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The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.
Multivalued functions of a complex variable have branch points. For example, for the nth root and logarithm functions, 0 is a branch point; for the arctangent function, the imaginary units i and −i are branch points. Using the branch points, these functions may be redefined to be single-valued functions, by restricting the range.
The preferences here can be represented by cardinal utility functions which take several variables (the attributes). [ 1 ] : 26–27 Such functions are the focus of the current article. The goal is to calculate a utility function u ( x 1 , . . . , x n ) {\displaystyle u(x_{1},...,x_{n})} which represents the person's preferences on lotteries of ...
The Burt table is the symmetric matrix of all two-way cross-tabulations between the categorical variables, and has an analogy to the covariance matrix of continuous variables. Analyzing the Burt table is a more natural generalization of simple correspondence analysis, and individuals or the means of groups of individuals can be added as ...
The g++ compiler implements the multiple inheritance of the classes B1 and B2 in class D using two virtual method tables, one for each base class. (There are other ways to implement multiple inheritance, but this is the most common.)
The first Cousin problem then asks for a meromorphic function on M such that is holomorphic on ; in other words, that shares the singular behaviour of the given local function. Now, let K be the sheaf of meromorphic functions and O the sheaf of holomorphic functions on M. The first Cousin problem can always be solved if the following map is ...
The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 × 2 contingency table. In principle, any number of rows and columns may be used. There may also be more than two variables, but higher order contingency tables are difficult to represent visually.
Let [a, b, c] be a primitive triple with a odd. Then 3 new triples [a 1, b 1, c 1], [a 2, b 2, c 2], [a 3, b 3, c 3] may be produced from [a, b, c] using matrix multiplication and Berggren's [11] three matrices A, B, C. Triple [a, b, c] is termed the parent of the three new triples (the children). Each child is itself the parent of 3 more ...