many is simply the equivalent of the inductive "All swans are white" argument, i.e. the observation is correct until you happen to pass by Australia and find a black swan. Later theories include Kuhn's theory of a scientific revolution. This proposes the theory that scientists will work within one given model, or paradigm, of the universe and make this useful and predictive until such a moment in time when a new idea or theory overthrows the old system, such as Galileo's observations of the solar system. Feyerabend however rejected the idea that scientists are rational creatures entirely in his book "Against Method" where he argues that scientists do not in fact follow any one given method but are much less rational than their propaganda makes them out to be. Thomas Aquinas. The ideas put forth by Popper, Kuhn, and Feyearbend, wrestle with an issue mentioned by Thomas Aquinas. He said, "...other sciences do not argue to prove their own principles, but argue from their principles to prove other things which the sciences include..." (Summa Theologica article eight or ). While he wasn't directly talking about the philosophy of science, his words are instructive of the present topic. If science cannot argue to prove its own principles, then something else must or science has no basis. Imre Lakatos. A fourth contemporay is Imre Lakatos, what he gained most renown for in the circles of philosophy of science was his attack on what he terms as pseudo-science. His demarcation lies in whether any given program is progressing or degenerating. As such the program that is producing most new knowledge is the one that will be favoured by scientists as the one closest to the truth.

Dutch/Lesson 6. Grammatica 6.1 ~ Numbers. Use the sound buttons to help you with the pronunciation. -teen = -tien. Dutch has a similar way of constructing the numbers for 13-19 as English, it is mainly the simple number (e.g. vijf, zes) followed by -tien, which means "ten" and is very similar to English -teen 13 dertien <br> 14 veertien <br> 15 vijftien <br> 16 zestien <br> 17 zeventien <br> 18 achttien <br> 19 negentien -ty = -tig. As another example of the relationship between English y versus Dutch g, the English ending -ty in twenty, thirty etc., is "-tig" in Dutch: 20 twintig <br> Starting at twenty one things get a little funny, Dutch puts the single unit before the ten-unit: 21 eenentwintig (literally: one-and-twenty)<br> 22 tweeëntwintig <br> 23 drieëntwintig <br> 24 vierentwintig <br> 25 vijfentwintig <br> 26 zesentwintig <br> 27 zevenentwintig <br> 28 achtentwintig <br> 29 negenentwintig <br> Notice that one way to deal with two subsequent vowels in Dutch spelling is the diaeresis ë. The same system goes for 30, 40, 50... 30 dertig <br> 32 tweeëndertig<br> 40 veertig <br> 50 vijftig<br> 60 zestig<br> 70 zeventig<br> 80 tachtig (!!) <br> 90 negentig<br> The only irregular one is tachtig.<br> Notice that 60 and 70 are pronounced with initial [s]. Large numbers. 100 honderd<br> Dutch does not use "one" as in "one hundred" or "one thousand" 101 honderdéén <br> 111 honderdelf <br> 112 honderdtwaalf <br> 113 honderddertien <br> 121 honderdéénentwintig <br> 957 negenhonderdzevenenvijftig <br> In Dutch all numbers lower than one thousand are written as one word. There should be a space after '1000' "(duizend)", though. There's also a space before and after: miljoen, biljoen, miljard, biljard, etc. 1000 duizend <br> 1001 duizend één <br> 1017 duizend zeventien <br> 1538 duizend vijfhonderdachtendertig "or" vijftienhonderdachtendertig <br> 2000 tweeduizend <br> 8000 achtduizend 100.000 honderdduizend<br> 143.000 honderddrieënveertigduizend <br> 143.500 honderddrieënveertigduizend vijfhonderd <br> 1.000.000 één miljoen<br> 2.000.000 twee miljoen<br> 453.897.245 vierhonderddrieënvijftig miljoen achthonderdzevenennegentigduizend tweehonderdvijfenveertig <br> For higher power of one thousand Dutch follows the British rather than the American system 1.000.000.000 één miljard<br> (not: biljoen, see below) 1.000.000.000.000 één biljoen 1.000.000.000.000.000 één biljard 245.078.476.453.879 tweehonderdvijfenveertig biljoen achtenzeventig miljard vierhonderdzesenzeventig miljoen vierhonderddrieënvijftigduizend achthonderdnegenenzeventig <br> Notice also that the interpunction is the reverse: English: $1,324,432.93 = Dutch: $1.324.432,93 Dutch has a decimal comma, not a decimal point. Grammatica 6.2 ~ Past and perfect tenses. Recall: These are examples of past and perfect tenses. There are three kinds of verbs in Dutch when it comes to forming them. The numbers: However, the strong and irregular verbs are amongst the most frequently used ones. The more specialized and recently formed ones are typically weak. Weak verbs. We have seen how the present tense is formed: Past tense. Notice the similarity with English: the past is formed with a dental suffix: -de (Dutch) -ed (English). However if the root ends in a voiceless consonant (t, k, f, s, ch, p and x) the endings are voiceless in Dutch "-te", "-ten": This happens in about a third of the weak verbs. Perfect tense. The perfect uses an "auxiliary" + "the past participle". For a weak verb is formed by prefixing "ge-" and suffixing an ending -d, or -t. Inseperable verbs. If the verb already has a prefix like "be-", "ont-" or "ver-" or "ge-" itself, the "ge-" prefix is omitted: These verbs are called inseparable verbs to distinguish them from a group of verbs that have a prefix that can be separated. We will revisit those in a later lesson. The inseparable ones are relatively simple. Apart from the suppression of the ge- prefix they behave like normal verbs. The past participle on -d and -t. The suffix of the participle is "-d" in the case of "leren": the perfect This is by far the most common way to form the past participle. However, if the root ends in a "voiceless" consonant (t, k, f, s, ch, p and x) the ending is a "voiceless -t": Dutch has "final obstruent devoicing", a fancy term for the fact that a consonant at the end of a word is always pronounced as voiceless. That means that both the -d of "geleerd" and the -t of "gepast" as actually pronounced the same, as [t]. However, as in English the participle can also be used as an adjective. As such it also has an inflected form with -e: In this case the /d/ of geleerde is actually also pronounced [d] and the /t/ of gepaste as [t]. If the root already ends in -d or -t the ending is omitted: Word order. In contrast to English the participle is put at the end of the sentence: Primitive tenses. Most Dutch verbs can be fully reconstructed in all their forms if you know three primitive tenses, de "stamtijden": infinitive - past tense singular - perfect participle This is why verbs are often represented this way in dictionaries, including in WikiWoordenboek. If you want a complete table of all possible forms, this becomes rather large especially if you list all the compound tenses. Take a look at the page ' and compare it with the full conjugation at '. Auxiliaries. The auxiliary is usually a form of "hebben" like it is "to have" in English (see below for its forms). However, unlike English there is a group of verbs (ergative verbs) that take "zijn" (to be) instead. Notice that "gebeuren" (to happen) is one such case: It is an ergative verb. Instead of an action such verbs express either a process or a movement. Compare: Strong verbs. The participle ends in -en in the case of strong verbs. Which verbs are strong? There are more than 150 strong roots and including all derived forms lopen, "be"lopen, "ver"lopen etc. there are more than 1500 strong verbs in Dutch. And you will just have to learn them. Few rules can be given which verbs are weak and which are strong, but we can try: The seven classes. There are seven distinct patterns (classes) of vowel change. These patterns are exceedingly old. They come from the Indo-European language and are much better preserved in Dutch than they are in English. The most common one (Class I) has ..ij... - ..ee.. - ..e..: English has far fewer strong verbs left and they have become "irregular", i.e. the patterns are no longer very recognizable, although sometimes the resemblance is still striking, compare: We will come back to strong verbs later, particularly in the practice lessons 6A and 7A. Fortunately for all Dutch verbs except a handful it is enough to memorize "de stamtijden" (the primitive times): If you are uncertain about the primitive tenses of a verb, a trip to WikiWoordenboek will easily remedy that. The primitive tenses are typically given in a small table on the right of the screen. Have a look at . Lopen is a verb of movement. This is why it uses "to be" as auxiliary if a direction of the movement process is specified. Compare: In the latter case the verb takes "hebben" because the emphasis is not on the movement process but on the activity (action). Notice that Dutch often uses the perfect tense where English uses a simple past. The past tense corresponds more to the past continuous in English, although the division of labor between the tenses is different in the two languages. The past of some of the strong verbs has a plural that undergoes lengthening of the vowel: Past continuous. Dutch does not have a past (or present) continuous as such, although there is a construction using "aan het" + infinitive that can be used to describe continuity rather emphatically: Verbs like lopen, staan, zitten, liggen (walk, stand, sit and lie) can also be used to express continuous action. They take "te" + infinitive: Irregular verbs. There are only a few verbs (actually 6) that demand more knowledge than that which is contained in the three "stamtijden" (primitive tenses) They are: "zijn", "hebben", "zullen", "mogen", "kunnen" and "willen" The auxiliary "to have". The most important irregular verbs are "hebben" and "zijn": The auxiliary "to be". Perfect. Notice that to be is seen as an ergative: it is not an action, but a 'process'. Infinitive. Wezen is quite common in certain parts of the Netherlands, but frowned upon in other regions. Subjunctive. Both are archaic but they are still be seen in certain expressions. Strong and weak verbs with irregularities. Some strong and weak verbs do not completely follow any of the regular patterns. We have seen one: Notice that the present tense and the infinitive do not have a "g". There is also a group of weak verbs ends in -cht rather than just -t: The vowel of these roots also changes, but historically these verbs are weak. Notice that English has something similar (brought, thought). In these cases it is still enough to know the three primitive tenses to reconstruct the entire verb. As this is the case for all Dutch verbs bar six it is customary to represent a verb whether weak, strong or irregular by these primitive tenses and reserve the term "irregular" for the handful cases where this does not suffice. Woordenschat 6. <br clear="all"> Quizlet. The vocabulary for this lesson can be studied at Quizlet (60 terms) Progress made. If you studied this lesson well you should Cumulative count: <br clear="all"> Also see Dutch/Vocabulary/The numbers for a synopsis and the hover test based on it.

Learning the vi Editor/Advanced tasks. Copying and Pasting. Copying and pasting tasks are done with three keys, (for "yank"), (for "delete"), and (for "paste"). In general, you type or to tell vi that you're at the position where you want to start yanking or deleting some text. Then you need to tell vi where to stop, using cursor movement or other commands. You can also simply use key to enter a visual mode. Then you can highlight text by moving cursor keys. And finally press to copy text to clipboard. And for paste. A Word. To delete a single word, move your cursor to the first letter, then type . To yank a single word, move your cursor to the first letter, then type . Other Methods. Move to the character past the last letter and type . To delete a word like "can't", which has an apostrophe, move to the first character and type . Note the capital W. This tells vi to go all the way to the first whitespace character after the word. Likewise, try dB. A Line. To delete a single line, type . Other Amounts. One of the great things about vi is that it lets you select a bunch of text without having to move your hand to your mouse. Type . This will mark the current position that your cursor is at as mark a. You can go back to this position anytime you want from now on by typing . (`a means "move to the character that has been marked as a") Now move to some other position. Type . This will delete everything from the current position to the position you marked as a. Note that you can use nearly any key in place of the used in this example. For instance, you might use to mark the "top" of a section, or to mark the "bottom". These mnemonics are strictly in the user's head – vi doesn't care that "t" means "top" or "b" means bottom. Vi will remember all unique bookmarks, allowing the user to easily and quickly jump between them. Some users find using to be a convenient temporary bookmark, because it can be typed so quickly. To the end or beginning of a line. or To the end or beginning of the file. or To the next occurrence of a pattern. /myPattern This is particularly useful when editing HTML files with d/< Adjusting the Screen. vi, as a visual screen-oriented editor has a number of useful commands to redraw or adjust the screen in case you find yourself somewhere where you don't want to be. If you run in a Unix shell, it is possible that some background process writes to the same terminal. This will disturb vi's screen layout. In order to force vi to redraw the complete screen, press or . Both commands do the same. If you want to adjust what is currently displayed, then the command is rather useful. It's a kind of Swiss army knife, and has a rather complex syntax: [/"pattern"/]["m"]codice_1["n"](<CR>|.|-) Before we explain the syntax in detail, here are some common applications of the command: Scroll the screen so the current line becomes the middle line of the screen. The cursor remains on that line: Scroll the screen so the current line becomes the top line on the screen: Scroll the screen, so the current line becomes the bottom line of the screen If a codice_2 or a number "m" is given the cursor is moved further after the adjustment. codice_2 indicates to move the cursor to the first match of that pattern. "m" indicates to move the cursor to the "m"th line on the screen. So, for example, codice_4 would first scroll the screen so the current line becomes the top line on the screen, and then move the cursor to the first 'while' in the text from that position on. The number "n" is a rather obscure parameter. If provided, it tells vi to behave as if the screen is just "n" lines high. The result is that only "n" number of lines are adjusted, and the rest of the screen is either ignored or cleared, presumably useful on slow terminals to avoid redrawing the screen unneccessarily.

Russian/Various Stuff. Warning: this stuff probably contains errors. Expressions. every day - каждый день, ежедневно <br> every week - каждую неделю, еженедельно <br> every month - каждый месяц, ежемесячно <br> every year - каждый год, ежегодно<br> compass points N S E W<br> Address notation. The lines are marked with abbreviations: г. (город - city), ул. (улица - street), д. (дом - building) or бл. (блок - blok), кв. (квартира - apartment) or ап. (апартамент - apartment): Борису Иванову <br> 115114 г. Москва <br> ул. Петрова, д. 14, кв. 15 <br> Note the name is in the dative case (because the letter is being sent to this person). Also note that an индекс (6 digits), which is something like an American zip code, should probably be included as well, but I've been told by Russians that the индекс is not vital to the arrival of your parcel. But correct индекс makes arrival more predictible in measure of time. Finally: If sending mail internationally between Russian post and non-Russian post, I recommend including the name of the addressee country in the language of the postal service of origin, as this part of the shipment must of course be handled by domestic post. The rest of the address should be written in the language (and script) of the destination. For example, if sending a letter to the address listed above from the United States, append the line "RUSSIA" to the beginning. Likewise if sending mail home to the U.S. from Russia, append "США" to the head of the address.

Russian/Loanwords. Warning: This might still contain errors. The Base Of The Russian Language. The Russian language is one that developed with the influx of various European and Middle Eastern languages. This is largely due to the geographical location of Russia, historical trade with other countries, and cultural Renaissance started by Russian royalty and other Bourgeoisie. Because of this, the Russian language is one that can be compared to languages such as Greek, Dutch, Italian, French, Arabic, Yiddish, and others that helped to mold it into the language known today. Though the base of the language is Slavic, many alphabetical, grammatical, and vocabulary forms are distinctly foreign. =Dutch= =English= Words that entered English. =German= Words that entered German. =French= =Italian= =Polish= Words that entered Polish. =Greek= As well as words from Greek, many letters of the Russian alphabet come from Greek. =Yiddish= Furthermore, the Russian letters Ш (Sh) and Щ (Sch) are believed to come from the Yiddish/Hebrew letter ש (Sh). =Arabic= =Miscellaneous=

Russian/Alphabet. The Russian alphabet consists of 33 letters, each having upper- and lower-case forms. There are 20 consonants, 10 vowels, 1 so-called semivowel (Й/й), and 2 letters (Ъ/ъ and Ь/ь) that are not themselves pronounced but indicate how other letters should be pronounced. The Russian alphabet descended from the Greek alphabet, so while some of the letters may look like English, their pronunciation might be very different. The pronunciations in the table below are just the most common ones; others are possible, as discussed below. "Key:" "Note:" While Ц and ц are most often pronounced like the ts in tsunami or the zz in pizza, it can also represent the English soft c sound in words borrowed from Latin, such as in (center). See the Wikipedia article for the letter for more information. Basic pronunciation rules. Notes on the Alphabet and Pronunciation of Russian Vowel reduction. The following vowel reductions occur in unstressed syllables in Standard Russian. Note that these mergers are not present in all dialects: See also. Lesson 1 »

Scouting/BSA/First Aid Merit Badge. Note: a Wikipedia book on First Aid is under development. Requirement 1. Satisfy your counselor that you have current knowledge of all first-aid requirements for Tenderfoot, Second Class, and First Class ranks. Requirement 2. At home: Keep emergency numbers posted at the phone along with your address. 911 service is available in most areas. If phones are not working, go to a neighbor that has emergency training. Know where the fire extinguishers are along with the first aid kit. Wilderness: Cell phone, radio, messenger, or evacuate. Signal fires and sounds are a last resort if you cannot evacuate. Be sure to leave a map and schedule at home to trigger an automatic rescue response. Open Water: Powered craft should be equipped with a marine band radio tuned to the emergency channel (#16). Flares and smoke bombs can be carried on any boat but must be used with caution. A distress flag (orange with a black dot and a black square) or signal mirror may be useful over short distances. Requirement 3. Triage: the process of sorting victims, as of a battle or disaster, to determine medical priority in order to increase the number of survivors; the determination of priorities for action in an emergency. During this requirement you also have to do 3b ( which is, "Explain the steps necessary to assess and handle a medical emergency until help arrives.") Requirement 4. Treat all blood as if it were contaminated with blood borne pathogens. Thoroughly wash your hands with soap and water before and after treating a sick or injured person. Never use your bare hands to stop bleeding. Use a protective barrier, preferably nonlatex disposable gloves (a new, unused plastic food storage bag will work in a pinch). Safely discard all soiled bandages, dressings, and other used first aid items by putting them in a double bag until they can be disposed of properly in a receptacle for bio-hazards. Always wash your hands and other exposed skin with soap and warm water or an alcohol-based hand sanitizer immediately after treating a victim, even if protective equipment was used. Requirement 6. Lay the victim down and elevate legs. Call 911. Keep warm, calm and comfortable. Monitor breathing as CPR may be required before help arrives. Transport only if no EMS is available. Under no circumstances should the patient attempt to drive to the hospital. Rescue breathing is used if the victim does not begin breathing when the airway is opened. It also helps warm a severely hypothermic person who is breathing very slowly. Chest compressions should only be used when there are no signs of circulation: coughing, moving, pulse, skin color takes more than 2 seconds to return after finger pressure is removed. Requirement 7. See First Aid/CPR summary Requirement 8. The four steps of severe bleeding are: Requirement 9. Bee stings can cause a fatal reaction called anaphylaxis in people who have a severe allergy to bee venom. It is possible to have the same reaction to foods and medicines (peanuts and shellfish are also common causes of anaphylactic reactions). The effects are nearly immediate -- swelling of the neck and face, sweating, difficulty breathing and hives are among the most common signs. Many people with severe allergies, especially bee stings, carry a device called an "Epi-Pen". An Epi-Pen is a dosage of a powerful hormone, epinephrine, which counteracts an anaphylactic reaction. To use it, remove the safety cap and simply press the needle end firmly against the victim's thigh, about midway between the knee and hip. The spring-loaded needle will automatically extend, delivering the epinephrine into the muscle where it will be rapidly transferred into the bloodstream. The effect of the epi-pen is temporary, however, and the person must still get medical attention quickly. Heatstroke occurs when the core body temperature rises too far for the body's natural defense mechanisms to function. Ordinarily, if the body temperature goes up, sweat is released; the sweat evaporates from the surface of the skin, thus removing heat from the body. In an absence of water or salt, sweating can not occur and heatstroke begins. It is a serious, life-threatening problem that can cause death in minutes. A victim should be cooled down, by removing clothing, placing in the shade or other methods, and should be given water to drink in small sips. Do not give large gulps. This will make it worse. If convulsions occur, do not attempt to restrain the victim. Do not move the victim! Requirement 10. Definition: If more pressure is put on a bone than it can stand, it will split or break. A break of any size is called a fracture. If the broken bone punctures the skin, it is called an open fracture (compound fracture). A stress fracture is a hairline crack in the bone that develops because of repeated or prolonged forces against the bone. Requirement 11. Anybody that has fallen more than standing height, been in a car crash, or hit their head should be suspected of having a back or neck injury. Symptoms may include the person is complaining of any pain in their head, neck, or back, or they have numbness in any of their extremities. However, the person may not be complaining of any pain at all and still have an injury. The problem with these injuries is that any damage to the back and especially the neck can lead to paralysis or even death. A head injury can lead to brain damage, blood loss, or death. The most important thing to remember about spinal injuries is not to move the person unless absolutely necessary. Moving the person can make a bad injury worse. The only times when you should move such a person is if: The best thing that you can do is to tell the person not to move. If needed, hold their head in place. Medical professionals call this "holding C-Spine, " or the inline neutral position. Make sure that the person can breathe and they have a pulse, then wait for help to arrive. If the person is bleeding from the head, try to stop the bleeding. Direct pressure is important here, but do not press too hard as you might further injure the skull. This is the one case where you do not treat for shock! If you notice a clear fluid coming from the ears, nose or mouth, do not stop it. Requirement 12. "Describe the symptoms, proper first-aid procedures, and possible prevention measures for the following conditions" Hypothermia occurs when the core body temperature becomes too cold. Ordinarily, the body begins shivering to regain lost heat. When there is no longer enough energy for this to occur, hypothermia begins and the victim will stop shivering and become confused or unconscious. Warming the victim's body may require extra clothing (or the replacement of wet clothing) or using a fire or body heat. Re-warming should occur over time (rather than suddenly) unless the victim's body temperature also dropped suddenly (i.e. fell into an icy lake). Rapid re-warming of a chronic hypothermia patient can lead to re-warming shock Convulsions are involuntary muscle spasms that can be caused by a variety of diseases and injuries. There is no emergency treatment, but it is important to not hold the victim down or otherwise restrain him, and to give nothing by mouth (contrary to widely-held opinion, the victim will not "choke on his tongue"). These seizures are not uncommon in people afflicted with epilepsy, and these convulsions are generally not dangerous (though a doctor should still be consulted if the seizure lasts longer than 5 minutes). You should also remove all loose furniture that the victim could injure themselves by flailing a body part into it. If the person does not regularly have seizures, medical help should be called for. Try to reassure the person and be sure that they can breathe. Medical professionals will want to know how long the seizure lasted and if the person injured themselves in any way, especially their head, neck, or back. Frostbite occurs when an extremity, often fingers or toes, freezes completely. The skin will first turn blue, then white, and finally black. Get the person to a warm area. Then warm the hand or foot slowly in water, beginning with a room temperature and gradually adding warmer and warmer water. Don't wrap the affected area in anything, this could cause the affected tissue to be killed off. Dehydration occurs when there is insufficient amount of water for the normal functioning of the body. It is a serious and potentially life-threatening condition that can result in lowered blood pressure, dizziness, and fainting, among other things. Treatment is usually by replenishing the body with necessary water and electrolytes. It is most important to give the person water. Beverages like soda are not good but are better than nothing. Eating solid food without water content does not help the condition. Black and blue marks are common bruises. Apply ice onto the bruise to prevent blood flow around the area. Next day apply a warm wet cloth. A Strain is an injury to a muscle or tendon. Apply ice pack to reduce swelling and pain. Wrap firmly with an elastic bandage to limit the swelling and to protect the injury. Stay off the injury. Good physical conditioning and proper warmup before exercise help to prevent strained muscles and tendons. A sprain is caused by twisting, wrenching, or lifting movements that tear or stretch tissues around a joint. Raise the injured part, apply cold compresses, and treat as a fracture or broken bone. Mild burns cause a painful reddening of the skin. A typical first-degree burn is a sunburn. A second-degree burn is a burn that raises blisters. Severe or third-degree burns char layers of skin and flesh. Do not treat burns with jellies, creams, greases, or sprays. First aid for mild burns, apply ice packs or damp, cold cloths, do not break blisters, let dry and cover it with a loose bandage. For serious burns, protect the burn by draping it with a clean, damp cloth. Do not apply ice, because it could cause shock. Treat for shock. If victim is able to drink, give lots of milk or water or other fluids. Seek medical attention, quickly. A stomachache is nothing more than a pain caused by overeating, eating too fast, or eating an odd mixture of strange or unusual foods. Have person lie down. Give an antiacid to help relieve the pain. Don’t give the person anything solid to eat. Gently clean. Place cold compress on face, to minimize swelling. Go to the dentist immediately. Pick up tooth carefully by the crown, not by the roots. If dirty gently rinse with water or victims saliva . place in container of milk or sterilized water and go immediately to the dentist. The dentist will prescribe antibiotics for infection. Muscle cramps are usually caused by lack of water and or electrolytes. Muscle cramps can be minor or painful. The pain might go away in a few minutes. If not, gently massage the cramped muscle you may also try applying ice. Drink plenty of water/fluids/ gatorade to help prevent future cramps. Requirement 13. Do the following: With helpers under your supervision, improvise a stretcher and move a presumably unconscious person. 'With your counselor's approval, arrange a visit with your patrol or troop to an emergency medical facility or through an American Red Cross Chapter for a demonstration of how an AED is used."

Scouting/BSA/Medicine Merit Badge. Key Historical Figures in Medicine. Discuss with your counselor the influence that EIGHT of the following people had on the history of medicine: of Cos (c. 460 BC - 377 BC) was an Ancient Greek physician, is commonly regarded as one of the most outstanding figures in medicine of all time and has been called "the father of medicine". (April 1, 1578 - June 3, 1657) was a doctor who first correctly described in exact detail the circulatory system of blood being pumped around the body by the heart. (October 24, 1632 - August 26, 1723) was a tradesman and scientist from Delft, in the Netherlands. He is best known for his contribution to improvement of the microscope and his contributions towards the establishment of cell biology. Using his handcrafted microscope he was the first to observe and describe muscles fibres, bacteria, spermatozoa and blood flow in capillaries (small blood vessels). (May 17, 1749 - January 26, 1823) was an English country doctor practicing in Berkeley, Gloucestershire, England, made famous by his invention of the vaccine. (May 12, 1820 - August 13, 1910) - The Lady With The Lamp - was the pioneer of modern nursing. (December 27, 1822 - September 28, 1895) was a French scientist who was a pioneer in microbiology. was born on July 22, 1822, in Heinzendorf, Austria (now Hyncice, Czech Republic). He studied the inheritance of traits in pea plants, discovering the basic laws of inheritance. He is often called the father of genetics. , 1st Baron Lister (April 5, 1827-February 10, 1912) was a famous British surgeon who promoted the idea of sterile surgery while working at the Glasgow Infirmary. He came from a rich Quaker home in Yorkshire. (December 11, 1843 - May 27, 1910) was a German physician. He became famous for the discovery of the tubercle bacillus (1882) and the cholera bacillus (1883) and for his development of Koch's postulates. He was awarded the Nobel Prize in Physiology or Medicine in 1905. He is considered one of the founders of bacteriology. (March 27, 1845 - February 10, 1923) was a German physicist, of the University of Würzburg, who, on November 8, 1895, produced wavelengths of electromagnetic radiation that are now known as x-rays. The machine which Röntgen built to emit these rays, was the x-ray machine. (November 7, 1867 – July 4, 1934) and (May 15, 1859 – died April 19, 1906) were pioneers in the early field of radiation. Both were Nobel Laureates in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena. (September 13, 1851 - November 23, 1902) was an American Army surgeon who led a team which discovered that yellow fever is transmitted by mosquitos rather than direct contact. This insight opened entire new fields of epidemiology and biomedicine and most immediately allowed the resumption and completion of work on the Panama Canal (1904-14) by the United States. (June 14, 1868 - June 26, 1943), was an Austrian biologist. In 1909 he developed the modern system of classification of blood groups and later identified agglutins and Rhesus factor for which he won the 1930 Nobel Prize in Physiology and Medicine. (August 6, 1881 - March 11, 1955) a Scottish biologist and pharmacologist. Fleming published many articles on bacteriology, immunology, and chemotherapy. His best-known achievements are the discovery of the enzyme lysozyme in 1922 and isolation of the antibiotic substance penicillin from the fungus Penicillium notatum in 1928, for which he shared the Nobel Prize in Physiology or Medicine in 1945 (October 28, 1914 - June 23, 1995) is the discoverer/inventor of the vaccine for Polio which proved to be the first successful vaccine against a virus. The vaccine provides the recipient with immunity against Polio, and was seminal in the near eradication of a once widely-feared disease. and are American molecular biologist who are best known as the co-discoverers of the structure of DNA. This earned them the 1962 Nobel Prize in Physiology and Medicine and a correct understanding of how "the molecular structure of nucleic acids transfer information in living material".[1] Hippocratic Oath. Explain the Hippocratic Oath to your counselor, and compare the original version to a more modern one. Discuss to whom those subscribing to the original version of the oath owe the greatest allegiance. Patient-Physician Relationship. Discuss the health care "provider-patient" relationship with your counselor, and the importance of such a relationship in the delivery of quality care to the patient. Describe the role of confidentiality in this relationship. Generalist and Specialists with Medicine. Primary Care. Tell what is meant by the term "primary care" within medicine. Briefly describe the types of work done by the physicians in the following "core" areas. Describe the educational requirements for these areas of medicine Specialty Care. Tell what is meant by the term "specialty care" within medicine. Briefly describe the types of work done by the FIVE of the specialty areas of medicine shown below. Describe the additional educational requirements for these specialty areas of medicine. Office Visit. Visit a physician's office, preferably one who delivers "primary care" (This may be that of your counselor) and do the following: Diagnostic Testing. Describe the characteristics of a good diagnostic test to screen for disease (e.g. routine blood pressure measurement). Explain briefly why diagnostic tests are not perfect. Each diagnostic tests has different properties or abilities to accurately determine results. A good diagnostic test would be one in which the test is highly reliable for accurately diagnosing the condition of interest, would be inexpensive to administer, and would provide results quickly. In addition to how the test itself performs, one must ask if the result from test can be used to guide subsequent decisions on starting, stopping, or modifying treatment. Consequently, the practical value of a diagnostic test can only be assessed by taking into account subsequent health outcomes. In determining the value of various diagnostic tests, it is important to distinguish between these two features of the test (accuracy of the test itself) and (ability of the test to guide therapeutic decision making in altering health outcomes). In terms of accuracy, diagnostic tests are judged by several characteristics, including: Example, using pregnancy test results: Taking a Blood Pressure Reading. Show how to take a blood pressure reading and a pulse reading. Global Health Care Delivery. Compare and discuss with your counselor the health care delivery systems in the United States, Sweden, and China. Health Care Volunteer. Serve as a volunteer at a health-related event or facility in your community (e.g. blood drive, "health fair", blood pressure screening, etc.) approved by your counselor.

Scouting/BSA/Citizenship in the World Merit Badge. Requirement 1. This is also a subjective question that requires the individual scout put in his opinions. An example for this part is, "I believe a good world citizen is one who contributes effort to strive for the good of his/her fellow citizens." Requirement 2. One can become an American citizen in various ways. The 2005 BSA "Citizenship in the World" handbook points these out: 1) "By blood if born to parents who are already citizens of [The United States]" "By soil if born within the legal borders of a nation" -"Through naturalization" (in which the person must meet certain requirements which can be found here) -"Through naturalization of parents" American citizens have a number of rights, such as freedom of speech, the right to bear arms, due process, religion, against quartering soldiers, and against double jeopardy (most of these rights also apply to non-citizens) and are also taxed in order to provide money for essential services. Other duties of American citizens might include obeying laws and voting. Obligations are those elements of citizenship which are required under the law, for example, the obligation to obey the law. A U.S. citizens' rights, duties, and obligations are briefly explained in subsection 2B. Here are examples of how they are similar from those of Chinese and Irish citizens' rights, duties, and obligations in the following manner: -Both Chinese citizens and U.S. citizens have the obligation to receive education. -Both Chinese citizens and U.S. citizens have the duty to get a Visa to travel to other countries. -Both Irish citizens and U.S. citizens have the right to vote. -Both Irish citizens and U.S. citizens have the duty to serve on a jury when called upon. Requirement 3. "Do the following:" After World War 1, Germany's economy was hard struck by the effects of the Treaty of Versailles, leading to a national sense of bitterness towards countries like France and the United Kingdom, which help set the stage for World War 2, when Germany invaded many of its neighbors. After World War 2, Japan adopted a constitution that does not allow the creation of a military force, hampering the country's ability to help in military operations with the United Nations and allies like the United States. In the run-up to the 2003 occupation of Iraq, many American commentators expressed bitterness over France's refusal to support the invasion. Many perceived a lack of gratitude for American aid during World War 2, while France's defenders pointed out that country's aid during the American War for Independence. Culture includes a society's language, religion, lifestyle, clothing, decor and many other aspects. Cultural splits within countries sometimes lead to strife because different parts of the country have different interests. The American Civil War is an example of a country torn apart by the opposing interests of culturally distinct regions. More recently, religious animosity has led to violence and chaos in many Middle-Eastern countries, especially Israel. The creation of Israel was prompted by fears of anti-Semitism leading to a repeat of the attempted genocide of the Jews during the Holocaust, and Israel's foreign relations have long been affected by fears of anti-Semitism harming Jews abroad. Conflicts over religion, geography, ethnicity and other issues have spread in different countries has caused strife and war. For example, the Kurds live in several countries, including Iraq and Turkey, the latter a key US ally in the region. With Kurdish leaders calling for an independent Kurdistan, the US was torn between supporting its Kurdish allies and the Turkish government, which believed that any independence for Iraqi Kurds could spur a revival of similar hopes among Turkish Kurds. Nationalism plays an important role in this phenomenon, which has also included calls for a Greater Somalia, a view that has twice led to war with Ethiopia over the Somali Ogaden region, and Greater Serbia|, a motivation for the Kosovo War. Demographics are the make-up of a country. Some countries have a very young population, such as Zambia, while others have a large elderly population, such as Sweden. Some countries are made up nearly entirely of one ethnic group speaking a single language, such as Iceland, while others are a melting pot of dozens or hundreds of ethnic groups, such as many of the equatorial African countries like the Republic of the Congo. Demographic conflict has long been a source of strife on the diverse continent of Africa. In South Africa, for example, a white minority long controlled a huge black majority (Apartheid), eventually straining relations with countries like the United States, which imposed an embargo as a result. Ethnically diverse states such as most of the Sub-Saharan African countries were created from European colonies in the region, which had no basis in rational geographic or cultural boundaries. As a result, many of the earliest leaders in these countries pursued as a high priority the formation of a national identity; this occurred in nations across Africa, including Zambia and Sudan. In the rush to create a distinctive culture, minorities and dissenters were often marginalized or oppressed, leading to revolutions and civil strife. Politics can occur within a single country or among countries. Activities involving the internal political landscape of a country can have an affect on national interests and foreign relations through the election or installment of leaders who enact foreign policy, while laws passed by a particular country may have an affect on the economy of a different country. Internal conflicts between political blocs of capitalists and socialists led to a polarization of international relations. Countries like the United States, France and Italy jockeyed for power with the Soviet Union and satellites in newly-independent countries across Africa, South America and Asia (see The Cold War). Following the internationally divisive US-led occupation of Iraq in 2003, foreign countries around the world were forced to pay close attention to the American political landscape. Some, like Israel, were supportive of the conservative right, while others, like France, supported the liberal left. The national interests of a country are often very complex, and hinge on multiple factors involving geography, natural resources and climate, as well as social values, security issues and concerns regarding foreign countries. Geography can affect a country's national resources through several ways. A country's shape can dictate its national interest. Nearly all countries have some kind of natural resources. It is always in the best interest of the producers of a product (for example oil) to keep prices and demand high. Because all countries need food and water, climate is extremely important. Without adequate rain, for example, agriculture can not occur and food will have to be imported and this can make a country's economy fall. Weather can also have debilitating effects on trade, both within and outside the boundaries of country. Below are two links to additional information. They will provide informative graphs that had answered the previous question 4, which is worded exactly as the current question 3b. Graphed Countries 1: Saudi Arabia Graphed Countries 2: United States, Tuvalu, Botswana, and Bolivia Requirement 4. "Do TWO of the following:" A state is ordinarily said to be sovereign - i.e. capable of enforcing its own laws on its own territory, and only on its own territory (for example, American laws do not apply in France, even if the people involved are all American). International law is a relatively recent invention, and concerns agreements between countries in pacts called treaties. International law can enforce standards (such as standardized weights and measures for the purposes of trade) and proscribe conduct according to treaties concerning human rights. With international organizations enforcing these treaties, often ineffectively, but also often with great success, countries whose governments ignore human rights treaties can be dealt with by multi-national alliances, which are perceived as having more legitimacy if a broken human rights treaty can be blamed. shaping the research agenda and stimulating the generation, translation and dissemination of valuable knowledge; setting norms and standards and promoting and monitoring their implementation; articulating ethical and evidence-based policy options; providing technical support, catalysing change, and building sustainable institutional capacity; and monitoring the health situation and assessing health trends. Requirement 5. "Do the following:" Constitutional governments have a written document stating their laws, rights and responsibilities. It must also be limited in power, follow a higher law, and have constitutional stability. Nonconstitutional governments are dictatorships and absolute monarchies. These are hard on the citizens because they don't have many rights. Totalitarian and authoritarian are the two types of nonconstitutional governments. In an authoritarian government, the power to make decisions is in the hands of one person or a small group. Totalitarian government is another form of authoritarian in which the government controls every aspect of society. United States- Federal republic, Representative democracy(democratic republic), Canada- Federal parliamentary democracy and constitutional monarchy, Spain- Parliamentary monarchy, Poland- Republic, Libya- People's Congress, North Korea- Single-party state, Brazil- Democratic federal republic, Niger- Parliamentary democracy. Requirement 6. "Do the Following": A government is represented abroad by an ambassador or a consul. The United States government is accredited to international organizations based on the requirements of each individual organization. For example, here are the requirements for the United Nations Ambassador: a diplomatic official of the highest rank, sent by one sovereign or state to another as its resident representative (ambassador extraordinary and plenipotentiary), usually for a specific length of time. He or she is a diplomatic official heading his or her country's permanent mission to certain international organizations; such as the United Nations; and is an authorized representative of a nation to deliver their nation's messages and protect the national interest of the nation they represent through diplomatic means. Consul: an official appointed by the government of one country to look after its commercial interests and the welfare of its citizens in another country, as well as providing assistance to Americans traveling abroad. Bureau of International Information Programs: The Bureau of International Information Programs (IIP) is the principal international strategic communications service for the foreign affairs community. IIP designs, develops, and implements a variety of information initiatives and strategic communications programs, including Internet and print publications, traveling and electronically transmitted speaker programs, and information resource services. These reach--and are created strictly for--key international audiences, such as the media, government officials, opinion leaders, and the general public in more than 140 countries around the world. U.S Agency for International Development: The United States Agency for International Development (USAID) is the United States federal government agency primarily responsible for administering civilian foreign aid. President John F. Kennedy created USAID in 1961 by executive order to implement development assistance programs in the areas authorized by the Congress in the Foreign Assistance Act of 1961. An independent federal agency, USAID receives overall foreign policy guidance from the United States Secretary of State and seeks to "extend a helping hand to those people overseas struggling to make a better life, recover from a disaster or striving to live in a free and democratic country. United States and Foreign Commercial Service: The U.S. Commercial Service (CS), the trade promotion arm of the U.S. Department of Commerce's International Trade Administration, helps U.S. companies succeed in markets around the world. Led by Assistant Secretary of Commerce and Director General Suresh Kumar and located across the United States and in U.S. Embassies and Consulates in nearly 80 countries, the CS global network of trade professionals helps thousands of U.S. companies to export goods and services worth billions of dollars every year. A passport is an official document issued to a citizen by a government affirming the individual’s nationality. The passport permits the citizen to travel or live abroad and entitles the citizen to privileges guaranteed by international custom and treaties: safe passage, lawful aid, and protection while under the foreign government’s jurisdiction. A visa is a permit to enter another country and must be issued by the country one wishes to enter. It is a special seal stamped on a valid passport that indicates an official of that country has approved the visit. Prior to leaving, the traveler should apply for a visa-if required by that particular country-at the appropriate foreign embassy or nearest consulate. A foreign national wishing to enter the United States must apply for a visa outside the United States at embassies and consulates worldwide. An immigrant visa permits a person to stay in the United States permanently. A non-immigrant visa allows a foreign national to enter the country for a temporary stay. Tourists, temporary workers, missionaries, business professionals, artists, and athletes travel on temporary visas. Requirement 7. "Do two of the following (with your parent's permission) and share with your counselor what you have learned:" Web Site: http://www.state.gov/ Issues Vary. Example Websites (news organizations): Al Jazeera Author's Note. Writing this article has been a pleasurable learning experience for me and I am happy to have been able to give back to the scouting community. I hope that my efforts serve as a reminder to the reader that it is important to both give and take information in order to be a good world citizen.

Russian/Numbers. 206202211633901 Use of numerals in context. In English (and in many other Indo-European languages) the items being counted by a numeral are found following the numeral, and in the plural form. In Russian, the syntax is somewhat more complex. The case of the item must first be considered. If the item needs to be in the nominative or inanimate accusative case, use the following rule. The numeral один (1) should be used in the proper form to indicate gender (and, number, believe it or not). For example: один мальчик (one boy), одна девушка (one girl), одно животное (one animal), одни джинсы (one [pair of] jeans). The plural form of the numeral (1) is a bit of an oddity, but its use will become clear with time. Following a form of один should come the item at hand in the nominative or inanimate accusative case, as appropriate. The numerals два (or две), три, and четыре all require the following item to be presented in the genitive singular form. The numeral два has two forms: два for masculine and neuter items and две for feminine items. After the numeral два, each numeral has only a single form. See for example: две девушки (two girls), три кошки (three cats), четыре мальчика (four boys). The numerals пять (5) through двадцать (20) require their attached items in the genitive plural forms, as in these examples: пять девушек (five girls), десять копеек (ten kopeks), шестнадцать рублей (sixteen rubles). Numerals larger than twenty follow the above rules using the last digit. Think of numerals ending in zero as ending in ten. For example: тридцать три рюмки (thirty-three shot glasses), сорок один год (forty-one years), шестьдесят девять слов (sixty-nine words). Numerals larger than 99 follow the above rules using the last two digits. For example: двести три собаки (two hundred and three dogs), двести тринадцать собак (two hundred and thirteen dogs). When the items at hand belong not in the nominative or inanimate accusative case, the numerals themselves must be declined in addition to the declension of the items following them. This topic shall be discussed here later. For now, be glad that these forms are relatively uncommon. Examples follow: Я видел двух друзей (I saw two friends), Ты не съела ни одной штуки (You didn't eat a single piece). In short, for nominative (and inanimate accusative) items, use the following rule to select the proper form of the item: 1 -> nominative 2, 3, 4 -> genitive singular 5 and more -> genitive plural Ordinal numbers. Ordinal numerals in Russian are relatively easy to deal with. They all decline like adjectives. For example: Только что фотографировала восемнадцатую девушку (She just photographed the eighteenth girl). 30th тридцатый <br> 40th сороковой <br> 100th сотый <br> 1000th тысячный<br> 10000th десятитысячный<br> 1000000th миллионный<br>

Vietnamese/Vietnamization. Yes, has to do with the Vietnam War, but that's not what it means in this case. With the dawn of television, computers, and the Internet, the use of words that originated with English has increased greatly. This has both increased the importance of English and diminished the importance of other languages. For other languages to keep up, their speakers have to come up with practical translations or transliterations. For Vietnamese, these translations and transliterations are called Vietnamizations. We'll take a look at:

Statistics. Welcome to the Wikibook of Statistics Statistics - Area of applied mathematics concerned with the data collection, analysis, interpretation and presentation. Statistics is used in almost every field of research: the discovery of the Higgs particle, social sciences, climate research... With this, and with its well established foundations, it is very well suited for a wikibook. This book is an ongoing effort to make this basic knowledge available for free. Since the concepts in probability are essential for statistics, a thorough knowledge of probability is needed before reading this book (especially for the advanced part), and so probability is a prerequisite of this book. Although some concepts in the probability are reviewed, the review is meant to be read by someone who is familiar with those concepts already, and so it is not too detailed. For a more detailed discussion on those concepts, you may refer to the wikibook Probability. This book is divided into two main parts: Basics and Advanced. The Basics part gives a brief introduction and idea about statistics, while the Advanced part gives a more formal and mathematical treatment on statistics. =Contents= Basics Advanced Examples Appendix

Macroeconomics/Multiplier Process. =! (k)= Derivation. Assume the MPC of a hypothetical economy is 0.5. If a person spends $1 on a widget, then the person who sells it receives $1 of income, of which a portion is spent (MPC), this person then uses their $0.5 to purchase another good "ad infinitum". Expressing this mathematically:

Macroeconomics/Expanded Multipliers. =Expanded Multipliers=

Waves/Waves in two and three Dimensions. Waves in Two and Three Dimensions. In this chapter we extend the ideas of the previous chapter to the case of waves in more than one dimension. The extension of the sine wave to higher dimensions is the "plane wave". Wave packets in two and three dimensions arise when plane waves moving in different directions are superimposed. "Diffraction" results from the disruption of a wave which is impingent upon an object. Those parts of the wave front hitting the object are scattered, modified, or destroyed. The resulting "diffraction pattern" comes from the subsequent interference of the various pieces of the modified wave. A knowledge of diffraction is necessary to understand the behavior and limitations of optical instruments such as telescopes. Diffraction and interference in two and three dimensions can be manipulated to produces useful devices such as the "diffraction grating".

Arabic/Arabic alphabet (by group). Recognising Characters. Written has 4 forms for each letter. This might appear much at first, but it's not as hard as you might think. For starters, Arabic does not have any capital letters, so this drops us from 4:1 ratio with the Roman alphabet to a meager 2:1 ratio. Secondly, Arabic does not have a separate cursive and manuscript versions of the letters; since what you're learning already "is" cursive, one could conceivably argue that we're dropping from a 2:1 to a 1:1 ratio. There's better news still. A lot of these letters are really just derivations of other letters, and many of the ones that aren't derivations behave in a similar enough fashion to be learned together. This page is aimed at exploiting these similarities to help you learn how to read and write Arabic letters. At a glance. Here are the letter-groups at a glance. We mentioned earlier that there are 4 forms for each character: isolated, initial, medial and final. In this table, we only show the isolated form of each character. But we also break the letters into groups that have similar shapes. Notice how some letters are derived from other letters by adding dots above or below some base form. You might be wondering why it is claimed that certain letters are similar to each other. (FIXME: for example). This is because the table is organised by similarity the medial form of each letter, that is the shape the letter takes when it is in the middle of a word. Let's proceed to the next set of tables, where you shall learn about these forms in greater detail. "Disclaimer: the organisation of letters into groups is based strictly on the authors' personal opinions. If an authority on the Arabic language tells you that things are otherwise, you should believe them and not us" Arabic letters in detail. Now, we will look at each of the letter classes in detail. Every row in this table represents a separate letter. There are 8 constant letters, 6 isolated ones, 5 curve-pointy ones, 5 hook ones, and 4 other ones. You'll note also that we group the rows by number of dots; this is to show you the similarities between letters that differ only by the dots that they use. Even though ba ( ب ) and tha ( ث ) are completely different letters, they pretty much act the same way. Constant. The constant forms behave roughly the same way no matter what position they are in. Note: technically fa and qa are not related to each other, but for us, being beginners, we'll pretend that they are for now. Isolated. The isolated characters do not connect to the next letter in the medial form. Consider alef and lam... written in the middle of words, they would look almost the same, but because alef does not connect to the next character (ـاـ) but lam does (ـلـ), you can tell them apart. Curve-pointy. The curve-pointy letters have a single curve in isolated or initial form, but when they are in the middle of a word, they form a simple point up. Hook. The hook letters have a downward hook in their final form and an upward hook in their medial form. Other. Finally, there are four letters which have their own idiosyncratic behaviours. Special letters. Tâ marbûta. One letter which you will encounter rather frequently is the tâ marbûta (ة, not to be confused with ه). This letter always occurs in final position and has two forms: Ligatures. Sometimes two letters combine (and form a ligature) to be written in a prettier or more convenient manner. When lam ( ل ) is followed by alif ( ا ), it generally forms the lam-alif ligature ( لا ):

Waves/Plane Waves. Plane Waves. A plane wave in two or three dimensions is like a sine wave in one dimension except that crests and troughs aren't points, but form lines (2-D) or planes (3-D) perpendicular to the direction of wave propagation. Figure 2.5 shows a plane sine wave in two dimensions. The large arrow is a vector called the wave vector, which defines (1) the direction of wave propagation by its orientation perpendicular to the wave fronts, and (2) the wavenumber by its length. We can think of a wave front as a line along the crest of the wave. The equation for the displacement associated with a plane sine wave in three dimensions at some instant in time is <br> Figure 2.5: Definition sketch for a plane sine wave in two dimensions. The wave fronts are constant phase surfaces separated by one wavelength. The wave vector is normal to the wave fronts and its length is the wavenumber. Since wave fronts are lines or surfaces of constant phase, the equation defining a wave front is simply formula_2. In the two dimensional case we simply set formula_3. Therefore, a wavefront, or line of constant phase formula_4 in two dimensions is defined by the equation This can be easily solved for formula_6 to obtain the slope and intercept of the wavefront in two dimensions. As for one dimensional waves, the time evolution of the wave is obtained by adding a term formula_7 to the phase of the wave. In three dimensions the wave displacement as a function of both space and time is given by The frequency depends in general on all three components of the wave vector. The form of this function, formula_9, which as in the one dimensional case is called the "dispersion relation", contains information about the physical behavior of the wave. Some examples of dispersion relations for waves in two dimensions are as follows: <br> Figure 2.6: Contour plots of the dispersion relations for three kinds of waves in two dimensions. In the upper panels the curves show lines or contours along which the frequency formula_17 takes on constant values. For light and ocean waves the frequency depends only on the magnitude of the wave vector, whereas for gravity waves it depends only on the wave vector's direction, as defined by the angle formula_18 in the upper right panel. These dependences for each wave type are illustrated in the lower panels. Contour plots of these dispersion relations are plotted in the upper panels of figure 2.6. These plots are to be interpreted like topographic maps, where the lines represent contours of constant elevation. In the case of figure 2.6, constant values of frequency are represented instead. For simplicity, the actual values of frequency are not labeled on the contour plots, but are represented in the graphs in the lower panels. This is possible because frequency depends only on wave vector magnitude formula_19 for the first two examples, and only on wave vector direction formula_18 for the third.

Waves/Plane Superposition. Superposition of Plane Waves. We now study of wave packets in two dimensions by asking what the superposition of two plane sine waves looks like. If the two waves have different wavenumbers, but their wave vectors point in the same direction, the results are identical to those presented in the previous chapter, except that the wave packets are indefinitely elongated without change in form in the direction perpendicular to the wave vector. The wave packets produced in this case march along in the direction of the wave vectors and thus appear to a stationary observer like a series of passing "pulses" with broad lateral extent. Superimposing two plane waves which have the same frequency results in a stationary wave packet through which the individual wave fronts pass. This wave packet is also elongated indefinitely in some direction, but the direction of elongation depends on the dispersion relation for the waves being considered. One can think of such wave packets as steady "beams", which guide the individual phase waves in some direction, but don't themselves change with time. By superimposing multiple plane waves, all with the same frequency, one can actually produce a single stationary beam, just as one can produce an isolated pulse by superimposing multiple waves with wave vectors pointing in the same direction. Two Waves of Identical Wavelength. If the frequency of a wave depends on the magnitude of the wave vector, but not on its direction, the wave's dispersion relation is called isotropic. In the isotropic case two waves have the same frequency only if the lengths of their wave vectors, and hence their wavelengths, are the same. The first two examples in figure 2.6 satisfy this condition. In this section we investigate the beams produced by superimposed isotropic waves. We superimpose two plane waves with wave vectors formula_1 and formula_2. The lengths of the wave vectors in both cases are formula_3: If formula_5, then both waves are moving approximately in the formula_6 direction. An example of such waves would be two light waves with the same frequencies moving in slightly different directions. <br> Figure 2.7: Wave fronts and wave vectors of two plane waves with the same wavelength but oriented in different directions. The vertical bands show regions of constructive interference where wave fronts coincide. The vertical regions in between the bars have destructive interference, and hence define the lateral boundaries of the beams produced by the superposition. The components formula_7 and formula_8 of one of the wave vectors are shown. Applying the trigonometric identity for the sine of the sum of two angles (as we have done previously), equation (3.15) can be reduced to This is in the form of a sine wave moving in the formula_6 direction with phase speed formula_11 and wavenumber formula_8, modulated in the formula_13 direction by a cosine function. The distance formula_14 between regions of destructive interference in the formula_13 direction tells us the width of the resulting beams, and is given by formula_16, so that Thus, the smaller formula_7, the greater is the beam diameter. This behavior is illustrated in figure 2.7. <br> Figure 2.8: Example of beams produced by two plane waves with the same wavelength moving in different directions. The wave vectors of the two waves are formula_19. Regions of positive displacement are illustrated by vertical hatching, while negative displacement has horizontal hatching. Figure 2.8 shows an example of the beams produced by superposition of two plane waves of equal wavelength oriented as in figure 2.7. It is easy to show that the transverse width of the resulting wave packet satisfies equation (2.17). Two Waves of Differing Wavelength. In the third example of figure 2.6, the frequency of the wave depends only on the direction of the wave vector, independent of its magnitude, which is just the reverse of the case for an isotropic dispersion relation. In this case different plane waves with the same frequency have wave vectors which point in the same direction, but have different lengths. More generally, one might have waves for which the frequency depends on "both" the direction and magnitude of the wave vector. In this case, two different plane waves with the same frequency would typically have wave vectors which differed both in direction and magnitude. Mathematically, we can represent the superposition of these two waves as a generalization of equation (2.15): In this equation we have given the first wave vector a formula_6 component formula_22 while the second wave vector has formula_23. As a result, the first wave has overall wavenumber formula_24 while the second has formula_25, so that formula_26. Using the usual trigonometric identity, we write equation (2.18) as To see what this equation implies, notice that constructive interference between the two waves occurs when formula_28, where formula_29 is an integer. Solving this equation for formula_6 yields formula_31, which corresponds to lines with slope formula_32. These lines turn out to be perpendicular to the vector difference between the two wave vectors, formula_33. The easiest way to show this is to note that this difference vector is oriented so that it has a slope formula_34. Comparison with the formula_32 slope of the lines of constructive interference indicates that this is so. <br> Figure 2.10: Example of beams produced by two plane waves with wave vectors differing in both direction and magnitude. The wave vectors of the two waves are formula_36 and formula_37. Regions of positive displacement are illustrated by vertical hatching, while negative displacement has horizontal hatching. An example of the production of beams by the superposition of two waves with different directions and wavelengths is shown in figure 2.10. Notice that the wavefronts are still horizontal, as in figure 2.8, but that the beams are not vertical, but slant to the right. <br> Figure 2.11: Illustration of factors entering the addition of two plane waves with the same frequency. The wave fronts are perpendicular to the vector average of the two wave vectors, formula_38, while the lines of constructive interference, which define the beam orientation, are oriented perpendicular to the difference between these two vectors, formula_39. Figure 2.11 summarizes what we have learned about adding plane waves with the same frequency. In general, the beam orientation and the lines of constructive interference are not perpendicular to the wave fronts. This only occurs when the wave frequency is independent of wave vector direction. Many Waves with the Same Wavelength. As with wave packets in one dimension, we can add together more than two waves to produce an isolated wave packet. We will confine our attention here to the case of an isotropic dispersion relation in which all the wave vectors for a given frequency are of the same length. Figure 2.12 shows an example of this in which wave vectors of the same wavelength but different directions are added together. Defining formula_40 as the angle of the formula_41th wave vector clockwise from the vertical, as illustrated in figure 2.12, we could write the superposition of these waves at time formula_42 as formula_43 where we have assumed that formula_45 and formula_46. The parameter formula_47 is the magnitude of the wave vector and is the same for all the waves. Let us also assume in this example that the amplitude of each wave component decreases with increasing formula_48: The exponential function decreases rapidly as its argument becomes more negative, and for practical purposes, only wave vectors with formula_50 contribute significantly to the sum. We call formula_51 the "spreading angle". <br> Figure 2.13: Plot of the displacement field formula_52 from equation (2.20) for formula_53 and formula_54. Figure 2.13 shows what formula_52 looks like when formula_56 and formula_54. Notice that for formula_58 the wave amplitude is only large for a small region in the range formula_59. However, for formula_60 the wave spreads into a broad semicircular pattern. <br> Figure 2.14: Plot of the displacement field formula_52 from equation (2.20) for formula_62 and formula_54. Figure 2.14 shows the computed pattern of formula_52 when the spreading angle formula_65. The wave amplitude is large for a much broader range of formula_13 at formula_58 in this case, roughly formula_68. On the other hand, the subsequent spread of the wave is much smaller than in the case of figure 2.13. We conclude that a superposition of plane waves with wave vectors spread narrowly about a central wave vector which points in the formula_6 direction (as in figure 2.14) produces a beam which is initially broad in formula_13 but for which the breadth increases only slightly with increasing formula_6. However, a superposition of plane waves with wave vectors spread more broadly (as in figure 2.13) produces a beam which is initially narrow in formula_13 but which rapidly increases in width as formula_6 increases. The relationship between the spreading angle formula_51 and the initial breadth of the beam is made more understandable by comparison with the results for the two-wave superposition discussed at the beginning of this section. As indicated by equation (2.17), large values of formula_75, and hence formula_76, are associated with small wave packet dimensions in the formula_13 direction and vice versa. The superposition of two waves doesn't capture the subsequent spread of the beam which occurs when many waves are superimposed, but it does lead to a rough quantitative relationship between formula_51 (which is just formula_79 in the two wave case) and the initial breadth of the beam. If we invoke the small angle approximation for formula_80 so that formula_81, then formula_82 and equation (2.17) can be written formula_83. Thus, we can find the approximate spreading angle from the wavelength of the wave formula_84 and the initial breadth of the beam formula_14:

Waves/Single slit Diffraction. Diffraction Through a Single Slit. <br> Figure 2.15: Schematic behavior when a plane wave impinges on a narrow slit and a broad slit. How does all of this apply to the passage of waves through a slit? Imagine a plane wave of wavelength formula_1 impingent on a barrier with a slit or opening of width formula_2. The barrier transforms the plane wave with infinite extent in the lateral direction into a beam with initial transverse dimensions equal to the width of the slit. The subsequent development of the beam is illustrated in figures 2.13 and 2.14, and schematically in figure 2.15. In particular, if the slit width is comparable to the wavelength, the beam spreads broadly as in figure 2.13. If the slit width is large compared to the wavelength, the beam doesn't spread as much, as figure 2.14 illustrates. Equation (2.22) gives us an approximate quantitative result for the spreading angle if formula_2 is interpreted as the width of the slit. One use of the above equation is in determining the maximum angular resolution of optical instruments such as telescopes. The primary lens or mirror can be thought of as a rather large “slit”. Light from a distant point source is essentially in the form of a plane wave when it arrives at the telescope. However, the light passed by the telescope is no longer a plane wave, but is a beam with a tendency to spread. The spreading angle formula_4 is given by equation (2.22), and the telescope cannot resolve objects with an angular separation less than formula_4. Replacing formula_2 with the diameter of the lens or mirror in equation (2.22) thus yields the telescope's angular resolution. For instance, a moderate sized telescope with aperture formula_7 observing red light with formula_8 has a maximum angular resolution of about formula_9.

Waves/Double slit Diffraction. Two Slits. Narrow Slits. Let us now imagine a plane sine wave normally impingent on a screen with two narrow slits spaced by a distance "d", as shown in Figure 2.16. Since the slits are narrow relative to the wavelength of the wave impingent on them, the spreading angle of the beams is large and the diffraction pattern from each slit individually is a cylindrical wave spreading out in all directions, as illustrated in figure 2.13. The cylindrical waves from the two slits interfere, resulting in oscillations in wave intensity at the screen on the right side of figure 2.16. Constructive interference occurs when the difference in the path lengths of the two rays is an integer multiple of the wavelength, "λ": Similarly, destructive interference occurs at: If the distance from the slits to the screen, "L" is much greater than the slit separation, "d", the rays "l"1 and "l"2 are approximately parallel and we can say that the path length difference is: Substituting these two equations gives the following condition for constructive interference: The integer "m" is called the "interference order" and is the number of wavelengths by which the two paths differ. At every angle corresponding to integer "m", constructive interference will be greatest and a "fringe" will be formed. The distance from a point on the screen to the centre line, "s", is related to "θ" as follows: When "θ" is small, we can say that: We can therefore equate the expressions for position on the screen and fringe angles: Rearranging gives an expression for the fringe spacing: The following conditions have to hold for this to be a good approximation: Example. Let us consider a setup with the following parameters: We expect to see a fringe spacing at 10m of: First, let's look at a "snapshot" of the wave at a certain instance in time. The amplitude at a point, ("x","y"), is given by: where "k" is the wavenumber, given by 2"π"/"λ". In this exercise, we will neglect the decreasing amplitude with distance, so the fringes stay bright over all space. The plot below shows a plot of this function. You can clearly see the circular propagation of each source, but an overall fringe structure is difficult to make out. Now, the human eye and all light-measuring equipment do not detect the individual oscillations of a light wave, they measure intensity. Here, intensity is a function of the phase difference between the two sources, which in turn is directly related to the path length difference. The plot below shows this intensity function. We see that a very clear fringe structure is revealed: At this scale, the fringe structure is not clearly radial, it "bends" around the source. However, we can see that if we were to zoom out, the frenges diverge, and the ones near the centre, which are closest to perfectly radial, will be the ones that matter: In this plot, we see the predicted bright fringes at x=0mm, x=±250mm and x=±500mm.

Waves/Diffraction Grating. Diffraction Gratings. Since the angular spacing formula_1 of interference peaks in the two slit case depends on the wavelength of the incident wave, the two slit system can be used as a crude device to distinguish between the wavelengths of different components of a non-sinusoidal wave impingent on the slits. However, if more slits are added, maintaining a uniform spacing formula_2 between slits, we obtain a more sophisticated device for distinguishing beam components. This is called a "diffraction grating". Figures 2.17-2.19 show the amplitude and intensity of the diffraction pattern for gratings with 2, 4, and 16 slits respectively. Notice how the interference peaks remain in the same place but increase in sharpness as the number of slits increases. The width of the peaks is actually related to the overall width of the grating, formula_3, where formula_4 is the number of slits. Thinking of this width as the dimension of large single slit, the single slit equation, formula_5, tells us the angular width of the peaks. Whereas the angular width of the interference peaks is governed by the single slit equation, their angular positions are governed by the two slit equation. Let us assume for simplicity that formula_6 so that we can make the small angle approximation to the two slit equation, formula_7, and ask the following question: How different do two wavelengths have to be in order that the interference peaks from the two waves not overlap? In order for the peaks to be distinguishable, they should be separated in formula_8 by an angle formula_9, which is greater than the angular width of each peak, formula_10: Substituting in the above expressions for formula_1 and formula_10 and solving for formula_14, we get formula_15, where formula_16 is the number of slits in the diffraction grating. Thus, the fractional difference between wavelengths which can be distinguished by a diffraction grating depends solely on the interference order formula_17 and the number of slits formula_4 in the grating: More information about diffraction and diffractive optics

Waves/2-3D Problems. Problems. <br> Figure 2.20: Graphical representation of the dispersion relation for shallow water waves in a river flowing in the formula_3 direction. Units of frequency are hertz, units of wavenumber are inverse meters. <br> Figure 2.21: Sketch of a beam expander for a laser.

Waves/Total Internal Reflection. Total Internal Reflection. When light passes from a medium of lesser index of refraction to one with greater index of refraction, Snell's law indicates that the ray bends "toward" the normal to the interface. The reverse occurs when the passage is in the other direction. In this latter circumstance a special situation arises when Snell's law predicts a value for the sine of the refracted angle greater than one. This is physically untenable. What actually happens is that the incident wave is "reflected" from the interface. This phenomenon is called "total internal reflection". The minimum incident angle for which total internal reflection occurs is obtained by substituting formula_1 into equation (3.2), resulting in

Waves/Anisotropic Media. Anisotropic Media. Notice that Snell's law makes the implicit assumption that rays of light move in the direction of the light's wave vector, i. e., normal to the wave fronts. As the analysis in the previous chapter makes clear, this is valid only when the optical medium is isotropic, i. e., the wave frequency depends only on the magnitude of the wave vector, not on its direction. Certain kinds of crystals, such as those made of calcite, are not isotropic -- the speed of light in such crystals, and hence the wave frequency, depends on the orientation of the wave vector. As an example, the angular frequency in anisotropic medium might take the form where formula_2 is the speed of light for waves in which formula_3, and formula_4 is its speed when formula_5. <br> Figure 3.3: The right panel shows the fate of a light ray normally incident on the face of a properly cut calcite crystal. The anisotropic dispersion relation which gives rise to this behavior is shown in the left panel. Figure 3.3 shows an example in which a ray hits a calcite crystal oriented so that constant frequency contours are as specified in equation (3.4). The wave vector is oriented normal to the surface of the crystal, so that wave fronts are parallel to this surface. Upon entering the crystal, the wave front orientation must stay the same to preserve phase continuity at the surface. However, due to the anisotropy of the dispersion relation for light in the crystal, the ray direction changes as shown in the right panel. This behavior is clearly inconsistent with the usual version of Snell's law! It is possible to extend Snell's law to the anisotropic case. We will not derive the equations here, but they are Later we will see a suggestive resemblance between these equation of geometrical optics and the equations of classical mechanics. For now, though, we will assume that isotropic optical media are used, and discuss optical instruments.

Waves/Optical Instruments. Thin Lens Formula and Optical Instruments. Given the laws of reflection and refraction, one can see in principle how the passage of light through an optical instrument could be traced. For each of a number of initial rays, the change in the direction of the ray at each mirror surface or refractive index interface can be calculated. Between these points, the ray traces out a straight line. Though simple in conception, this procedure can be quite complex in practice. However, the procedure simplifies if a number of approximations, collectively called the "thin lens approximation", are valid. We begin with the calculation of the bending of a ray of light as it passes through a prism, as illustrated in figure 3.4. The pieces of information needed to find formula_1, the angle through which the ray is deflected are as follows: The geometry of the triangle defined by the entry and exit points of the ray and the upper vertex of the prism leads to which simplifies to Snell's law at the entrance and exit points of the ray tell us that where formula_5 is the index of refraction of the prism. (The index of refraction of the surroundings is assumed to be unity.) One can also infer that This comes from the fact that the sum of the internal angles of the shaded tetrahedron in figure 3.4 is formula_7. Combining equations (3.6), (3.7), and (3.8) allows the ray deflection formula_1 to be determined in terms of formula_9 and formula_10, but the resulting expression is very messy. However, great simplification occurs if the following conditions are met: With these approximations it is easy to show that Generally speaking, lenses and mirrors in optical instruments have curved rather than flat surfaces. However, we can still use the laws for reflection and refraction by plane surfaces as long as the segment of the surface on which the wave packet impinges is not curved very much on the scale of the wave packet dimensions. This condition is easy to satisfy with light impinging on ordinary optical instruments. In this case, the deflection of a ray of light is given by equation (3.9) if formula_10 is defined as the intersection of the tangent lines to the entry and exit points of the ray, as illustrated in figure 3.5. A "positive lens" is thicker in the center than at the edges. The angle formula_10 between the tangent lines to the two surfaces of the lens at a distance formula_17 from the central axis takes the form formula_18, where formula_19 is a constant. The deflection angle of a beam hitting the lens a distance formula_17 from the center is therefore formula_21, as indicated in figure 3.5. The angles formula_22 and formula_23 sum to the deflection angle: formula_24. However, to the extent that the small angle approximation holds, formula_25 and formula_26 where formula_27 is the distance to the object and formula_28 is the distance to the image of the object. Putting these equations together and cancelling the formula_17 results in the "thin lens formula": The quantity formula_31 is called the "focal length" of the lens. Notice that formula_32 if the object is very far from the lens, i. e., if formula_27 is extremely large. <br> Figure 3.6 shows how a positive lens makes an image. The image is produced by all of the light from each point on the object falling on a corresponding point in the image. If the arrow on the left is an illuminated object, an "image" of the arrow will appear at right if the light coming from the lens is allowed to fall on a piece of paper or a ground glass screen. The size of the object formula_34 and the size of the image formula_35 are related by simple geometry to the distances of the object and the image from the lens: Notice that a positive lens inverts the image. An image will be produced to the right of the lens only if formula_37. If formula_38, the lens is unable to converge the rays from the image to a point, as is seen in figure 3.7. However, in this case the backward extension of the rays converge at a point called a "virtual image", which in the case of a positive lens is always farther away from the lens than the object. The thin lens formula still applies if the distance from the lens to the image is taken to be negative. The image is called virtual because it does not appear on a ground glass screen placed at this point. Unlike the real image seen in figure 3.6, the virtual image is not inverted. <br> A "negative lens" is thinner in the center than at the edges and produces only virtual images. As seen in figure 3.8, the virtual image produced by a negative lens is closer to the lens than is the object. Again, the thin lens formula is still valid, but both the distance from the image to the lens and the focal length must be taken as negative. Only the distance to the object remains positive. <br> Curved mirrors also produce images in a manner similar to a lens, as shown in figure 3.9. A concave mirror, as seen in this figure, works in analogy to a positive lens, producing a real or a virtual image depending on whether the object is farther from or closer to the mirror than the mirror's focal length. A convex mirror acts like a negative lens, always producing a virtual image. The thin lens formula works in both cases as long as the angles are small.

Waves/Fermat's Principle. Fermat's Principle. An alternate approach to geometrical optics can be developed from Fermat's principle. This principle states (in its simplest form) that light waves of a given frequency traverse the path between two points which takes the least time. The most obvious example of this is the passage of light through a homogeneous medium in which the speed of light doesn't change with position. In this case shortest time is equivalent to the shortest distance between the points, which, as we all know, is a straight line. Thus, Fermat's principle is consistent with light traveling in a straight line in a homogeneous medium. Fermat's principle can also be used to derive the laws of reflection and refraction. For instance, figure 3.10 shows a candidate ray for reflection in which the angles of incidence and reflection are not equal. The time required for the light to go from point A to point B is where formula_2 is the speed of light. We find the minimum time by differentiating formula_3 with respect to formula_4 and setting the result to zero, with the result that However, we note that the left side of this equation is simply formula_6, while the right side is formula_7, so that the minimum time condition reduces to formula_8 or formula_9, which is the law of reflection. <br> A similar analysis may be done to derive Snell's law of refraction. The speed of light in a medium with refractive index formula_10 is formula_11, where formula_2 is its speed in a vacuum. Thus, the time required for light to go some distance in such a medium is formula_10 times the time light takes to go the same distance in a vacuum. Referring to figure 3.11, the time required for light to go from A to B becomes This results in the condition where formula_16 is now the refracted angle. We recognize this result as Snell's law. Notice that the reflection case illustrates a point about Fermat's principle: The minimum time may actually be a local rather than a global minimum -- after all, in figure 3.10, the global minimum distance from A to B is still just a straight line between the two points! In fact, light starting from point A will reach point B by both routes -- the direct route and the reflected route. Figure 3.13 illustrates a rather peculiar situation. Notice that "all" the rays from point O which intercept the lens end up at point I. This would seem to contradict Fermat's principle, in that only the minimum (or maximum) time trajectories should occur. However, a calculation shows that all the illustrated trajectories in this particular case take the "same" time. Thus, the light cannot choose one trajectory over another using Fermat's principle and all of the trajectories are equally favored. Note that this inference applies not to just any set of trajectories, but only those going from one focal point to another.

Waves/Geometrical Problems. Problems. <br> Figure 3.14: Refraction through multiple parallel<br> layers with different refractive indices. <br> Figure 3.15: Refraction through a formula_1-formula_1-formula_3 prism. <br> Figure 3.16: Focusing of parallel rays by a parabolic mirror. <br> Figure 3.17: Refraction through a wedge-shaped prism.

Modern Physics/Math/Four Vectors. Math Tutorial - Four-Vectors. We have seen that a wave is described by four numbers, the components of the spatial vector k, and the frequency ω In special relativity these four numbers form a four-vector It is called a "four"-vector because it has 3 spacelike components, forming a vector, and one timelike component when there are 3 space dimensions. It is called a four-"vector" because of the way it behaves when we change reference frames. The spacelike component of the wave four-vector is just formula_1 when there are 3 space dimensions, while the timelike component is formula_2 where the "c" is in the denominator to give the timelike component the same dimensions as the spacelike component. Let us define some terminology. We indicate a four-vector by underlining and write the components in the following way: formula_3, where formula_4 is the wave four-vector, formula_5 is its spacelike component, and formula_6 is its timelike component. For three space dimensions, where we have a wave vector rather than just a wavenumber, we write formula_3. Another example of a four-vector is simply the position vector in spacetime, formula_8, or formula_9 in three space dimensions. The formula_10 "multiplies" the timelike component in this case, because that is what is needed to give it the same dimensions as the spacelike component. In three dimensions we define a vector as a quantity with magnitude and direction. Extending this to spacetime, a four-vector is a quantity with magnitude and direction in spacetime. Implicit in this definition is the notion that the vector's magnitude is a quantity independent of coordinate system or reference frame. We have seen that the invariant interval in spacetime is so it makes sense to identify this as the magnitude of the position vector. This leads to a way of defining a dot product of four-vectors. Given two four-vectors then the dot product is This is consistent with the definition of invariant interval if we set since then Now, the key point about dot products for 3-vectors is that they are scalars, independent of the observer. They do not change if the axes are rotated, as was proven earlier. For our definition of the dot product of four-vectors to be useful, it should also be independent of the observer. In particular, it should not depend on the observers velocity, else it would violate the principle of relativity. We can easily check that our definition does satisfy this criterion. It's clear that its independent of rotation, since it is the difference between a dot product and the product of two scalars, both of which terms aren't affected by rotating the coordinates. Is it also frame velocity independent? To check, first we need to be able to write down our four-vectors in the new reference frame. We know how to do this for the position vector — use the Lorentz transform. It can be shown that the same transform must hold for all vectors , so the components of a four vector in the new reference frame, moving at velocity v along the "x"-axis with respect to the previous one, are The dot product in this frame is Simplifying, we get which is just the dot product in the original frame, exactly as we wanted. We now know that the dot product of two four-vectors is a scalar result, i. e., its value is independent of coordinate system. This can be used to advantage on occasion. In the odd geometry of spacetime it is not obvious what "perpendicular" means. We therefore define two four-vectors formula_19 and formula_20 to be perpendicular if their dot product is zero, in the same way as with three-vectors. Because the dot product is a scalar, if vectors are perpendicular in one frame, they will be perpendicular in all frames. We can also consider the dot product of a four-vector formula_19 which resolves into formula_23 in the unprimed frame. Let us further suppose that the spacelike component is zero in some primed frame, so that the components in this frame are (0, "A"t' ) The fact that the dot product is independent of coordinate system means that This constitutes an extension of the spacetime Pythagorean theorem to four-vectors other then the position four-vector. Thus, for instance, the wavenumber for some wave may be zero in the primed frame, which means that the wavenumber and frequency in the unprimed frame are related to the frequency in the primed frame by formula_25. Proper time. Classically, the temporal derivative, "d"/"dt" acts like a scalar so we can multiply a vector by it, and get another vector. In relativity "t" is part of a four-vector, which means "d"/"dt" also is, so we can't simply differentiate vectors with respect to "t" and expect to get vectors. For example, the position of a stationary particle is (0, "ct"). Viewed from a frame moving at "v" to the right, its position becomes (-"v"τ, "c"τ), where τ=γ"t" is the time as measured in the moving frame. If we differentiate with respect to τ the velocity would be (-"v", "c") If we differentiate with respect to "t", we get (0, "c") in the stationary frame, which would be (using the Lorentz transform) (-γ"v", -γ"c") in the moving frame, if this were a four vector. These two expressions differ by a factor of γ, when measured in the same frame, so this can not be a four vector. However, if the moving observer divides by γ, which is the time dilation, they will get the same vector as the stationary observer. Doing this is equivalent to differentiating by the time "in the particles own rest frame". Since this works for the position vector, we can expect it to work for all vectors. The time measured in a particle's rest frame is called its "proper time". Differentiating a vector with respect to proper time gives another vector, which is the relativistic equivalent of the temporal derivative.

Modern Physics/Principle of Relativity Applied. An application of relativity to waves. Returning to the phase of a wave, we immediately see that Thus, a compact way to write a wave is formula_2(6.8) Since formula_3 is known to be a four-vector and since the phase of a wave is known to be a scalar independent of reference frame, it follows that formula_4 is indeed a four-vector rather than just a set of numbers. Thus, the square of the length of the wave four-vector must also be a scalar independent of reference frame Resolution of a four-vector into components in two different reference frames. Let us review precisely what this means. As this figure shows, we can resolve a position four-vector "x" into components in two different reference frames, e.g ("X","T") and ("X′","T′"), but these are just different ways of writing the same vector. This is exactly the same as the way a three-vector has different components in a rotated frame. Similarly, just as a three-vector has the same magnititude in all frames, so does a 4-vector; i.e, Applying this to the wave four-vector, we infer that where the unprimed and primed values of "k" and ω refer to the components of the wave four-vector in two different reference frames. Up to now, this argument applies to any wave. However, waves can be divided into two categories, those for which a "special" reference frame exists, and those for which there is no such special frame. As an example of the former, sound waves look simplest in the reference frame in which the gas carrying the sound is stationary. The same is true of light propagating through a material medium with an index of refraction not equal to unity. In both cases the speed of the wave is the same in all directions only in the frame in which the material medium is stationary. If there is no material medium, then there is no unambiguous way of finding a special frame so the waves must fall into the second category. This includes all waves in a vacuum, such as light. In this case the following argument can be made. An observer moving with respect to waves of frequency ω and wave number "k" sees waves of frequency ω′ and wave number "k′". If the observer can tell in any way that they come from a source moving with respect to them, then they can use this to identify a special frame for those waves, so the waves must look just like ones from a stationary source of frequency ω This forces us to conclude that for such waves where μ is a constant. All waves in a vacuum must have this form, a much more restricted choice than in classical physics.

Modern Physics/Characteristics of Relativistic Waves. In classical physics, ω and "k" for light are related by In relativistic physics, we've seen that for waves with no special reference frame, such as light, ω and "k" are related by If μ=0 then the relativistic equation reduces to the classical, so we can assume that, for light, μ does equal zero. This means that light does not have a mimimum frequency. If μ is not zero then the wave being described are dispersive. The phase speed is This phase speed always exceeds "c", which at first may seem like an unphysical conclusion. However, the group velocity of the wave is which is always less than "c". Since wave packets and hence signals propagate at the group velocity, waves of this type are physically reasonable even though the phase speed exceeds the speed of light. Another interesting property of such waves is that the wave four-vector is parallel to the world line of a wave packet in spacetime. This is easily shown by the following argument. The spacelike component of a wave four-vector is k, while the timelike component is ω/"c". The slope of the four-vector on a spacetime diagram is therefore ω/"kc". However, the slope of the world line of a wave packet moving with group velocity is "c"/"ug", which is also ω/"kc". Note that when we have "k" is zero we have ω=μ. In this case the group velocity of the wave is zero. For this reason we sometimes call μ the rest frequency of the wave.

Modern Physics/The Doppler Effect. The Doppler Effect You have probably heard how the pitch of a train horn changes as it passes you. When the train is approaching, the pitch or frequency is higher than when it is moving away from you. This is called the Doppler effect. A similar, but distinct effect occurs if you are moving past a source of sound. If a stationary whistle is blowing, the pitch perceived from a moving car is higher while moving toward the source than when moving away. The first case thus has a moving source, while the second case has a moving observer. In this section we will compute the Doppler effect as it applies to light moving through a vacuum. The figure below shows the geometry for computing the time between wave fronts of light for a stationary and a moving reference frame. Since the world lines of the wave fronts have a slope of unity, the sides of the shaded triangle both have the same value, "C". If the observer is moving at speed "U" , the slope of the observer's world line is "c"/"U", i.e Solving this for "X" and substituting in give "cT′"="cT"+"X" gives In classical physics "T′" and τ are the same so this formula, as it stands, leads directly to the classical Doppler shift for a moving observer. However, in relativity "T′" and τ are different. We can use the Lorentz transformation to correct for this. The second wavefront passes the moving observer at ("UT′","cT′") in the stationary observers frame, but at (0,"c"τ) in its own frame. The Lorentz transform tells us that. Substituting in equation (1) gives From this we infer the relativistic Doppler shift formula for light in a vacuum: since frequency is inversely proportional to time. We could go on to determine the Doppler shift resulting from a moving source. However, by the principle of relativity, the laws of physics should be the same in the reference frame in which the observer is stationary and the source is moving. Furthermore, the speed of light is still "c" in that frame. Therefore, the problem of a stationary observer and a moving source is conceptually the same as the problem of a moving observer and a stationary source when the wave is moving at speed "c". This is unlike the case for, say, sound waves, where the stationary observer and the stationary source yield different formulas for the Doppler shift.

Modern Physics/Addition of Velocities. In classical physics, velocities simply add. If an object moves with speed "u" in one reference frame, which is itself moving at "v" with respect to a second frame, the object moves at speed "u"+"v" in that second frame. This is inconsistant with relativity because it predicts that if the speed of light is "c" in the first frame it will be "v"+"c" in the second. We need to find an alternative formula for combining velocities. We can do this with the Lorentz transform. Because the factor "v"/"c" will keep recurring we shall call that ratio β. We are considering three frames; frame O, frame O' which moves at speed "u" with respect to frame O, and frame O" which moves at speed "v" with respect to frame O'. We want to know the speed of O" with respect to frame O,"U" which would classically be "u"+"v". The transforms from O to O' and O' to O" can be written as matrix equations, where we are defining the β's and γ's as We can combine these to get the relationship between the O and O" coordinates simply by multiplying the matrices, giving This should be the same as the Lorentz transform between the two frames, These two sets of equations do look similar. We can make them look more similar still by taking a factor of 1+ββ' out of the matrix in (1) giving# This will be identical with equation 2 if Since the two equations "must" give identical results, we know these conditions must be true. Writing the β's in terms of the velocities equation 3a becomes which tells us "U" in terms of "u" and "v". A little algebra shows that this implies equation 3b is also true Multiplying by "c" we can finally write. formula_8 Notice that if "u" or "v" is much smaller than "c" the denominator is approximately 1, and the velocities approximately add but if either "u" or "v" is "c" then so is "U", just as we expected.

Arabic/Edited Work. This is an attempt to make a long text to organize my thoughts. The book is composed of the following parts:

Probability. Welcome to the Wikibook of PROBABILITY This book is an introduction to the mathematical theory of probability.

Geometry/Angles. An angle is the union of two rays with a common endpoint, called the "vertex". The angles formed by vertical and horizontal lines are called right angles; lines, segments, or rays that intersect in right angles are said to be perpendicular. Angles, for our purposes, can be measured in either degrees (from 0 to 360) or radians (from 0 to formula_1). Angles length can be determined by measuring along the arc they map out on a circle. In radians we consider the length of the arc of the circle mapped out by the angle. Since the circumference of a circle is formula_1, a right angle is formula_3 radians. In degrees, the circle is 360 degrees, and so a right angle would be 90 degrees. Naming Conventions. Angles are named in several ways. Classification of Angles by Degree Measure. Acute Angle Right Angle Obtuse Angle

Probability/Introduction. Overview. Probability theory provides a mathematical model for the study of randomness and uncertainty. Many important decisions, whether from business, government, science, recreation or even one's personal life must be made with incomplete information or some degree of uncertainty. Hence, a formalized study of uncertain or random outcomes occupies an important role in modern society. In situations where one of any number of possible outcomes may occur, the mathematical model of probability theory offers methods for quantifying the likelihoods associated with those outcomes. Probability also provides tools which allow us to move beyond simply describing the information contained within a set of data (descriptive statistics) to actually inferring further information from that data (inferential statistics). Many of the early attempts to model likelihood arose from games of chance. For a brief history of probability see this Wikipedia article. Although probability theory is now a very formal branch of mathematics, the language of probability is often used informally in everyday speech. We express our beliefs about likelihoods of outcomes in situations involving uncertainty using intuition guided by our experiences and in some cases statistics. Consider the following examples: Notice that in the previous examples the likelihood of any particular outcome is expressed as a percentage (between 0% and 100%), as is common in everyday language. However, probabilities in formal probability theory are always expressed as real numbers in the interval formula_2 (e.g. a probability of .25 may be expressed as 25%, or a probability of formula_3 may be expressed as approximately 31.83%). Other differences exist between common expressions of probabilities and formal probability theory. For example, a probability of 0% is typically taken to mean that the event to which that probability is assigned is impossible. However, in probability theory (usually in cases where there are infinitely many possible outcomes) an event ascribed a probability of zero may actually occur. In some situations, it is certain that such an event will occur (e.g. in selecting a real number between 0 and 1, the probability of selecting any given number is zero, but it is certain that one such number will be selected). Another way to express the probability of an outcome is by its "odds": the ratio of the probability of "success" (event occurs) to the probability of "failure" (event does not occur). In gambling odds are expressed as the ratio of the stakes risked by each participant in a wager. For instance: a bookmaker offering odds of 3 to 1 "against" a horse will pay a punter three times their stake (if the horse wins). In fact, the bookmaker (ignoring factors such as his potential need to "lay off" bets which are exposing him to the possibility of an unacceptable overall loss) is announcing that he thinks the horse has a formula_4 chance of winning. If we express odds as "chance of winning": "chance of not winning", then 3 to 1 against would be represented as formula_5 or formula_6 . So an event with a probability of formula_4 or 25% has odds of 33%. This disparity is even more clear where an event has a probability of 50% (e.g., the odds of a coin showing heads is 50%:50% = 1:1 or formula_8). Types of probability. As mentioned earlier, probability can be expressed informally in a variety of different ways, but even formal definitions and approaches vary. The most general and rigorous approach is known as axiomatic probability theory, which will be the focus of later chapters. Here we briefly discuss a few other approaches, their uses and limitations. All of these approaches rely in one way or another on the concept of an "experiment". Recall that probability provides means to study randomness and uncertainty. An experiment is any action or process whose outcome is subject to uncertainty or randomness. Here the term experiment is used in a wider sense than its usual connotation with controlled laboratory situations. Further clarification on experiments will be given later, but for now the following examples of experiments will suffice: Assuming that an experiment can be repeated under identical conditions, then each repetition of an experiment is called a "trial". Basic Concepts. There are two standard approaches to conceptually interpreting probabilities: the relative frequency approach and the subjective belief (or confidence approach). In the Frequency Theory of Probability, probability is the limit of the relative frequency with which certain outcomes occur in repeated trials (note that the outcome of any single trial cannot depend on the outcome of other trials). The relative frequency approach requires that experiments be random and that all possible outcomes be known before execution of the experiment. The probability of any set of outcomes is expressed as the relative frequency with which those outcomes will occur among many repeated trials. Physical probabilities fall within the category of objective or frequency probabilities, and are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given outcome (such as a die yielding a six) tends to occur at a persistent rate, or 'relative frequency', in a long run of trials. Physical probabilities either explain, or are invoked to explain these stable frequencies. Relative frequency probabilities are always expressed as a figure between 0% (the outcome essentially never happens) and 100% (the outcome essentially always happens), or similarly as a figure between 0 and 1. According to the Frequency Theory of Probability, saying that "the probability that A occurs is p%" means that if you repeat the experiment many times under essentially identical conditions, the percentage of time for which A occurs will converge to p. For example, a 50% chance that a coin lands "heads up" means that if you toss the coin over and over again, then the ratio of times the coin lands heads to the total number of tosses approaches a limiting value of 50% as the number of tosses grows. Notice that the outcome of one toss never depends on another toss, and that the ratio of heads to total number of tosses is always between 0% and 100%. In the Subjective Theory of Probability, probability measures the speaker's "degree of belief" that a set of outcomes will result, on a scale of 0% (complete disbelief that the event will happen) to 100% (certainty that the event will happen). According to the Subjective Theory, saying that "the probability that A occurs is formula_9 " means that I believe that A will happen twice as strongly as I believe that A will not happen. The Subjective Theory is particularly useful in assigning meaning to the probability of outcomes that in principle can occur only once. For example, how might one assign meaning to the following statement: "there is a 25% chance of an earthquake on the San Andreas fault with magnitude 8 or larger before 2050"? It would be very hard to qualify this measure in terms of relative frequency. One way to represent an individual's degree of belief in a statement, given available evidence, is with the Bayesian approach. Evidential probability, also called Bayesian probability, can be assigned to any statement whatsoever, even when no random process is involved. On most accounts evidential probabilities are considered degrees of belief, defined in terms of dispositions to gamble at certain odds. The primary evidential interpretations include the classical interpretation, the subjective interpretation, the epistemic or inductive interpretation, and the logical interpretation. The next several sections discuss the principal theories within the relative frequency approach to probability. Classical theory of probability. The classical approach to probability expresses probability as a ratio of the number of favorable outcomes in a series of successive trials to the number of total possible outcomes. Note the immediate implication that the number of total possible outcomes be known. Furthermore, all possible outcomes are assumed to be equally probably and no two possible outcomes can both result from the same trial. Here, the term "favorable" is not subjective, but rather indicates that an outcome belongs to a group of outcomes of interest. This group of outcomes is called an "event", which will be formalized with the introduction of axiomatic probability theory. For example, a standard deck of cards (without jokers) has 52 cards. If we randomly draw a card from the deck, we can think of each card as a possible outcome. Therefore, there are 52 total outcomes. We can now look at various events and calculate their probabilities: Classical probability suffers from a serious limitation. The definition of probability implicitly defines all outcomes to be equiprobable. While this might be useful for drawing cards, rolling dice, or pulling balls from urns, it offers no method for dealing with outcomes with unequal probabilities. This limitation can even lead to mistaken statements about probabilities. An often given example goes like this: Of course, the problem here is not with the classical theory, merely the attempted application of the theory to a situation to which it is not well adapted. This limitation does not, however, mean that the classical theory of probability is useless. At many points in the development of the axiomatic approach to probability, classical theory is an important guiding factor. Empirical or Statistical Probability or Frequency of occurrence. This approach to probability is well-suited to a wide range of scientific disciplines. It is based on the idea that the underlying probability of an event can be measured by repeated trials. It is of course impossible to conduct an infinite number of trials. However, it usually suffices to conduct a large number of trials, where the standard of large depends on the probability being measured and how accurate a measurement we need. A note on this definition of probability: How do we know the sequence formula_17 in the limit will converge to the same result every time, or that it will converge at all? The unfortunate answer is that we don't. To see this, consider an experiment consisting of flipping a coin an infinite number of times. We are interested in the probability of heads coming up. Imagine the result is the following sequence: with each run of formula_18 heads and formula_18 tails being followed by another run twice as long. For this example, the sequence formula_17 oscillates between roughly formula_6 and formula_9 and doesn't converge. We might expect such sequences to be unlikely, and we would be right. It will be shown later that the probability of such a run is 0, as is a sequence that converges to anything other than the underlying probability of the event. However, such examples make it clear that the limit in the definition above does not express convergence in the more familiar sense, but rather some kind of convergence in probability. The problem of formulating exactly what this means belongs to axiomatic probability theory. Axiomatic probability theory. Although axiomatic probability theory is often frightening to beginners, it is the most general approach to probability and has been employed in tackling some of the more difficult problems in probability. It begins with a set of axioms which, although not immediately intuitive, are guided by the more familiar classical probability theory. These axioms are discussed in the (as yet unwritten) following chapter. About This Book. This book is going to discuss the topic of mathematical probability using Calculus and Linear Algebra. Readers of this book should have a good understanding of both those topics before attempting to read and understand this book completely.

Quantum Mechanics.

German/Lesson 9. Lektion 9 Einkaufen gehen ~ Going shopping Lernen 9 ~ Die Kleidungsstücke (articles of clothing). German English German plural die Bluse blouse die Blusen der Gürtel belt die Gürtel das Hemd shirt die Hemden das Kleid dress die Kleider die Hose pants (US)/trousers die Hosen der Hut hat die Hüte die Kleidung clothes (casual) die Kleidungsstücke die Jeans jeans die Jeans die Mütze/Haube cap die Mützen der Pullover pullover die Pullis, die Pullover der Rock skirt die Röcke der Schuh shoe die Schuhe die Shorts shorts die Shorts die Socke sock die Socken der Stiefel boot die Stiefel das T-Shirt T-shirt die T-Shirts Gespräche 9-1 ~ Katrin macht Besorgungen. Katrin macht Besorgungen—besonders sucht sie neue Schuhe. Sie geht in das Einkaufszentrum. Katrin probiert ein Paar Schuhe an. Vokabeln 9-1. Included in this vocabulary lesson are the German nouns for various articles of clothing ("Lernen 9" above). die Besorgungen errands das Einkaufszentrum shopping mall der Euro Euro die Farbe color die Klamotten clothes das Paar pair, couple der Preis price der Verkäufer sales clerk, sales assistant neununddreißig Euro neunzehn € 39.19 anprobieren try on brauchen need kaufen buy kosten cost mögen would like passen fit [clothing] suchen seek, look for besonders especially billig cheap prima topnotch, super welche which 2-2 Shopping-related Verbs. There are a lot of verbs that have to do with shopping for clothes. The most prominent are listed below. anziehen - to put on (clothes)<br> aussehen - to appear<br> nehmen - to take<br> wollen - to want (somewhat impolite) These verbs are used often, so it is necessary to learn them. Among them are separable verbs, irregular verbs, and modals. Separable Verbs Anprobieren, aussehen and anziehen are "separable verbs". It is easy to see this, as they each have a prefix of 'aus' or 'an'. When using the verb as the main verb of a sentence, separate the prefix and put it at the end of the sentence. When the verb is in infinitive form, leave it just as you see it. Irregular Verbs Ausehen and nehmen are the two irregular verbs on this list. Both experience a change in the first 'e' in the du-form and er/sie/es-form. Du siehst ... aus und er/sie/es sieht ... aus. Du nimmst und er/sie/es nimmt. Modals Möchten and wollen are the two modals introduced here. Modals are similar to the helping verbs in English and cause the other verb to go to the end in the infinitive form. They also have a strange conjugation. Möchten changes in er/sie/es form to möchte (the same as the ich-form). In fact all modals have the same er/sie/es-form and ich-form. Wollen is like most other modals: it has a different vowel in singular and plural, except when using formal you. Ich will (not to be confused with future tense), du willst, er/sie/es will, wir wollen, ihr wollt, und sie/Sie wollen. All of this verb conjugation and more can be found in Reference Table II. 3 Accusative Case. You have already learned the pronouns and articles in the "nominative case". Now it is time for the "accusative case". 3-1 Example Story 2. You now need more clothes. You drive to a mall and go to the clothing department store. Du suchst zwei Jeans, drei Hemden und einen Gürtel. Du siehst die Jeans und nimmst zwei. Du kaufst jetzt nur die Hemden und den Gürtel. VERKÄUFERIN: Die Gürtel sind da.<br> DU: Haben Sie auch Gürtel in Braun?<br> VERKÄUFERIN: Ja, da hinten. Du nimmst den Gürtel in Braun, aber er ist billig. Du kaufst zwei. VERKÄUFERIN: Noch etwas?<br> DU: Ja, ich brauche drei Hemden.<br> VERKÄUFERIN: Hemden haben wir. Sie sind hier.<br> Du nimmst ein Hemd in Blau, und zwei in Rot. Du probierst die Hemden, die Jeans, und die Gürtel an. Alles passt. DU: Was kosten diese Klamotten?<br> VERKÄUFERIN: Zwei Jeans, drei Hemden, und zwei Gürtel kosten fünfundsechzig Euro. You give the clerk the money and take the clothing home. 3-2 Accusative Case Articles. Remember that in the nominitive case, the articles are "der, die, das," and "die", listed in MFNP (masculine, feminine, neuter, and plural) order. Well, in the accusative case, only the masculine form changes to den. An easy memory hook is "Der goes to den and the rest stay the same." The ein-forms undergo the same change. Masculine "ein" goes to "einen" and the rest stay the same. 3-3 Prices. Two easy words describe prices. billig - cheap<br> teuer - expensive These adjectives are applied to the products you buy, never to the word "Preis". Anyway, you rather say "Das ist billig/teuer." (meaning the product you buy) than "Der Preis ist niedrig/hoch." 3-4 A DDR Joke. In einem Kaufhaus in der DDR fragt ein Kunde: "Haben Sie keine Unterhosen?". Die Verkäuferin antwortet: "Nein, wir haben keine Badehosen. Im zweiten Stock haben wir keine Unterhosen!" fragen to ask DDR Deutsche Demokratische Republik (German Democratic Republic, long since reunited with the BRD) Kaufhaus very big shop Kunde client Unterhosen underpants Badehosen swimming trunks Im zweiten Stock on the second floor