...and where it is stressed that only in this context the notion of a random variable becomes meaningful).
...n X(\omega)<x\}$ belongs to the class $\mathcal{A}$. Let $X$ be any random variable and $\mathcal{A}_X$ the class of subsets $C\subset\mathbf{R}^1$ for which $
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''object variable''
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''bound occurrence of a variable''
...nt of a bound variable, where it occurs, by a new (for a given expression) variable leads to an expression with the same meaning. For example, in the expressio
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''surplus variable''
A non-negative variable $y_i$ that is introduced for a (linear) constraint $\sum_ja_{ij}x_j\leq b_i
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$#C+1 = 36 : ~/encyclopedia/old_files/data/F041/F.0401660 Free variable,
''free occurrence of a variable''
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$#C+1 = 15 : ~/encyclopedia/old_files/data/P074/P.0704380 Predicate variable,
''second-order variable''
2 KB (229 words) - 08:07, 6 June 2020
$#C+1 = 46 : ~/encyclopedia/old_files/data/V096/V.0906080 Variable\AAhdirections method
...sed on operators that are equivalent in spectrum and suitable for use with variable coefficients and non-linear problems.
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$#C+1 = 116 : ~/encyclopedia/old_files/data/A110/A.1100220 Accessible random variable
An accessible random variable will be defined in terms of Borel cylinder functions, a special class of ac
11 KB (1,627 words) - 06:28, 26 March 2023
In applications of the variable-grid method, at each instant the working region is divided into a finite nu
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...s representations of solutions in terms of analytic functions of a complex variable.
...partial, complex-variable methods|Differential equation, partial, complex-variable methods]]),
11 KB (1,622 words) - 06:29, 30 May 2020
...ional vectors $x_1$ and $x_2$. The properties of a convex function of one variable are correspondingly generalized to functions of several variables; for exa
...valign="top"> N. Bourbaki, "Elements of mathematics. Functions of a real variable" , Addison-Wesley (1976) pp. Chapt. 1 Sect. 4 (Translated from French)</T
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...the representation of solutions by way of analytic functions of a complex variable.
of the complex variable $ z = x + iy $
30 KB (4,345 words) - 09:02, 21 January 2024
...valign="top"> G.M. Goluzin, "Geometric theory of functions of a complex variable" , ''Transl. Math. Monogr.'' , '''26''' , Amer. Math. Soc. (1969) (Transl
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...edia/old_files/data/A013/A.0103000 Approximation of functions of a complex variable
...chlet series, etc.). The theory of approximation of functions of a complex variable is intimately connected with other branches of complex analysis, and with m
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...= 73 : ~/encyclopedia/old_files/data/F042/F.0402120 Functions of a complex variable, theory of
...ex plane $ \mathbf C = \mathbf C ^ {1} $ (functions of a single complex variable) or on a set of points $ z = ( z _ {1} \dots z _ {n} ) $
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...heir local and global properties. The modern theory of functions of a real variable typically involves a wide application of set-theoretic methods, along, natu
Thus, the object studied in the theory of functions of a real variable is a function. About this concept N.N. Luzin [[#References|[3]]] wrote "It
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...of]]; [[Functions of a complex variable, theory of|Functions of a complex variable, theory of]]).
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''simple function (of a complex variable)''
...older, names for a [[Univalent function|univalent function]] of a complex variable.
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''bound occurrence of a variable''
...nt of a bound variable, where it occurs, by a new (for a given expression) variable leads to an expression with the same meaning. For example, in the expressio
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...ign to a [[Convex function (of a real variable)|convex function (of a real variable)]].
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...ual variable of the corresponding type (here also it is necessary to avoid variable collisions).
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$#C+1 = 15 : ~/encyclopedia/old_files/data/P074/P.0704380 Predicate variable,
''second-order variable''
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The curve representing the ends of the variable vector $x(t)$ ($t$ is a real variable, such as time) whose origin for all $t$ is a given fixed point $O$.
...ograph. For example, if the velocity of a moving point is represented by a variable vector $\mathbf{v}$, then by drawing the values of $\mathbf{v}$ at differen
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...ude characterizing the [[Dispersion|dispersion]] of the values of a random variable $ X $.
is the distribution function of the random variable. Another variable which is also occasionally considered is the Gini dispersion coefficient
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''surplus variable''
A non-negative variable $y_i$ that is introduced for a (linear) constraint $\sum_ja_{ij}x_j\leq b_i
445 bytes (72 words) - 18:21, 18 October 2017
$#C+1 = 36 : ~/encyclopedia/old_files/data/F041/F.0401660 Free variable,
''free occurrence of a variable''
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...and the set of conditional probabilities $\mathrm P_\theta$ of the random variable $X$ given $\Theta=\theta$. According to the [[Bayes formula|Bayes formula]]
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A function $f(z)$ of a complex variable $z$ which is single-valued in this domain and which has a finite derivative
[[Category:Functions of a complex variable]]
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.../> is a [[Convex function (of a real
variable)|convex function (of a real
variable)]] for <img align="absmiddle" border="0" src="https://www.encyclopediaofmat
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A [[periodic function]] $f(z)$ of the complex variable $z$ all periods $p$ of which are integer multiples of a single unique funda
...riod $2\omega\in X$. A non-constant continuous periodic function of a real variable is necessarily simply-periodic.
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The argument of a function is the variable (also called the independent variable) on which the value of the function depends.
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...ibly others) in accordance with the following rules: 1) each propositional variable is a propositional formula; and 2) if $A,B$ are propositional formulas, the
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...esis is called the hypothesis distribution. E.g., if one observes a random variable $X$, then the statement "X is subject to the Poisson law with parameter 1"
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...mber for each set of values of the parameters ($x$ in this term is a bound variable). Syntactically, terms are characterized by the fact that they can be subst
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...on a [[probability space]] $(\Omega,\mathcal{F},\mathbb{P})$, to a random variable $X$, defined in the following way: $X_n \stackrel{\mathrm{P}}{\rightarrow}
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''in the theory of functions of a complex variable''
[[Category:Functions of a complex variable]]
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