...le, where it occurs, by a new (for a given expression) variable leads to an expression with the same meaning. For example, in the expressions
...expression, whereas by writing $z$ everywhere instead of $z$ one obtains an expression with exactly the same meaning.
2 KB (315 words) - 19:45, 2 March 2018
...le the expression $B$ is called the consequence. The precise meaning of the expression $A\supset B$ differs in the classical, constructive and other approaches to
1 KB (166 words) - 16:47, 30 December 2018
...s) of a variable must not lead to an absurd expression. For example, in the expression $ \{ {( x, y) } : {x ^ {2} + y ^ {2} = z ^ {2} } \} $,
respectively, then in the expression $ f ( x, y) $
3 KB (500 words) - 19:40, 5 June 2020
...x$ with not more than a countable number of discontinuities has an analytic expression $A(x)$ involving only three operations (addition, multiplication, passing t
If there is at least one analytic expression describing a given function, there are infinitely many such expressions. Th
1 KB (210 words) - 13:18, 12 December 2013
A linguistic expression containing variables, in place of which one may substitute propositions, th
Sometimes a propositional form is an expression, constructed in analogy with a [[propositional formula]], in which symbols
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* the algebraic theory of [[regular expression]]s.
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...x$ as the name of the letter $x$, and is using "$x+3=2$" as the name of the expression $x+3=2$. If one says "12 is divisible by 2", then the term "12" is used in
...tors for distinguishing between the autonymous and non-autonymous use of an expression. However, such a differentiation may be difficult in certain cases. Special
2 KB (318 words) - 14:25, 30 December 2018
...ere are only axioms at the vertices of the derivation tree, then the formal expression at the end of the derivation is said to be deducible (or derivable) in the
...a derivation must satisfy the same requirement. The concept of a deducible expression in effective formal systems is, generally speaking, not effective.
3 KB (392 words) - 12:21, 19 August 2014
...al is equal to the number of permutations of $n$ elements. The more general expression
1 KB (162 words) - 13:41, 14 February 2020
A logical operator which serves to form propositions using the expression "for all x" . In formal languages the universal quantifier is most often d
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An expression indicating that one speaks about all $x$ of a measure space $X$ with the po
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...same syntactic structure. A specific axiom scheme is usually realized by an expression $\mathfrak A$ (which is most often formulated in a language different from
...ulated or unambiguously understandable rules for generating axioms using an expression $\mathfrak A$, an axiom scheme is usually referred to as the self-expressio
2 KB (337 words) - 16:00, 5 August 2014
(a "quadratic form modulo 2" ). The expression
...e is a symplectic basis on all elements of which $\psi_0$ vanishes; if this expression equals one, then there is a symplectic basis on all elements of which, exce
2 KB (287 words) - 07:17, 24 December 2017
...o make up the fraction. The numerator of an algebraic fraction $A/B$ is the expression $A$ (cf. [[Fraction|Fraction]]).
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The expression
The following expression is often also referred to as a symmetric difference:
1 KB (225 words) - 08:24, 6 June 2020
...ns, and $x$, $a$, $b$ are variables whose values are real numbers, then the expression $\int_a^bf(x)dx$ is a term with three parameters $a$, $b$, $f$, which denot
1 KB (225 words) - 22:30, 2 November 2014
An expression of the form
...the context of constructive logic) restrict the term "sequent" to mean an expression of the form
1 KB (231 words) - 13:27, 14 February 2020
...sion $\Gamma\vDash A$ is read as "$\Gamma$ semantically entails $A$" . The expression $\Gamma\vdash A$ is similarly read as "$\Gamma$ syntactically entails $A$"
2 KB (295 words) - 21:24, 8 December 2016
The expression "square" for $a\cdot a$ is (just as "cube" for $a\cdot a\cdot a$) a rem
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...umbers $p$ diverges also; see, e.g., [[#References|[a1]]], Thm. 427, for an expression of its partial sums.
1 KB (234 words) - 10:24, 10 December 2012
...make up the fraction. The denominator of an algebraic fraction $A/B$ is the expression $B$ (see [[Fraction|Fraction]]).
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The square root of the expression
The expression \eqref{*} itself is sometimes referred to as the mean-squared error or mean
2 KB (285 words) - 14:22, 30 December 2018
...equations" also occurs when the system in question is non-linear. By this expression one means a characteristic exponent of the system of equations in variation
2 KB (284 words) - 16:43, 4 June 2020
...about their values are called expressions. The first element of a list — an expression $ E $—
...of bound variables that denote the arguments of a function, and exp is the expression that computes the value of a function and contains $ x 1 \dots x n $
4 KB (620 words) - 22:17, 5 June 2020
...called the difference. Subtraction is denoted by $-$ (minus). Thus, in the expression
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An element directly following another element; more precisely, the expression "$b$ covers $a$ in the partially ordered set $(P,{<})$" means that $a < b
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...ce and $\mu$ is the mathematical expectation ($\mu$ must be positive). This expression is often used in its percentage form, viz., $V=100\sigma/\mu$ %. This defin
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A logical operation used in forming statements with the expression "for a certain x" ( "an x exists for which", "there exists an x such that
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More generally, an expression of the form $a^b$ is called a power (that of the form $x\to a^x$ a power fu
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The parameter $k$ which enters into the expression of the [[elliptic integral]] in Legendre normal form. For example, in the i
...\theta=k$ is called the modular angle. The modulus $k$ also enters into the expression of the [[Jacobi elliptic functions]], which arise from the inversion of ell
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...mal and minimal extensions]] of an operator defined by a given differential expression on the subspace of functions of compact support. The domains of definition
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The logical operation used for forming the expression "A and B" from two expressions $A$ and $B$. In formalized languages, the
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the expression $ y(m + 1)/y(m) $
The expression $ y (m +1 )/y (m) $
3 KB (496 words) - 09:54, 29 May 2020
...sgue space]] $L_p(E)$ with $0<p<1$, in which a quasi-norm is defined by the expression
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The expression
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and the latter is substituted in the expression for $ J( x) $,
The expression $ {J _ {1} } ( {x _ {0} } )( h) $,
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...point $(0,0)$ into a similar Euclidean $(u,v)$-plane. It is the coordinate expression of the bijection $\phi$ generated by the [[Bendixson sphere|Bendixson spher
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The problem of finding an asymptotic expression for
...numbers. Analogous to this problem is the problem of finding an asymptotic expression for
2 KB (314 words) - 11:02, 17 March 2023
A numerical factor in an algebraic expression, a known factor in front of a power of an unknown or a constant factor mult
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...is an operation that converts an expression in one logical language into an expression in another while preserving deductive properties. Immersion operations are
3 KB (395 words) - 21:23, 30 April 2014
...re satisfied, then $A$ must be true (sufficient conditions). Frequently the expression "necessary and sufficient" is replaced by "if and only if". Necessary an
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...deducible in $S_2$; 2) every axiom of $S_2$ is deducible in $S_1$; 3) if an expression $B$ follows immediately from expressions $A_1,\ldots,A_n$ by virtue of a de
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...sion $P_x'+Q_y'$ has constant sign (i.e. the sign remains unchanged and the expression vanishes only at isolated points or on a curve), then the system \eqref{*}
2 KB (364 words) - 15:57, 14 February 2020
A formula that gives an expression for the $n$-th derivative of the product of two functions in terms of their
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...atives, generally taken with a functionally transformed argument. Here, the expression of the functional transformation may include the unknown function, as a res
1 KB (145 words) - 19:04, 31 March 2017
then the expression $ A \cdot ( \Delta x) ^ {n} $
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Sometimes, a degree of a number $a$ is an expression of the form $a^b$ where $b$ is also a (suitable) number, see [[Power|Power]
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The differential expression
The expression (1) is sometimes written in the form
3 KB (480 words) - 22:14, 5 June 2020
An expression of the form
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The limit of the expression $(1+1/n)^n$ as $n$ tends to infinity:
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...alues of formulas of a given language, then a propositional function is any expression of the type $\Omega^n\to\Omega$ ($n\geq0$). These functions are interpreted
1 KB (154 words) - 17:37, 23 November 2014
and the expression via these zeros of the number of prime numbers not exceeding a real number
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An expression of the type
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Another expression for the condition number is $\kappa(A) = \dfrac{\sigma_{\max}}{\sigma_{\min
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an expression constructed from propositional variables (cf. [[Propositional variable|Prop
1 KB (139 words) - 13:57, 30 December 2018
The expression "exterior form of degree r on the space V" usually denotes a skew-symmetr
1 KB (155 words) - 19:38, 5 June 2020
See also: [[Composition (combinatorics)]], an expression of a natural numbers as an ordered sum of positive integers; [[Composition
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...l extension of the domain of summation or integration, or to reduce a given expression to another to which given formulas or transformations can be applied. Other
1 KB (147 words) - 19:35, 5 June 2020
The expression
In analogy with the Dirichlet kernel [[#References|[3]]], the expression
3 KB (508 words) - 23:39, 29 December 2021
...s, etc.). The value itself is called an interpretation of the corresponding expression.
...values of $x$, $y$ are, respectively, $6$ and $2.5$, then the value of the expression $x\cdot y$ is the number 15. As the value (interpretation) of a statement o
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of finite support by the expression
1 KB (160 words) - 10:37, 20 January 2024
is approximately equal to the expression obtained by the [[Ray method|ray method]]. On the shadowed part one sets $
The expression $ u _ {K} $
3 KB (486 words) - 16:22, 6 January 2024
...oint differential equation]]). Begin with a formally symmetric differential expression
3 KB (586 words) - 10:02, 15 June 2015
An expression of the form
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...e alphabet $A$ are defined inductively: 1) every letter of $A$ is a regular expression; and 2) if $R_1$ and $R_2$ are regular expressions, then so are $R_1 \cup R
...ssion defining this event; and the problem of synthesis: Given some regular expression, to construct an automaton representing the corresponding event.
5 KB (830 words) - 14:27, 12 November 2023
An argument of an operation; a grammatical construction signifying an expression that gives the value of the argument of an operation; sometimes the place o
1 KB (217 words) - 18:54, 19 October 2014
...electromagnetic field exerts on a moving electrically-charged particle. An expression of the Lorentz force $ \mathbf F $
is the velocity of light in vacuum. The expression for the Lorentz force is relativistically invariant (that is, it holds in a
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A linear expression $\sum_{i=1}^md_it_i^r$ in a region $U\subset\mathbf R^n$, where $t_i^r$ are
1 KB (211 words) - 15:34, 20 April 2014
A composition of a natural number $n$ is an expression of $n$ as an ordered sum of positive integers. Thus the compositions of $4
1 KB (143 words) - 14:20, 12 November 2023
...he arguments $x_1,\dots,x_n$ into the object expressed by the term $A$. The expression \eqref{*} is also called a Church $\lambda$-abstraction. This Church $\lamb
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The simplest expression of a language. It is a concatenation of words that has an independent meani
1 KB (203 words) - 05:16, 21 June 2013
which generalizes the expression given in [[Gegenbauer transform]].
3 KB (369 words) - 19:56, 16 January 2024
...ters provided in the heading of the procedure with the given identifier. An expression may contain function designators, which call the procedure for the computat
4 KB (632 words) - 17:21, 7 February 2011
in the expression
1 KB (210 words) - 08:28, 6 June 2020
...oordinates of a certain physical system that do not occur explicitly in the expression of the characteristic function of this system. When one uses the correspond
1 KB (239 words) - 14:39, 28 August 2014
...n the coadjoint representation are even-dimensional). To obtain an explicit expression for $ B _ \Omega $
see [[#References|[3]]]). The coordinate expression for the Berezin bracket is
4 KB (606 words) - 17:45, 4 June 2020
...ion may be divided into two stages. In its first stage, the initial regular expression is used to construct some automaton, not necessarily minimal, representing
which are included in the regular expression. The automata $ \mathfrak A _ {1} , \mathfrak A _ {2} $
7 KB (1,011 words) - 18:49, 5 April 2020
The expression "stochastic sequence" is rarely used in the West; one usually says "stoc
1 KB (216 words) - 23:31, 25 November 2018
An algebraic expression of the form
...ology on $A'$. Let $x_1,\ldots,x_n$ be elements of $\mathfrak{a}'$. Then an expression
6 KB (1,093 words) - 08:26, 16 March 2023
...s obtained from tables) or involves considerable difficulties (the analytic expression of the function is complicated).
5 KB (779 words) - 19:35, 5 June 2020
...X_1)$; $\cov(X, X) = DX = \var(X) $. The covariance naturally occurs in the expression for the variance of the sum of two random variables:
2 KB (232 words) - 10:53, 18 October 2014
An expression in Algol-68 may contain an assignment statement, or any sequence of stateme
...eralize such Algol-60 concepts as block, compound statement and conditional expression and statement. Collateral clauses signify non-ordered sets of component phr
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A [[Self-adjoint operator|self-adjoint operator]] generated by a differential expression
sometimes any operator generated by a quasi-differential expression analogous to $ l $
9 KB (1,365 words) - 12:24, 10 February 2020
be the [[Lamé coefficients|Lamé coefficients]] appearing in the expression for the square of the line element of the space in the curvilinear coordina
be the quantities appearing in the expression for the line elements $ d \sigma _ {i} $
4 KB (653 words) - 07:55, 25 April 2022
is the expression
2 KB (236 words) - 17:31, 5 June 2020
...e manifolds or else on a space dual to a space of this type. A differential expression is a mapping $ \lambda $
...ntial expression and the order of the differential operator defined by this expression.
17 KB (2,519 words) - 19:35, 5 June 2020
...o all domains $G_\alpha$ for sufficiently large $\alpha$. In this case, the expression
...ier sum of the function $f$ corresponding to the domain $G_\alpha$, and the expression
6 KB (1,047 words) - 11:37, 13 February 2024
...*) is closely connected with the [[Poisson integral|Poisson integral]]. The expression
...mportant and more difficult problem arises concerning the existence and the expression of the boundary values of the imaginary part $ v( z) $
5 KB (698 words) - 18:20, 26 January 2022
Taking $\phi = v _ { i }$ in (a10) gives the following expression for the acceleration:
...rmines $D \mathbf{v} / D t$ directly in terms of $\mathbf{x}$ and $t$; this expression therefore serves as a formula for acceleration in the spatial form.
12 KB (1,877 words) - 17:01, 1 July 2020
...s. A special class of function routines, the body of which is defined by an expression, has been introduced. It is possible to display the counting of natural num
2 KB (260 words) - 17:20, 7 February 2011
The expression
1 KB (242 words) - 14:34, 16 December 2012
An expression in the language of formal logic. An exact definition of a logical formula i
2 KB (252 words) - 16:42, 30 December 2018
If two spheres $(y)$ and $(z)$ intersect, the expression
2 KB (263 words) - 13:12, 7 April 2023
The expression
The expression
5 KB (717 words) - 08:28, 6 June 2020
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> E.T. Whittaker, "An expression of certain known functions as generalized hypergeometric functions" ''Bull
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...function]] $F(\lambda)$. As an estimator of this function one often uses an expression of the form
2 KB (288 words) - 13:47, 27 August 2014
...umber|$e$ (number)]]). More precisely, $p$ should be chosen to maximize the expression
2 KB (291 words) - 18:52, 11 December 2020
The same as [[Continued fraction|continued fraction]], i.e. an expression of the form
6 KB (886 words) - 17:03, 7 February 2011
...uted and assume one of two values 0 and 1 with probability of 1/2 each; the expression $S_n = \sum_{k=1}^n X_k$ will then give the number of successful trials in
2 KB (236 words) - 10:23, 8 February 2017
the expression
2 KB (245 words) - 08:07, 6 June 2020