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From Wikipedia
In computer programming, a global variable is a variable that is accessible in every scope (unless shadowed). Interaction mechanisms with global variables are called global environment (see also global state) mechanisms. The global environment paradigm is contrasted with the local environment paradigm, where all variables are local with no shared memory (and therefore all interactions can be reconducted to message passing).
They are usually considered bad practice precisely because of their nonlocality: a global variable can potentially be modified from anywhere (unless they reside in protected memory), and any part of the program may depend on it. A global variable therefore has an unlimited potential for creating mutual dependencies, and adding mutual dependencies increases complexity. See action at a distance. However, in a few cases, global variables can be suitable for use. For example, they can be used to avoid having to pass frequentlyused variables continuously throughout several functions.
Global variables are used extensively to pass information between sections of code that do not share a caller/callee relation like concurrent threads and signal handlers. Languages (including C) where each file defines an implicit namespace eliminate most of the problems seen with languages with a global namespace though some problems may persist without proper encapsulation. Without proper locking (such as with a mutex), code using global variables will not be threadsafe except for read only values in protected memory.
The C language does not use the term global, though in a small program contained in a single file it is possible to get the same effect by declaring a variable outside all functions (see below). However, such a variable should be called external, not global, since its scope is limited to the single file. In a larger program, broken up into several files, the variable will only be accessible from those modules where it is declared again. It is possible to prevent conflicts between external variables (or functions) with the same name in different files by qualifying them as static, which turns off any linkage to other files.
An example of a "global" variable in C: /* Note that this example is wrong. global does not qualify as a global variable as it is not "in scope everywhere". */
 include
int global = 3; /* This is the external variable. */
static void ChangeGlobal(void) { global = 5; /* Reference to external variable in a function. */ }
int main(void) { printf("%d\n", global); /* Reference to external variable in another function. */ ChangeGlobal(); printf("%d\n", global); return 0; } As the variable is an external one, there is no need to pass it as a parameter to use it in a function besides main. It belongs to every function in the module.
The output will be: 3 5
The use of global variables makes software harder to read and understand. Since any code anywhere in the program can change the value of the variable at any time, understanding the use of the variable may entail understanding a large portion of the program. They make separating code into reusable libraries more difficult because many systems (such as DLLs) don't directly support viewing global variables in other modules. They can lead to problems of naming because a global variable makes a name dangerous to use for any other local or object scope variable. A local variable of the same name can shield the global variable from access, again leading to harder to understand code. The setting of a global variable can create side effects that are hard to understand and predict. The use of globals make it more difficult to isolate units of code for purposes of unit testing, thus they can directly contribute to lowering the quality of the code.
Some languages, like Java, don't have global variables. In Java, all variables that are not local variables are fields of a class. Hence all variables are in the scope of either a class or a method. In Java, static fields (aka class variables) exist independently of any instances of the class and one copy is shared among all instances; hence static fields are used for many of the same purposes as global variables in other languages because of their similar "sharing" behavior.
The commaseparated values file format is a set of file formats used to store tabular data in which numbers and text are stored in plain textual form that can be read in a text editor. Lines in the text file represent rows of a table, and commas in a line separate what are fields in the tables row. Different implementations of CSV arise as the format is modified to handle richer table content such as allowing a different field separator character, (which is useful if numeric fields are written with a comma instead of a decimal point); or extensions to allow numbers, the separator character, or newline characters in text fields.
CSV is a simple file format that is widely supported, so it is often used to move tabular data between different computer programs that support compatible CSV formats. For example: a CSV file might be used to transfer information from a database program to a spreadsheet.
Example of a USA/UK CSV file (where the decimal separator is a period/full stop and the value separator is a comma):
Year,Make,Model,Length 1997,Ford,E350,2.34 2000,Mercury,Cougar,2.38
Example of a German CSV file (where the decimal separator is a comma and the value separator is a semicolon):
Year;Make;Model;Length 1997;Ford;E350;2,34 2000;Mercury;Cougar;2,38
Technical background
A file format is a particular way to encode information for storage in a computer file. Particularly, files encoded using the CSV format are used to store tabular data. The format dates back to the early days of business computing and is widely used to pass data between computers with different internal word sizes, data formatting needs, and so forth. For this reason, CSV files are common on all computer platforms.
CSV is a delimited text file that uses a comma to separate values (many implementations of CSV import/export tools allow other separators to be used). Simple CSV implementations will not allow field values that contain a comma or other special characters such as newlines. More sophisticated CSV implementations permit commas and other special characters in a field value. Many implementations use " (double quote) characters around values that contain reserved characters (such as commas, double quotes, or newlines); embedded double quote characters may be represented by a pair of consecutive double quotes. Some CSV implementations may use an escape character such as a backslash to encode reserved characters as an escape sequence.
In computer science terms, a CSV file is a "flat file".
History
Commaseparated values are old technology and predate personal computers by more than a decade: the IBM Fortran (level G) compiler under OS/360 supported them in 1967. Commaseparated value lists were often easier to type into punched cards than fixedcolumnaligned data, and were less prone to producing incorrect results if a value was punched one column off from its intended location.
The comma separated list (CSL) is a dataformat originally known as commaseparated values (CSV) in the oldest days of simple computers. In the industry of personal computers (then more commonly known as "Home Computers"), the most common use was small businesses generating solicitations using boilerplateform letters and mailing lists.
Some early software applications, such as word processors, allowed a stream of "variable data" to be merged between two files: a form letter, and a CSL of names, addresses, and other data fields. Many applications still do, simply because tasks requiring human input (such as constructing a list) are natural and easy using comma delimiters. CSL/CSVs were also used for simple databases.
Specification
Background
Comma separated lists date from before the earliest personal computers, but were widely used in the earliest preIBM PC era personal computers for tape storage backup and interchange of database information from machines of two different architectures. In that day, affordable hard drives did not exist, and many small businesses tried to achieve the benefits of computing using floppy disk based software.
No general standard specification for CSV exists. Variations between CSV implementations in different programs are quite common and can lead to interoperation difficulties. For Internet communication of CSV files, an Informational IETF document (RFC 4180 from October 2005) describes the format for the "text/csv" MIME type registered with the IANA. Another relevant specification is provided by Fielded Text which also covers the CSV format.
Many informal documents exist that describe the CSV format. provides an overview of the CSV format in the most widely used applications and explains how it can best be used and supported.
Basic rules
The basic rules from a lot of these specifications are as follows:
CSV is a delimited data format that has fields/columns separated by the commacharacter and records/rows terminated by newlines. Fields that contain a special character (comma, newline, or double quote), must be enclosed in double quotes. If a line contains a single entry which is the empty string, it may be enclosed in double quotes. If a field's value contains a double quote character it is escaped by placing another double quote character next to it. The CSV file format does not require a specific character encoding, byte order, or line terminator format.
Note: While experiment.
The test result can be qualitative (yes/no), categorical, or quantitative (a measured value). It can be a personal observation or the output of a precision measuring instrument.
Usually the test result is the dependent variable, the measured response based on the particular conditions of the test or the level of the independent variable. Some tests, however, involve changing the independent variable to determine the level at which a certain response occurs: in this case, the test result is the independent variable.
Importance of test methods
In software development, engineering, science, manufacturing, and business, it is vital for all interested people to understand and agree upon methods of obtaining data and making measurements. It is common for a physical property to be strongly affected by the precise method of testing or measuring that property. It is vital to fully document experiments and measurements and to provide needed definitions to specifications and contracts.
Using a standard test method, perhaps published by a respected standards organization, is a good place to start. Sometimes it is more useful to modify an existing test method or to develop a new one. Again, documentation and full disclosure are very necessary.
A wellwritten test method is important. However, even more important is choosing a method of measuring the correct property or characteristic. Not all tests and measurements are equally useful: usually a test result is used to predict or imply suitability for a certain purpose. For example, if a manufactured item has several components, test methods may have several levels of connections:
 test results of a raw material should connect with tests of a component made from that material
 test results of a component should connect with performance testing of a complete item
 results of laboratory performance testing should connect with field performance
These connections or correlations may be based on published literature, engineering studies, or formal programs such as quality function deployment. Validation of the suitability of the test method is often required.
Content of a test method
Quality management systems usually require full documentation of the procedures used in a test. The document for a test method might include:
 Descriptive title
 Scope over which class(es) of materials or articles may be evaluated
 Date of last effective revision and revision designation
 Reference to most recent test method validation
 Person, office, or agency responsible for questions on the test method, updates, and deviations.
 The significance or importance of the test method and its intended use.
 Terminology and definitions to clarify the meanings of the test method
 A listing of the types of apparatus and measuring instrument (sometimes the specific device) required to conduct the test
 Safety precautions
 Required calibrations and metrology systems
 Environmental concerns and considerations
 Sampling procedures: How samples are to be obtained, and Number of samples (sample size).
 Conditioning or required environmental chamber: temperature, humidity, etc., including tolerances
 Preparation of samples for the test and test fixtures
 Detailed procedure for conducting the test
 Calculations and analysis of data
 Interpretation of data and test method output
 Report: format, content, data, etc.
Test Method Validation
Test methods are often scrutinized for their validity, applicability, and accuracy. It is very important that the scope of the test method be clearly defined, and any aspect included in the scope is shown to be accurate and repeatable through validation.
Test method validations often encompass the following considerations:
 Accuracy and precision: Demonstration of accuracy may require the creation of a reference value if none is yet available.
 Repeatability and Reproducibility, sometimes in the form of a Gauge R&R.
 Range, or a continuum scale over which the test method would be considered accurate. Example: 10 N to 100 N force test.
 Measurement resolution, be it spatial, temporal, or otherwise.
 mathematics, the symbolic method in invariant theory is an algorithm developed by Arthur Cayley, , , and in the 19th century for computing invariants of algebraic forms. It is based on treating the form as if it were a power of a degree one form.
Symbolic notation
The symbolic method uses a compact but rather confusing and mysterious notation for invariants, depending on the introduction of new symbols a, b, c, ... (from which the symbolic method gets its name) with apparently contradictory properties.
Example: the discriminant of a binary quadratic form
These symbols can be explained by the following example from . Suppose that
 \displaystyle f(x) = A_0x_1^2+2A_1x_1x_2+A_2x_2^2
is a binary quadratic form with an invariant given by the discriminant
 \displaystyle \Delta=A_0A_2A_1^2
The symbolic representation of the discriminant is
 \displaystyle 2\Delta=(ab)^2
where a and b are the symbols. The meaning of the expression (ab)^{2} is as follows. First of all, (ab) is a shorthand form for the determinant of a matrix whose rows are a_{1}, a_{2} and b_{1}, b_{2}, so
 \displaystyle (ab)=a_1b_2a_2b_1
Squaring this we get
 \displaystyle (ab)^2=a_1^2b_2^22a_1a_2b_1b_2+a_2^2b_1^2
Next we pretend that
 \displaystyle f(x)=(a_1x_1+a_2x_2)^2=(b_1x_1+b_2x_2)^2
so that
 \displaystyle A_i=a_1^{2i}a_2^{i}= b_1^{2i}b_2^{i}
and we ignore the fact that this does not seem to make sense if f is not a power of a linear form. Substituting these values gives
 \displaystyle (ab)^2= A_2A_02A_1A_1+A_0A_2 = 2\Delta
Higher degrees
More generally if
 \displaystyle f(x) = A_0x_1^n+\binom{n}{1}A_1x_1^{n1}x_2+\cdots+A_nx_2^n
is a binary form of higher degree, then one introduces new variables a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2}, with the properties
 f(x)=(a_1x_1+a_2x_2)^n=(b_1x_1+b_2x_2)^n=(c_1x_1+c_2x_2)^n=\cdots
What this means is that the following two vector spaces are naturally isomorphic:
 The vector space of homogeneous polynomials in A_{0},...A_{n} of degree m
 The vector space of polynomials in 2m variables a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2}, ... that have degree n in each of the m pairs of variables (a_{1}, a_{2}), (b_{1}, b_{2}), (c_{1}, c_{2}), ... and are symmetric under permutations of the m symbols a, b, ....,
The isomorphism is given by mapping a''a, b'b, .... to A_{j}. This mapping does not preserve products of polynomials.
More variables
The extension to a form f in more than two variables x_{1}, x_{2},x_{3},... is similar: one introduces symbols a_{1}, a_{2},a_{3} and so on with the properties
 f(x)=(a_1x_1+a_2x_2+a_3x_3+\cdots)^n=(b_1x_1+b_2x_2+b_3x_3+\cdots)^n=(c_1x_1+c_2x_2+c_3x_3+\cdots)^n=\cdots
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Answers:In solving a PDE, separation of variables means that you write the solution as the product of functions of one variable: v = f(t)*g(x) then f'(t)g(x) = (1/4) f(t)g''(x) or f'(t)/f(t) = (1/4) g''(x)/g(x) The LHS depends only on t, and the RHS depends only on x, but the equation is assumed to hold for all x and t. That can only be if both sides are equal to the same constant: f'(t)/f(t) = (1/4) g''(x)/g(x) = C Solving f'(t)/f(t) = C, we get f(t) = A e^(Ct) where A is an unknown constant. Solving (1/4) g''(x)/g(x) = C, and realizing that C is going to turn out to be negative, we get g(x) = B sin(2sqrt(C)x) + D cos(2sqrt(C)x) where B and D are unknown constants. To eliminate the square roots, rename C as p^2. The overall solution is then v(x,t) = A e^(p^2t) (B sin(2px) + D cos(2px)) One constant is redundant. We eliminate A: v(x,t) = e^(p^2t) (B sin(2px) + D cos(2px)) [*] Since dv/dx = 2p e^(p^2t) (B cos(2px)  D sin(2px)) The boundary conditions at x=0 and x=1 imply B = 0 (from BC at x=0) and Bcos(2p)Dsin(2p) = 0 ( from BC at x=1) Combining, we get Dsin(2p) = 0 B and D cannot both be zero (the solution would be 0, which does not satisfy the initial conditions), it must be that sin(2p) = 0 In other works, p is a multiple of pi/2: p=0, pi/2, 2*pi/2, 3*pi/2, 4*pi/2, 5*pi/2, ... In order to satisfy the initial conditions, we in general need all of the terms. We can sum together any number of terms of the form [*] above. We see now that we need to do this for particular values of p. Writing p = n*pi/2, v(x,t) = sum (n=0 to infinity) Dn e^((n*pi)^2t) cos(n*pi*x) where the Dn values are yet to be determined. We can determinine them by applying the initial condition v(x,0) = sum (n=0 to infinity) Dn e^((n*pi)^2*0) cos(n*pi*x) = sum (n=0 to infinity) Dn cos(n*pi*x) This is a cosine series that then must be equal to the given initial condition sum(n=0 to infinity) Dn cos(n*pi*x) = [ a if 0<= x < 0.5 [ 0 if 0.5 <= x < 1 Reference your text book, but I think that Dn = 2 * int [from x=0 to x=0.5] (initial condition) cos(n*pi*x) dx There may be a factor of 2 or something missing  I am going from memory. This is then Dn = 2* [sin(n*pi*x)/(n*pi)]  [from x=0 to x=0.5] = (2/(n*pi)) * [sin(n*pi/2)  0] = (2/(n*pi)) * sin(n*pi/2) = 0 if n is even (1)^n*2/(n*pi) if n is odd and we are done.
Answers:There are quite a few experiments outlined and described in the Journal of Parapsychology archive: http://findarticles.com/p/articles/mi_m2320 Most of these experiments do not demonstrate active Psi energies, but some have some statistical significance. The researchers, for the most part, are sincere in their efforts to come to a realistic, experimentally based conclusion. I hope that you can find something interesting ther TR. *********************************** Followup: Here's a brief description of one experiment I conducted.  2 subjects claimed the ability to perform remote viewing and/or telepathy. The goal of the experiment was to determine whether their claims could be verified. We theorized that we could legitimately test these subjects and come to a reasonable conclusion concerning their claim.  The subjects were separated in different houses, miles from each other. Observers were with the subjects to insure there was not communication between subjects. No cell phones or wireless electronic communication devises were in either location. A wired telephone was in each home, but was not used during the experiment. Nobody left either location during the experiment.  The subjects were asked to attempt to make contact and initiate a conversation on a topic defined by the researchers and hidden from the subject until the experiment began. The subjects had 14 hours to complete the conversation.  After 14 hours, the observers asked the subjects to describe the conversation that they had. The descriptions were documented by the observers and compared.  The results: The conversational records were very similar. The order of the topics discussed were the same. Exact phrases appeared in both summaries in the same order. Though the discussion was less than 10 sentences, both summaries listed the same topics being discussed in the same order in the same number of sentences. Each subject identified the speaker for each phrase, and both subjects connected the same phrases with the same speaker.  Conclusion: With the lack of electronic communication, and the hidden selection of the topic to be discussed by the observers, it was highly unlikely that the subjects had been able to prearrange their responses. The similarity of the responses, especially the length, specific word choices, and identification of the speakers that appeared in the summaries indicated a strong probability that there was a common knowledge between the subjects of what had been discussed. Testing appeared to have been successfully completed in this case. 2 other attempts to verify with the same subject using similar techniques did not show the same results. Postmortem: The experiments could have been better designed to eliminate the possibility of prearranged conversations between the subjects or the possibility that the observers were working together to falsify the results of the experiments. The additional steps would have made for better experimental design and should be employed in the future. Also, one test showing significantly different results from 2 other test cases does not show evidence of repeatable results. The results did not definitively show that there was communication between the individuals, but we did conclude that we were able to test the individuals for this ability. ************************************ My personal opinion in this case (not specifically scientifically based): Knowing the observers in this case and their motivations, I do not believe that there was any "cheating" occuring in these experiments. The results for these cases, though not the result of flawless expermental design, seem to accurately reflect the events. In one trial, the subjects showed strong signs of having communicated from a distance. The similarity of the data in that one case was so strikingly similar that it is unreasonable to believe that it is due to coincidence. If they actually had this ability, it was not an ability that was always available to them or was not consistently accurate. ***************************** This is just one experiment, and not a particularly spectacular one. It gives you a sense of the work that I have done, though it does not reflect how my style has changed over the years. The details aren't all there, but this really isn't the forum to go into *complete* experimental design or examine data. I hope that this information reflects what you were asking about.
Answers:Take equations 1 and 2 and eliminate a variable. Eliminate the same variable with equations 2 and 3. This will give you a system of 2 equations in 2 variables. Here you can eliminate one variable, and then back substitute to find the other variables. For example: x 2y+3z= 11 4x +y z = 4 2x y +3z= 10 Multiply the first equation by 4 and At the same time multiply the last equation by 2. 4x+8y12z = 44 4x +y z = 4 4x+2y 6z = 20 Next we add the second equation to the first and third equations. Doing this will eliminate the x variable from the first and third equations. 0x+9y13z = 40 4x +y z = 4 0x +3y 7z = 16 Then we can use the first and third equations and eliminate one of the two remaining variable while solving for the other.
Answers:manipulate one of the equations so its a variable by itself. for example x= 4 y Now plug that in for its counterpart in the other equation, so the new x would be 4 y to give you the equation (4y) y =2 Then solve for the variable that is left. 4 2y= 2 2y =6 y=3 Then plug that variable into the other equation to solve for the other variable x = 4 (3) x = 1
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