...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
565 bytes (96 words) - 06:07, 23 April 2023
An element directly following another element; more precisely, the expression "$b$ covers $a$ in the partially ordered set $(P,{<})$" means that $a < b
351 bytes (59 words) - 07:37, 24 January 2016
...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
500 bytes (77 words) - 19:25, 8 November 2014
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
732 bytes (107 words) - 05:42, 22 April 2023
More generally, an expression of the form $a^b$ is called a power (that of the form $x\to a^x$ a power fu
330 bytes (54 words) - 22:02, 11 April 2014
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
667 bytes (93 words) - 16:55, 7 February 2011
The logical operation used for forming the expression "A and B" from two expressions $A$ and $B$. In formalized languages, the
623 bytes (106 words) - 07:28, 12 August 2014
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
491 bytes (78 words) - 21:36, 29 May 2016
The expression
659 bytes (104 words) - 15:21, 10 April 2023
and the latter is substituted in the expression for $ J( x) $,
The expression $ {J _ {1} } ( {x _ {0} } )( h) $,
5 KB (687 words) - 08:27, 6 June 2020
...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
698 bytes (110 words) - 15:19, 17 July 2014
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
599 bytes (108 words) - 16:38, 11 April 2014
...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
878 bytes (131 words) - 14:36, 30 August 2014
...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} $
890 bytes (134 words) - 10:40, 20 January 2024
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
998 bytes (149 words) - 08:02, 6 June 2020
The limit of the expression $(1+1/n)^n$ as $n$ tends to infinity:
775 bytes (107 words) - 15:10, 30 December 2018
...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
1 KB (160 words) - 20:17, 18 October 2014
An expression of the type
712 bytes (119 words) - 20:23, 1 January 2019
Another expression for the condition number is $\kappa(A) = \dfrac{\sigma_{\max}}{\sigma_{\min
974 bytes (157 words) - 19:31, 15 December 2020
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
7 KB (1,091 words) - 18:50, 14 August 2014
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
1 KB (158 words) - 14:03, 28 June 2020
...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
4 KB (546 words) - 04:11, 6 June 2020
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
1 KB (214 words) - 17:18, 14 February 2020
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
6 KB (897 words) - 20:29, 5 December 2023
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
2 KB (298 words) - 15:09, 14 February 2020
...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
in which the expression
2 KB (252 words) - 22:14, 5 June 2020
the space integral in (2) disappears, and one obtains an expression for the sum of the indices $ \chi _ {F} $
i.e. an expression for the degree of the mapping from the surface $ P $
5 KB (718 words) - 22:15, 5 June 2020
...name by N. Aronszajn and K.T. Smith in 1961. More important than the exact expression for the kernel is the fact that it is a suitable modification of the (Marce
5 KB (766 words) - 20:14, 19 November 2023
are integers, the binary quadratic form is said to be integral. The expression $ d = ac - {b ^ {2} } /4 $
is called the discriminant or determinant of the binary quadratic form. The expression $ b ^ {2} - 4ac $
7 KB (977 words) - 15:17, 31 March 2024
A linguistic expression to denote a specified object. The object denoted by a given name is called
2 KB (323 words) - 19:06, 29 March 2024
...ons simultaneously executed on distinct calculators (processors). E.g., the expression
can be transformed into the equivalent expression
11 KB (1,714 words) - 03:17, 5 June 2016
The clear-cut fixing of linguistic means of expression that can be achieved in a formalized language enables one to eliminate vagu
...e with the semantics of the language, a name form denotes an object, and an expression form denotes a judgement. Variables are said to belong to or to occur in th
9 KB (1,407 words) - 19:01, 21 November 2018
...p" is used instead of supersolvable. The literal translation of the Russian expression is fully-solvable Lie group.
2 KB (303 words) - 18:20, 12 December 2019
...eoretical geodesy, the probability density of random errors is given by the expression
2 KB (312 words) - 16:10, 19 August 2014
...al operator by difference operators]]). One says that the finite-difference expression $ L _ {h} u _ {h} = 0 $,
consists in replacing each derivative in the expression $ Lu $
6 KB (908 words) - 14:48, 7 April 2020
Another common notation and an expression by hypergeometric functions is:
2 KB (323 words) - 20:19, 16 March 2024
...ipal significance of the Boltzmann $H$-theorem consists in the mathematical expression of the fundamental assumptions of macroscopic thermodynamics, according to
2 KB (326 words) - 17:14, 30 December 2018
The expression "pseudo-periodic function" is also used to indicate a function with a pse
2 KB (319 words) - 08:08, 6 June 2020
...on $E ^ { 2 k }$ which is globally defined and has, in any chart, the local expression
...}$ in the local expression for the volume form, the components in the local expression of $\mathcal{E} ( L )$ are slightly modified from above to
17 KB (2,575 words) - 17:45, 1 July 2020
...he structure of the curve near a double point one considers the sign of the expression
2 KB (417 words) - 11:59, 26 March 2023
The simplest form of an algebraic expression, a [[Polynomial|polynomial]] containing only one term.
2 KB (376 words) - 08:01, 6 June 2020
A primitive model is an expression whose value is a line, and the success of a comparison consists of the occu
is a line expression whose value in a successful comparison replaces the selected subline in $
6 KB (915 words) - 08:14, 6 June 2020
is rational expression in $ z $,
i.e. an expression obtained from an independent variable $ z $
8 KB (1,257 words) - 03:49, 4 March 2022
that is, a linear expression in the vectors $ \partial x ^ {i} / \partial u $,
2 KB (379 words) - 08:11, 6 June 2020
A rational expression $ y = y( x _ {1} \dots x _ {n} ) $
be a rational expression in $ x _ {1} \dots x _ {n} $
7 KB (1,042 words) - 19:53, 16 January 2024
A continued fraction is an expression of the form
are finite or infinite sequences of complex numbers. Instead of the expression (1) one also uses the notation
11 KB (1,649 words) - 11:41, 4 September 2013
the expression for the scalar product of a vector with itself is a semi-definite quadratic
3 KB (376 words) - 20:16, 10 January 2024
...toroidal harmonic or a surface toroidal harmonic, this in contrast with the expression (*) which, as a function of the three variables $ ( \sigma , \tau , \phi
3 KB (366 words) - 09:57, 10 March 2021
...ated by $ u $ and $ v $ is free. The Campbell-Hausdorff formula provides an expression for $ u \circ v $ as a power series in $ u $ and $ v $:
The first investigation of the expression $ w $ is due to J.E. Campbell. F. Hausdorff ([[#References|[2]]]) proved th
6 KB (1,020 words) - 17:41, 4 May 2017
The expression between square brackets in (4) can be rewritten in the form
In an extremal field the expression (5) is the total differential of some function of $ x , y _ {1} \dots y _
8 KB (1,167 words) - 20:20, 10 January 2024
The expression $ \delta f( x _ {0} , h) $
3 KB (391 words) - 14:29, 15 April 2023
...nomials of degree $m$ — for example, the real and the imaginary part of the expression $(x_1+ix_2)^m$. If $n=3$, the number of linearly independent homogeneous po
2 KB (365 words) - 13:05, 14 February 2020
The differential expression
3 KB (443 words) - 11:10, 30 December 2018
The expression $b^2-4ac$ is called the [[Discriminant|discriminant]] of the equation. It i
2 KB (384 words) - 07:34, 18 December 2014
...eir world lines time-like geodesics or isotropic geodesics. This fact is an expression of the [[Law of inertia|law of inertia]] in relativity theory.
3 KB (393 words) - 08:10, 6 June 2020
...d elementary positive-definite kernels with respect to a given differential expression [[#References|[1]]].
3 KB (383 words) - 08:07, 6 June 2020
A formula giving an expression for the derivative of a [[Trigonometric polynomial|trigonometric polynomial
3 KB (397 words) - 20:25, 10 January 2021
and an expression of the form $ B _ {N} A ( B _ {N} ( \lambda - \lambda _ {0} ) ) $.
3 KB (480 words) - 08:22, 6 June 2020
and the expression for the Larmor radius takes the form
3 KB (435 words) - 12:41, 1 November 2023
An expression of the type
8 KB (1,155 words) - 17:43, 6 January 2024
In the semantics adopted by [[#References|[a3]]], every expression of a theory $ {\mathcal T} $
...ermined in an essentially unique way and depend on the formal aspect of the expression and on valuation of the constants and variables occurring in it. Therefore,
17 KB (2,488 words) - 06:37, 26 March 2023
...tudes are neglected, and the deformation tensor \eqref{*} is defined by the expression:
4 KB (616 words) - 15:37, 14 February 2020
take only a finite number of values, the expression for $ I ( \xi , \eta ) $
4 KB (517 words) - 16:27, 6 January 2024
be a formal self-adjoint differential expression on the interval $ ( a, b) $,
be an elliptic differential expression of the second order in a region $ G $
20 KB (2,924 words) - 19:38, 5 June 2020
...formed on $x_1,\dots,x_n$" ; let $ y (x _{1} \dots x _{n} ) $ denote the expression in quotation marks. Secondly, there is the decomposition of the object doma
...$ and $ \exists v \ (v \in x \ \& \ \phi ) $ , respectively, and the expression $ u \subseteq v $ is an abbreviation for $ \forall z \ (z \in u \ \s
8 KB (1,261 words) - 20:30, 13 December 2019
denotes that the entire expression before it is to be rewritten with the indices $ j $
Consequently, the geodesics in such a space have the local expression $ {\overline{x}\; } ^ {i} = a ^ {i} s + b ^ {i} $,
10 KB (1,411 words) - 10:58, 29 May 2020
The expression obtained after simplification is:
3 KB (465 words) - 08:28, 6 June 2020
...</TR><TR><TD valign="top">[1b]</TD> <TD valign="top"> J.C. Burkill, "The expression of area as an integral" ''Proc. London Math. Soc. (2)'' , '''22''' (1924)
3 KB (563 words) - 09:54, 27 November 2018
A quantitative expression for the error of an approximation. When the discussion is about the approxi
4 KB (599 words) - 07:22, 26 March 2023
the required orthonormal system is obtained. An explicit expression of the vectors $ b _ {i} $
4 KB (542 words) - 08:33, 13 May 2022
The expression
3 KB (504 words) - 08:28, 6 June 2020
An abbreviated notation for the expression
3 KB (550 words) - 10:36, 23 May 2017
is an expression of the type $ ( \omega ) = P _ {1} ^ {\alpha _ {1} } {} \dots P _ {n} ^ {
conversely, the expression $ \omega = R (z, w) dz $
11 KB (1,603 words) - 16:08, 1 April 2020
...is denoted by $x$. For a ''multiindex'' $\a=(\a_1,\dots,\a_n)\in\Z_+^n$ the expression $x^\a$ denotes the product, $x_\a=x_1^{\a_1}\cdots x_n^{\a_n}$. Other expre
3 KB (512 words) - 06:16, 13 June 2022
This proves, in particular, that not every expression
...o variables. This is a difference from functions of one variable, where any expression $ A ( x) d x $
15 KB (2,211 words) - 11:44, 26 March 2023
...lass operator (cf. also [[Nuclear operator|Nuclear operator]]). An explicit expression for $E ( a )$ is not known yet (as of 2000), apart from special cases relat
...{ r } ^ { 2 } - \beta _ { r } ^ { 2 } )$. An explicit, but more complicated expression is known for the constant $E$. It has turned out that in some cases the Fis
13 KB (1,838 words) - 07:22, 13 February 2024
...interfacial energy or surface tension. To first order in an expansion, the expression for the total free energy takes the form
...abelled $c _ { \alpha }$ and $c _ { \beta } > c _ { \alpha }$. A similar expression for free energy was introduced much earlier by J.D. van der Waals in [[#Ref
11 KB (1,642 words) - 16:59, 1 July 2020
the last expression in \eqref{a7} would follow also from \eqref{a4} in light of the definition
4 KB (577 words) - 14:03, 11 November 2023
commute under multiplication, then the expression
4 KB (598 words) - 05:33, 19 March 2022
...algebraically in $x$, $\ln x$ and $e^x$ up to order $x\ln^{-n}x$, then the expression must be \eqref{*}. After this, Chebyshev introduced two new distribution fu
3 KB (542 words) - 16:58, 14 February 2020
is the effective frequency of pulse transmission, defined by the expression:
4 KB (585 words) - 08:27, 6 June 2020
An approximate expression for the error is given by the quantity
4 KB (538 words) - 17:45, 20 January 2022
by a linear expression in $ h $,
6 KB (918 words) - 19:35, 5 June 2020
i.e. the expression
6 KB (840 words) - 16:48, 20 January 2024
Mathematical probability is an expression of the qualitatively specific relation between random and non-random events
...lity of certain statements concerning individual events is no longer a mere expression of the subjective belief that the event will or will not take place. Such a
9 KB (1,350 words) - 18:22, 27 May 2012
...se of a uniform shear, the crack face displacements are approximated by the expression
There is no general expression for the stress intensity factor for any shape other than circular. Some par
10 KB (1,410 words) - 19:39, 5 June 2020
An expression
4 KB (573 words) - 12:52, 6 January 2024
gives the following expression for the first variation of the functional:
4 KB (627 words) - 08:01, 6 June 2020
...on a smooth variety of dimension $n$; e) the [[Künneth formula]], giving an expression for the homology spaces of certain sheaves on a product of varieties; f) co
4 KB (573 words) - 18:20, 17 April 2017
is the expression
4 KB (557 words) - 10:41, 20 January 2024
It is considered to be applicable in the concretization of an expression of the form $ \mathbf K \phi {\mathcal E} \dot{-} $,
4 KB (579 words) - 08:10, 6 June 2020
is an expression $ \sum _ {i = - N } ^ {M} a _ {i} X ^ {i} $,
8 KB (1,203 words) - 10:36, 20 January 2024
If two circles $(y)$ and $(z)$ intersect, the expression
4 KB (597 words) - 18:10, 1 June 2023
In the expression (2), called the Lagrange interpolation formula for equidistant nodes, the c
4 KB (640 words) - 14:37, 13 January 2024
...better than before the enormous "intermediate expression swellintermediate expression swell" that so often takes place in exact computations. Still, there are s
9 KB (1,292 words) - 20:51, 18 September 2016
The same expression can be obtained if one uses the operator form of (2) and the differentiatio
4 KB (608 words) - 13:08, 18 June 2020
...ds of coding and decoding. Owing to the difficulty of obtaining an accurate expression for $ P _ {e} ^ { \mathop{\rm opt} } $,
6 KB (837 words) - 11:58, 7 January 2024
An expression composed of one or more functions, their partial derivatives of various ord
5 KB (725 words) - 19:35, 5 June 2020
A series defined by the expression
4 KB (578 words) - 11:31, 21 March 2022
The expression (2) with $ \max $
8 KB (1,082 words) - 17:09, 17 January 2024
in the expression for the work of the given active forces $ F _ \nu $
4 KB (661 words) - 14:38, 10 March 2024
...ants, $f(x)$ is a known function and $\phi(x)$ is the unknown function. The expression $(x-s)^{-\alpha}$ is called the kernel of the Abel integral equation, or Ab
4 KB (633 words) - 19:23, 22 December 2018
(The term "square metric" refers to the expression $ [ \sqrt n (F _{n} (x) - F (x))]^{2} $,
4 KB (572 words) - 11:08, 26 March 2023
The differential expression
5 KB (694 words) - 16:29, 14 January 2024
...efinitions of completeness are based on a single general idea, the concrete expression of which depends on the particular type of space. The general feature in th
5 KB (764 words) - 17:23, 9 December 2013
then the expression "a is visible from b in K" means that the segment $ [ a, b] $
4 KB (649 words) - 22:10, 5 June 2020
...) for sufficiently regular fields then yields the following pointwise local expression of the Clausius–Duhem inequality:
...become customary to give the name Clausius–Duhem inequality, per se, to the expression of equation (a3) (also called the residual dissipation inequality) obtained
9 KB (1,358 words) - 17:44, 4 June 2020
...ysics, mathematical problems in]]), equal to a normalization constant in an expression for the density (or for the density matrix in a quantum system) in a canoni
5 KB (650 words) - 14:34, 13 January 2024
An expression of the form
5 KB (741 words) - 17:20, 24 April 2016
be a self-adjoint differential expression of order $ 2n $
4 KB (589 words) - 16:33, 14 January 2024
If the integrand $f$ is given by a Fortran-like expression, then one can use symbolic methods, interval-methods or numerical methods.
4 KB (650 words) - 15:07, 14 February 2020
..., after having replaced the integrals in (5) by sums and having obtained an expression interconnecting the values of $ \phi $
4 KB (633 words) - 19:42, 19 January 2024
atom is an expression of the form $ \mathbf r ( t _ {1} \dots t _ {n} ) $
is an expression and $ \alpha $
15 KB (2,311 words) - 04:11, 6 June 2020
...be made more precise as follows. A property (more accurately, a linguistic expression for the relevant property) is called non-predicative if it contains a bound
4 KB (713 words) - 17:07, 14 February 2020
...give an exact meaning to the above-said one must specify the meaning of the expression "the mappings $f_t$ continuously depend on $t$" . The most natural procedu
5 KB (806 words) - 12:44, 15 December 2019
An expression of the form
5 KB (776 words) - 08:31, 23 November 2023
The expression
6 KB (901 words) - 17:32, 5 June 2020
is a formal expression of the form $ F _ {+} ( x + i0) - F _ {-} ( x - i0) $,
The expression $ f ( x) $
17 KB (2,506 words) - 16:24, 22 February 2021
The expression on the right-hand side equals the index $ \mathop{\rm ind} _ {0} f ( \p
5 KB (749 words) - 18:48, 5 April 2020
The expression obtained for the Hamilton function has the same structure as in the classic
5 KB (753 words) - 19:43, 5 June 2020
...ctor]]), the matrix of $T\alpha (m)$ is given by the Jacobian matrix of the expression for $\alpha$ in the local coordinates.
5 KB (893 words) - 11:45, 20 May 2017
...produce arbitrary values. If there is a difference between data types in an expression, there is automatic conversion to the type required in the concrete context
4 KB (681 words) - 12:48, 16 July 2014
...$B$ under $m$ is a $\Sigma$-subalgebra $m^{-1}(B')\subseteq A$ of $A$. The expression $m^{-1}(B')$ can be defined analogously to $m(A')$ and is omitted here {{
13 KB (2,332 words) - 14:56, 21 April 2013
...eks estimators based on the observations of the parameters involved in this expression for the spectral density (see [[Maximum-entropy spectral estimator|Maximum-
5 KB (740 words) - 19:58, 16 January 2024
...let series (see, for example, [[#References|[a2]]]), which give an integral expression of the Dirichlet polynomial $p _ { n } ( s ) = \sum _ { m = 1 } ^ { n } a _
5 KB (706 words) - 17:03, 1 July 2020
it yields the expression
5 KB (745 words) - 09:18, 6 January 2024
by integrating the expression $ (v,\ Lu) $
5 KB (747 words) - 22:14, 28 January 2020
-
4 KB (718 words) - 15:32, 11 November 2023
th order finite-difference equation (10) gives an expression for $ u _ {z} $
be given and suppose it is required to construct the expression $ \phi ^ {n} ( x) $(
23 KB (3,277 words) - 19:16, 16 January 2024
and its expression). The inversion formula for the Fourier transform is very simple:
6 KB (971 words) - 12:28, 1 February 2020
One can carry out the Fermionic integration using the expression
...auge invariance requires justification and is generally false: Although the expression $ \| F \| ^ {2} $
27 KB (3,739 words) - 06:51, 26 March 2023
...a4]</TD> <TD valign="top"> J. Hilgevoord, J. Uffink, "The mathematical expression of the uncertainty principle" F. Selleri (ed.) A. van der Merwe (ed.) G.
5 KB (746 words) - 07:22, 6 May 2022
...><TR><TD valign="top">[a4]</TD> <TD valign="top"> H. Kargupta, "The gene expression messy genetic algorithm" , ''Proc. IEEE Internat. Conf. on Evolutionary Com
6 KB (810 words) - 15:55, 10 July 2014
The basic problem is to find as accurate as possible an expression of the sum function, and for a sum function which does not have asymptotics
6 KB (821 words) - 01:34, 26 April 2022
...l reaction, its functional dependence is given empirically by the Arrhenius expression: $ k = A { \mathop{\rm exp} } ( - {E / {( RT ) } } ) $.
5 KB (707 words) - 16:08, 1 April 2020
then if this system is in involution, the expression
6 KB (940 words) - 19:10, 11 January 2024
...hree. This is the smallest value of the exponent that leads to a polynomial expression for the [[Differential invariant|differential invariant]]
5 KB (686 words) - 16:45, 1 July 2020
such as its support, its discrete part and its full explicit expression. In the case of a real non-compact semi-simple Lie group this program was s
6 KB (796 words) - 08:06, 6 June 2020
...ctric field in a frame $R _ { C } ( x , t )$ co-moving with the charge. The expression of $\mathbf{E} ^ { \prime }$ in terms of the electric field $\mathbf E$ in
...re of two types: through the above-given expressions and through the energy expression. The latter contains such celebrated effects as piezo-electricity (more gen
12 KB (1,786 words) - 17:46, 1 July 2020
...erally speaking, alter the expression, but not the function realized by the expression. For instance, the absorption laws yield the law of idempotency $ x \lor
Thus, the expression $ x \& y \& z + x \& y + 1 $
27 KB (3,984 words) - 15:58, 22 December 2019
...mporal relations, from the point of view of relativistic physics, finds its expression in the presence of vectors of various natures in space-time: space-like, ti
6 KB (840 words) - 13:26, 15 August 2014
...noted by $(fx)$. For simplicity the brackets are often omitted, so that the expression $fx_1\dots x_n$ stands for $(\dots(fx_1)\dots x_n)$. A function $f$ satisfy
5 KB (843 words) - 09:41, 20 September 2014
...$, find the necessary and sufficient conditions for the existence of and an expression for a positive distribution (a non-decreasing function with possibly infini
6 KB (888 words) - 18:32, 21 December 2020
This expression has the meaning of the free-energy density for a system with Hamiltonian $
6 KB (788 words) - 10:59, 29 May 2020
...eld or a larger segment of rationals). The extension is done using the same expression, i.e., without increasing the degree of the colouring polynomial.
...check is trickier.) A transparent proof is the collection of values of this expression, where summation is taken only over the first several variables. The other
11 KB (1,701 words) - 10:26, 24 August 2014
Then the expression
7 KB (945 words) - 19:50, 29 May 2020
...ferential equations]]), apply it to the system (a4), and make the resulting expression vanish on the solution set of (a4).
...are now independent of each other. It is tacitly assumed that the resulting expression is now a polynomial in the $ u _ {\mathbf J} ^ {l} $.
23 KB (3,178 words) - 22:16, 5 June 2020
All three cases can be reduced to a uniform expression by the choice of coordinates $ z ^ {i} $:
6 KB (845 words) - 18:59, 11 January 2024
a) an expression for an algebraic inverse to subdivision;
b) an expression for the homotopy addition lemma;
13 KB (1,937 words) - 13:10, 24 December 2020
In expression (2) the value of the Robin constant $ \gamma ( R ; p _ {0} ) $
6 KB (914 words) - 10:37, 5 March 2022
...Thus, the most important properties of the variance are connected with the expression for the variance $\Var(X_1+\cdots+X_n)$ of the sum of random variables $X_1
7 KB (1,127 words) - 20:19, 27 January 2020
and their first and second derivatives at that point. Such an expression for $ K $
6 KB (891 words) - 19:41, 5 June 2020
By studying the properties of the sum \eqref{eq1}, Gauss found the exact expression for the modulus of this sum:
6 KB (921 words) - 19:40, 29 March 2024
...at the angle between their position radii is no longer inside an irrational expression.
the last expression yields
18 KB (2,501 words) - 14:54, 7 June 2020
is the Kronecker delta. Corresponding to formula (4) there is an expression for the correlation function of the form
Corresponding to the spectral representation (5), there is the following expression for the correlation function $ B ( r) $:
17 KB (2,406 words) - 20:00, 12 January 2024
An expression analogous to the polar decomposition has been obtained for operators on a [
7 KB (1,052 words) - 08:06, 6 June 2020
An expression of the form
6 KB (915 words) - 05:56, 13 June 2022
are functions chosen so that the expression (2) should satisfy equation (1) up to quantities of order $ \epsilon ^ {m
8 KB (1,178 words) - 22:15, 5 June 2020
...on so that the inequality becomes an equality. Jenkins' theorem is an exact expression and generalization of Teichmüller's principle (stated without proof, [[#Re
7 KB (1,016 words) - 17:42, 13 January 2024
...n completely described. Boundary value problems take a simple form when the expression $ L _ {0} ^ \prime $
then the spectrum of the differential operator generated by the expression $ l u = - u ^ {\prime\prime} + q ( x ) u $
32 KB (4,393 words) - 08:22, 6 June 2020
(In the notation $x^\g$, the expression $x^{\a\b}$ is to be read as $(x^\a)^\b$, i.e. first $\a$, then $\b$.)
7 KB (1,262 words) - 20:15, 27 September 2016
...cannot be expressed in terms of only one elementary function. When such an expression is possible, then (1) is said to be a [[Pseudo-elliptic integral|pseudo-ell
11 KB (1,593 words) - 19:37, 5 June 2020
...contacts, intermediate contacts and windings of the circuit. An asymptotic expression for the complexity of the simplest relay-contact circuit realizing the most
8 KB (1,204 words) - 01:44, 5 March 2022
An expression
7 KB (1,052 words) - 14:55, 7 June 2020
well be the first expression of an indeterministic world-view.
formulations of the Gaussian law as an expression of the differential
16 KB (2,419 words) - 16:35, 14 August 2023
are different. Multiplying out in the expression
the remaining expression will correspond to a dead-end test. Thus, considering the above example, wi
23 KB (3,205 words) - 08:10, 6 June 2020
in space, the analytic expression of a motion is:
7 KB (1,100 words) - 03:33, 21 March 2022
is some differential expression. If one seeks solutions of (1) of the form
15 KB (2,091 words) - 19:37, 5 June 2020
(see, e.g., [[#References|[a7]]]). Therefore the limiting expression $1 / x ( x + 1 )$ is by no means unique and there are as many possible limi
...rences|[a22]]] on problems of biological taxonomy, introduced the following expression for $\alpha ( x )$:
26 KB (3,987 words) - 14:54, 18 March 2023
The MacWilliams formula now gives an explicit expression for $ W _ {H _ {m} } $
6 KB (942 words) - 02:58, 18 May 2022
...representable event (super-event) may be effected with the aid of a regular expression (cf. [[Regular event|Regular event]]). Such events may also be specified as
...behaviour of a finite, non-deterministic acceptor is described by a regular expression, as in the case of a deterministic acceptor. Other generalizations of finit
25 KB (3,544 words) - 07:31, 26 March 2023
for which the expression $ {\mathsf E} ( Y - g ( X) ) ^ {2} $
10 KB (1,524 words) - 08:10, 6 June 2020
...s/b/b015/b015110/b01511067.png" />. Generalization of formula (*) yields an
expression for the balayaged measure <img align="absmiddle" border="0" src="https://ww
21 KB (2,931 words) - 16:56, 7 February 2011
are integers, to find a similar expression for $ e $.
8 KB (1,278 words) - 19:39, 5 June 2020
given by the differential expression $ P ( x, \partial / \partial x) $,
7 KB (1,032 words) - 19:27, 26 March 2023
with respect to Lebesgue measure is given by the expression
9 KB (1,282 words) - 08:24, 6 June 2020
of the manifold defined by (7). In (8), $F$ denotes the expression
9 KB (1,496 words) - 08:59, 13 February 2024
...some mathematical (or even non-mathematical) theory, more precisely, as an expression of both its factual contents and its deductive structure. The general proce
17 KB (2,707 words) - 10:02, 25 April 2020
The expression (1) naturally includes the case of a system of Fredholm equations.
...e of (4) may be computed in a finite number of arithmetical operations. The expression $ \psi ( \widetilde{A} , \widetilde{f} ) $
20 KB (3,019 words) - 03:31, 14 June 2022
In this method, an explicit expression for the fundamental solution need not be specified, but if it is known, the
7 KB (1,101 words) - 17:33, 5 June 2020
...informant-speaker, whom the researcher asks questions of the type "Is this expression correct?" and "Do these two expressions have the same or a different mean
8 KB (1,194 words) - 08:24, 6 June 2020
then the explicit expression for the partial derivatives $ \partial f _ {j} / \partial x _ {i} $,
12 KB (1,760 words) - 08:00, 21 January 2024
...ial $\sigma ( \xi , x )$ are replaced by symmetric operator products in the expression $\sigma( \mathcal {D , X} )$. Harmonic analysis in phase space is a succinc
...orphism and there may be no spectral mapping property, so the commonly used expression "functional calculus" is somewhat optimistic.
17 KB (2,575 words) - 16:58, 1 July 2020
The expression for the wave field constructed with the aid of the ray method loses smoothn
8 KB (1,156 words) - 08:04, 6 June 2020
-
6 KB (960 words) - 08:11, 4 November 2023
...alysis|multi-dimensional statistical analysis]], serving for a quantitative expression and processing of the available information in accordance with the criterio
...optimality criterion is determined by the nature of the problem itself. The expression on the left-hand side of (3) is said to be the [[Discriminant function|disc
19 KB (2,811 words) - 19:36, 5 June 2020
.... Secondly, instead of a segment of a MacLaurin series, one may subtract an expression differing from it by a polynomial in the momenta of the same degree and hav
8 KB (1,152 words) - 08:11, 6 June 2020
...attractor, although the important attractors do possess this property.) The expression "complicated structure" is rather indefinite, as is the term "strange attra
7 KB (982 words) - 12:14, 18 August 2014
...in some element of $\gamma$. The concept of star refinability serves as an expression of the idea of unlimited division of a space, and can be interpreted as the
9 KB (1,401 words) - 14:04, 30 July 2014
(the expression under the root sign is the absolute value of the [[Gram determinant|Gram de
8 KB (1,344 words) - 08:28, 6 June 2020
...(x_1,\ldots,x_n)[v(x_1\leftarrow t_1,\ldots,x_n\leftarrow t_n)]\big)$. The expression $v(x_1\leftarrow t_1,\ldots,x_n\leftarrow t_n)$ denotes an assignment funct
8 KB (1,390 words) - 18:36, 11 December 2020
...in the formal variables $y _ { n }$, $n \in \mathbf{N} + 1 / 2$. The formal expression
8 KB (1,142 words) - 16:46, 1 July 2020
...the theory of the distribution of prime numbers. In particular, he found an expression for the difference $ \pi ( x) - \mathop{\rm li} x $
the following asymptotic expression for $ \pi _ {k} ( x) $
36 KB (5,530 words) - 08:29, 14 January 2024
...as equally probable; it is connected with the entropy of the system by the expression
9 KB (1,335 words) - 19:41, 5 June 2020
Its expression in terms of the coefficients of the series is
11 KB (1,638 words) - 11:32, 16 April 2023
...\dots,x_n(m))$, then $Xf$ is the function given in local coordinates by the expression
8 KB (1,509 words) - 05:24, 22 May 2017
the curl is defined by the expression
7 KB (1,148 words) - 18:18, 21 June 2020
An expression of the form
9 KB (1,497 words) - 10:44, 27 June 2015
Equation (8) is a mathematical expression of a conservation law, whence the term "energy inequality" , which is equi
In addition, (7) is usually derived from an expression such as $ ( Lu , Q u ) _ {2} $,
21 KB (3,008 words) - 17:33, 5 June 2020
...of convergence, later authors have given improved rates. To get a very good expression for the rate of convergence, one needs to be very much more careful over th
8 KB (1,270 words) - 16:56, 1 July 2020
...ch can be derived in classical predicate calculus. This theorem is an exact expression of the idea of a formalization of classical logic: In classical predicate c
9 KB (1,370 words) - 18:05, 22 September 2014
has the expression
A number of formal conditions on the expression (1) that guarantee that the operator is hypo-elliptic are known.
25 KB (3,768 words) - 09:07, 14 June 2022
A similar expression is obtained for $ | z | > 1 $.
12 KB (1,576 words) - 01:14, 21 January 2022
...scr E_{t_*}=(t-t_*)\frac d{dt}$ to check the condition at $t_*\in\CC$). The expression for $L$ can be transformed using the Leibnitz rule $\mathscr E(fg)=f\cdot\m
7 KB (1,237 words) - 11:48, 23 November 2023
...g base of Weierstrass' functions. It is also possible to obtain an explicit expression of the Weierstrass elliptic functions in terms of the Jacobi elliptic funct
11 KB (1,535 words) - 13:55, 18 May 2023
In view of (*), on may write the following expression for $ u $
10 KB (1,515 words) - 20:30, 29 May 2020
...and the number of bound states of the Schrödinger operator generated by the expression $- \nabla ^ { 2 } + q ( x )$ in $L ^ { 2 } ( \mathbf{R} _ { 3 } )$ from the
10 KB (1,490 words) - 05:45, 15 February 2024
It is sometimes convenient to replace the expression \eqref{eq:1} for the norm of $f\in W^l_p(\Omega)$ by the following:
8 KB (1,334 words) - 17:47, 30 November 2012
by the expression $ L _ {u ^ {n} } ^ \prime ( z) $,
9 KB (1,320 words) - 22:17, 5 June 2020
On taking absolute values in the above expression and using the triangle inequality, this gives
10 KB (1,639 words) - 07:05, 15 February 2024
have an explicit expression in terms of the numbers $ a _ {k} $
11 KB (1,595 words) - 17:13, 2 January 2021
...ve world lines located on the light cone. In general relativity theory, one expression of the law of inertia is the so-called [[Geodesic hypothesis|geodesic hypot
22 KB (3,285 words) - 08:10, 6 June 2020
A [[Trigonometric polynomial|trigonometric polynomial]] is an expression in one of the equivalent forms $ a _ {0} + \sum _ {1} ^ {n} [ a _ {j} \
9 KB (1,334 words) - 13:15, 26 March 2023
one observes that the expression $\nu / \lambda$ is independent of the gas motion and homogeneous to a speed
9 KB (1,338 words) - 15:30, 1 July 2020
Thus, if one defines the subprincipal symbol as the above analytic expression $b ^ { s } _{m - 1}$ where $b = b _ { m } + b _ { m - 1} + \ldots$ is the
The Fefferman–Phong inequality has also a simple expression in this framework: Let $a$ be a non-negative symbol in $S ( H ^ { - 2 } , G
30 KB (4,520 words) - 19:54, 6 February 2024
at certain points, by expansion with respect to the parameters in an analytic expression of the function, by majorants or minorants, etc.
9 KB (1,335 words) - 08:01, 6 June 2020
...ian geometry); the Riemannian curvature tensor of this space reduces to the expression $ C _ {mh} ^ {j} C _ {ik} ^ {m} - C _ {mk} ^ {j} C _ {ih} ^ {m} $.
12 KB (1,843 words) - 19:39, 5 June 2020
...y $e ( f ) ( z ) ( y ) = f ( z , y )$, $z \in Z$, $y \in Y$. This law is an expression of the standard idea that a function of two variables can be thought of as
10 KB (1,545 words) - 18:18, 20 January 2021
This is the problem of the best asymptotic expression for the sum
11 KB (1,578 words) - 11:58, 26 March 2023
Probability laws gain a statistical expression on the strength of the law of large numbers (probabilities are realized app
21 KB (3,113 words) - 12:48, 13 January 2024
...TR><TR><TD valign="top">[4]</TD> <TD valign="top"> J.H.C. Whitehead, "An expression of the Hopf invariant as an integral" ''Proc. Nat. Acad. Sci. USA'' , '''3
12 KB (1,812 words) - 22:11, 5 June 2020
mode of expression. Even Fisher, who as a young man had also felt the
8 KB (1,250 words) - 14:47, 18 March 2023
...desic boundaries, to form hyperbolic surfaces. The Kähler form has a simple expression in terms of these coordinates:
10 KB (1,540 words) - 17:43, 1 July 2020
The expression under the sign $ \sum $
14 KB (1,997 words) - 02:16, 15 June 2022
...ation is useful (in other words, the method of superposition), based on the expression
is defined by the expression (see [[#References|[10]]])
24 KB (3,433 words) - 13:09, 13 January 2024
...perator is mostly used in the case where $X$ and $Y$ are vector spaces. The expression $A(x)$ is often written as $Ax$.
14 KB (2,265 words) - 17:06, 24 January 2020
...s of a point before and after transformation, with the restriction that the expression
14 KB (2,020 words) - 12:57, 13 January 2024
be the finite differences. The expression $ \Delta ^ {m} y _ {n} $
14 KB (1,916 words) - 19:59, 12 January 2024
the [[Fibonacci numbers|Fibonacci numbers]]). One seeks an expression for the general term of the sequence. Let $ f (x) $,
27 KB (3,799 words) - 17:14, 12 November 2023
In other cases the expression for $ g _ {nk } $
11 KB (1,489 words) - 09:00, 13 January 2024
...rithmetic, the expressive potential of the latter must be investigated. The expression of many number-theoretic functions in terms of formal arithmetic is especia
12 KB (1,840 words) - 19:36, 9 February 2024
...changes with x. The value of a function can be given either by an analytic expression or by a condition which gives a means of testing all numbers and choosing o
34 KB (5,509 words) - 22:06, 28 January 2020
...re are several equivalent reformulations of $t ( M )$; the most useful such expression is recursive, using the matroid operations of deletion and contraction:
11 KB (1,736 words) - 06:27, 15 February 2024
...i } ( \Omega )$. Alternatively, in (a1) one can use the Orlicz norm and any expression equivalent to the summation (such as $\operatorname{max}$). Also, it is pos
11 KB (1,684 words) - 19:25, 12 February 2024
and the Chern polynomial is the expression $ c _ {t} = 1 + c _ {1} t + c _ {2} t ^ {2} + \dots $,
13 KB (1,910 words) - 19:40, 7 January 2024
The expression "universal algebra" is often used in the sense of "the theory of univers
11 KB (1,662 words) - 04:57, 24 February 2022
This is an expression of the fact that perturbations of the Cauchy–Dirichlet problem are propag
12 KB (1,807 words) - 17:47, 13 January 2024
...s]], which arose as a result of attempts to formalize the common use of the expression "A implies B" by removing the paradoxes of material implication and rejec
12 KB (1,934 words) - 19:30, 28 October 2023
in the polynomial should be even. Thus, an expression in Wu generators is obtained for any element of the ring $ \mathbf Z ( p
14 KB (1,987 words) - 19:15, 16 January 2024
In provability logic the modal expression $ \square A $
13 KB (1,978 words) - 20:34, 14 January 2021
...mmon part of these definitions [[#References|[9]]] consists in the analytic expression for the parallel displacement of an object or in the condition of being par
15 KB (2,257 words) - 17:31, 5 June 2020
...program; basic operators are the operators of assignment of the value of an expression to a variable, the operator of control transfer (unconditional or condition
12 KB (1,804 words) - 16:56, 7 February 2011
...eries in perturbation theory by powers of a small parameter is a convergent expression. The problem of the convergence of series in perturbation theory as a whole
so that expression (6), with $ a $
35 KB (5,181 words) - 07:24, 8 June 2020
(the tensor product of graded modules on the right-hand side of this expression is over $ \mathbf Z _ {2} = \mathbf Z /(2) $),
12 KB (1,704 words) - 08:36, 26 March 2023
then this expression holds also for these half-variance parameters.
Further differentiation yields the expression
23 KB (3,576 words) - 22:10, 12 March 2016
In a typical application of the Riemann hypothesis, one starts with an expression such as
12 KB (1,769 words) - 08:31, 26 March 2023
...on, $M(x)$ designates the result of the processing of input $x$ by $M$. The expression $M(x)=1 $ indicates a termination in an accepting state, whereas $M(x)=0$ i
12 KB (1,954 words) - 17:47, 26 December 2013
...n problems in elementary particle physics. Its matrix entries have a simple expression in terms of the Green function of the field $ \Phi(x) $:
...odel $ \mathscr{L}_{\text{int}} = - \lambda \Phi^{4} $, proportional to the expression
35 KB (5,270 words) - 23:26, 6 December 2016
The expression on the left is the odds on guilt, given $E$;
10 KB (1,658 words) - 13:01, 18 March 2023
an explicit analytic expression is available
10 KB (1,615 words) - 10:21, 10 March 2024
...groups — an alternative formulation of the Feit–Thompson theorem — and the expression of properties of simple groups in terms of centralizers of involutions have
12 KB (1,742 words) - 09:10, 4 July 2020
...ar combination of the vectors $x_\alpha\in E$ is a vector $x$ defined by an expression
14 KB (2,558 words) - 11:28, 21 June 2016
...differential equations, so that the equations themselves are a quantitative expression of these laws. For instance, Newton's laws of mechanics make it possible to
...ain a closed formula yielding (in explicit, implicit or parametric form) an expression for the dependence of a specific solution on $ t $
33 KB (4,933 words) - 01:50, 23 January 2022
...is the principal linear part of increment of the function (its geometrical expression is the segment $ LT $
lies in this neighbourhood). In this context, the expression
37 KB (5,252 words) - 11:45, 26 March 2023
...timate (6) of the error of the grid method has the disadvantage that in the expression of the function $ \psi ( \lambda ) $
17 KB (2,540 words) - 19:55, 12 January 2024
then the expression
18 KB (2,425 words) - 14:55, 7 June 2020
is irreducible, an explicit expression of the stabilizers of the points in general position has been found (see [[
13 KB (2,049 words) - 19:35, 17 January 2024
then the expression (1) is called the $ N $-
18 KB (2,673 words) - 19:54, 3 February 2021
one often chooses an expression of the type $ \max _ {t ^ {n} \in \omega _ {t} } \| u ^ {n} \| $,
15 KB (2,220 words) - 08:52, 10 April 2023
...1$, are formulas, and $F_n$ is a connective of arity $n$, then the symbolic expression $F_{n}A_{1}A_{2}... A_n$ is a formula;
...me terms of $\mathcal{L}'$, each ''atomic formula'' of $\mathcal{L}'$ is an expression of the form:
33 KB (5,175 words) - 19:12, 7 December 2023
In 1967, S. Tachibana [[#References|[a16]]] gave a tensorial expression for $ {\widetilde{B} } $
15 KB (2,270 words) - 08:28, 26 March 2023
an explicit expression is known, as well as a recurrence relation, a differential equation of whic
19 KB (2,911 words) - 18:54, 26 March 2023
...commonly used to find an approximate solution in the form of an analytical expression. Methods applicable for this purpose also include the [[Chaplygin method|Ch
32 KB (4,604 words) - 16:55, 7 February 2011
...he mathematical theory of diffraction may also be obtained when an explicit expression of the solution is known. Using a well-developed method (the so-called Wats
14 KB (2,042 words) - 19:35, 5 June 2020
The integral expression obtained for the required quantity (which also follows from the integral tr
13 KB (1,879 words) - 11:25, 31 January 2022
...structure of the differential manifold itself. The simplest example is the expression of the characteristic classes in terms of the curvature of a differentiable
17 KB (2,329 words) - 01:38, 30 December 2021
term. In the expression $ \lambda x M $
15 KB (2,306 words) - 16:57, 1 July 2020
which is simply the mathematical expression of the statement that (1) (with $ N = \mu $)
17 KB (2,639 words) - 04:38, 29 December 2021
...if in a neighbourhood of each of its points it can be given by an analytic
expression <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
34 KB (5,010 words) - 17:24, 7 February 2011
...ce relation between them. (Instead of the word "incident" one can use the expression "passes through" or "lies on" .) Let the set of lines of $ N $
16 KB (2,475 words) - 19:16, 18 January 2024
...), each of which is itself a summation over multinomial coefficients, to an expression involving but a single summation index. In the Wigner $ 6 - j $
coefficient are inherited from its expression in terms of WCG coefficients, or, equivalently, from the triangles in the
46 KB (6,595 words) - 13:20, 27 January 2020
this property is a rigorous expression of the statement, very common in the theory of errors, that "the estimator
30 KB (4,211 words) - 22:16, 5 June 2020
(1981). In Quetelet's work she found expression of the "laws of moral
11 KB (1,692 words) - 13:48, 4 November 2023
not confined to the distribution which bears his name or to the expression "Law
11 KB (1,710 words) - 19:08, 6 March 2024
the expression $ {\mathcal L} w - f = R( w) $
15 KB (2,260 words) - 08:17, 9 January 2024
the elegant probabilistic expression $E((X_{n+1} - X_{n})^2) = 2\mu \, P$.
11 KB (1,571 words) - 07:00, 15 March 2024
\sum y_i/n$. Substituting this expression into the optimality
10 KB (1,609 words) - 18:41, 6 March 2024
...of $k ( C )$ (cf. also [[Differential field|Differential field]]), i.e., an expression of type $ud v$ with $u , v \in k ( C )$, and shows that if the differential
16 KB (2,510 words) - 17:43, 1 July 2020
...problems it is usually not possible to express the solutions as an analytic expression in the corresponding parameters. Therefore, problems of operations research
16 KB (2,473 words) - 09:45, 7 August 2014
...of forms, expressed in terms of the curvature form (an example here is the expression of the Euler characteristic in the [[Gauss–Bonnet theorem|Gauss–Bonnet
30 KB (4,462 words) - 07:59, 6 June 2020
...hat the measure $ \mu $ be $ G $-invariant. This condition is the Euclidean expression of relativistic invariance.
15 KB (2,298 words) - 22:02, 7 November 2017
The type of a Monge–Ampère equation depends on the sign of the expression
17 KB (2,601 words) - 08:01, 6 June 2020
...s than three, equal to three, as in the CGS and MKS systems, and others. An expression of a derived unit of measurement in terms of the basic units is called a di
16 KB (2,568 words) - 20:00, 4 January 2024
counted with multiplicities. The expression on the left-hand side of the formula is called the logarithmic residue of t
16 KB (2,407 words) - 07:56, 11 January 2022
...endered necessary both by practical applications of mathematics — viz., the expression of the value of a given magnitude by a definite number — and by the inter
26 KB (4,086 words) - 09:51, 4 April 2020
a large accelerating step is performed in accordance with the expression
17 KB (2,572 words) - 12:56, 13 January 2024
...berg [[#References|[a2]]] and his school in Krasnoyarsk took up the Russian expression lineinaya vypuklost', which in English translations became "linear convexit
16 KB (2,533 words) - 09:46, 18 February 2024
...theory) have been made, it is possible to give a quantitative, more precise expression of the somewhat vague statement made above to the effect that the frequency
...of formula (4) and of the addition theorem yields an accurate, but unwieldy expression for the probability value sought, namely:
42 KB (6,282 words) - 08:07, 6 June 2020
in both variables. The expression $ \Phi ^ {(j)} (t _ {0} ) $
17 KB (2,509 words) - 03:12, 13 January 2022
generated by the differential expression $ l[ y] = - y ^ {\prime\prime} + q( x) y $
22 KB (3,140 words) - 13:01, 13 January 2024
The expression
26 KB (3,804 words) - 08:11, 13 February 2022
...notion of a [[Bicategory(2)|bicategory]] [[#References|[a17]]] is a further expression of this idea. $ 3 $-
...[[#References|[a2]]] (which, together with enriched category theory, is an expression of the idea that $ \mathop{\rm Set} $
43 KB (6,447 words) - 09:17, 26 March 2023
...a. It turns out that these two theories are completely parallel; this finds expression in the fact that the corresponding homotopy categories are equivalent (the
32 KB (4,905 words) - 09:31, 13 February 2024
-
13 KB (1,939 words) - 18:16, 13 August 2023
the expression
23 KB (3,288 words) - 19:36, 5 June 2020
have an explicit expression, e.g.
27 KB (3,803 words) - 07:21, 26 March 2023
equation for $\Phi(\tau,\:\rho)$ by means of an integral expression
12 KB (1,866 words) - 14:20, 10 March 2024
philosopher found in mathematics the special expression of the
13 KB (1,947 words) - 18:43, 4 March 2024
each of the digits in their expression (in any base whatever) being
14 KB (2,139 words) - 18:37, 8 March 2024
...ution to the Seiberg–Witten equations; then the left-hand side of this last expression is zero and all the integrands on the right-hand side are positive, so the
16 KB (2,663 words) - 10:57, 13 February 2024
does not have any useful explicit expression. However, the investigation of $ \phi _ {t} ( A) $
20 KB (3,033 words) - 22:16, 5 June 2020
{{Cite|Ka2}}, which gives an explicit expression for the formal power series $\def\tr{\textrm{tr}\;}\tr_{L(\L)} e^{\sum_i x_
15 KB (2,514 words) - 20:27, 15 November 2017
correlation. Since he was not able to give a concrete expression for
16 KB (2,352 words) - 07:17, 19 March 2023
...nd position $z = m l$, $m$ an integer, in a fluid at rest (cf. Fig.a2), the expression becomes
19 KB (3,002 words) - 17:46, 1 July 2020
In each term of expression (1) all factors $ a ( y _ {j} ) $,
by means of the expression (2), where $ a ( f ) $,
51 KB (7,267 words) - 07:39, 14 January 2024
...wever, that in much of the literature the AIC is defined as minus the above expression, in which case one selects the
17 KB (2,653 words) - 16:21, 10 March 2024
are the initial and transition densities of the distribution. This expression is similar to the likelihood function for a sequence of independent observa
27 KB (3,850 words) - 14:55, 7 June 2020
...(4) can be solved by the method of successive approximation. An approximate expression of the Riemann function can be obtained in this way.
30 KB (4,345 words) - 09:02, 21 January 2024
...es (hence the treatment of the non-linearity of a gravitational field as an expression of its self-interaction). The equation of motion of a test point mass in an
18 KB (2,719 words) - 19:42, 5 June 2020
the expression $ e $
21 KB (3,241 words) - 08:25, 6 June 2020
the expression $ | x - x _ {0} | ^ {2 - n } $
33 KB (4,788 words) - 08:53, 13 May 2022
...$\text{Pic}X$ and the dual Abelian variety. This expression generalizes the expression for the residue of the Dedekind zeta-function at the point $s=1$ which is f
45 KB (7,251 words) - 02:20, 29 June 2022
in the expression for $ p ( x , \xi ) $.
29 KB (4,077 words) - 04:02, 4 January 2022
...t, which is directed outwards. The condition of energetic equilibrium is an expression of the equality of the amount of energy produced in a given volume of the s
22 KB (3,445 words) - 09:41, 15 August 2023
...is obtained from atomic languages by regular operations is termed a regular expression.
28 KB (4,202 words) - 08:53, 1 February 2020
to realize an extremum of the functional (3). Hence — and also from the expression for the variation $ \delta J $—
28 KB (4,182 words) - 07:56, 16 April 2023
...definability of principal congruences. The deduction theorem is the formal expression of one of the most important and useful properties of classical logic: to p
...invariant consequence relation between sequents; a sequent is a syntactical expression of the form $\varphi _ { 0 } , \ldots , \varphi _ { n - 1 } \rhd \varphi _
76 KB (11,425 words) - 02:12, 15 February 2024
...the spectral theorem makes it possible to assign a meaning to the function
expression <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
67 KB (9,247 words) - 17:12, 29 October 2017
and an expression (see [[#References|[17]]]) in terms of generalized Gauss sums. Formula (3)
32 KB (4,863 words) - 08:08, 12 August 2022
following L. Wittgenstein and A. Church. The second expression also shows that the natural numbers object is the least fixpoint of the fun
24 KB (4,067 words) - 20:57, 21 December 2017
replaced by the expression $ 3K( \epsilon - \alpha T) \delta _ {ij} $.
28 KB (4,176 words) - 05:30, 19 March 2022
which give a single-valued expression of $ z $
34 KB (4,972 words) - 13:13, 6 January 2022
by an expression similar to (a1), with $ m \rightarrow + \infty $
39 KB (5,692 words) - 14:54, 7 June 2020
...onditional well-posedness was also found by B.L. Phillips {{Cite|Ph}}; the expression "Tikhonov well-posed" is not widely used in the West.
33 KB (5,246 words) - 00:23, 25 April 2012
...0100214.png" /> obtained in [[#References|[a31]]] is given by a complicated
expression. One knows that <img align="absmiddle" border="0" src="https://www.encyclop
88 KB (12,202 words) - 17:19, 23 October 2017
...$\delta\colon Q\times\Sigma\to Q\times\Sigma \times \{L,R,N\}$, wherein the expression $\{L,R,N\}$ does not represent a set of states but a set of head actions. A
27 KB (4,213 words) - 18:53, 26 April 2014
which gives a simple expression for $ A $.
36 KB (5,132 words) - 08:10, 30 January 2022
...H.-G.}, \textsc{Chiou, J.-M.} and \textsc{Leng, X.} (2008). Inferring gene expression dynamics via functional regression analysis. ''BMC Bioinformatics'' '''9''
29 KB (4,005 words) - 20:28, 13 March 2024
-
29 KB (4,109 words) - 19:54, 18 March 2018
giving an alternative expression for the $\alpha$-permanent
36 KB (5,856 words) - 18:32, 17 April 2024
...n terms of the characters of $M$ and $N$. Before getting on to the specific expression of these virtual characters we will need the following notion. Let $\mbf{X}
48 KB (8,458 words) - 18:22, 13 August 2023
...tructure of a curve in a neighbourhood of a singular point, the sign of the expression $$
66 KB (9,825 words) - 01:45, 23 June 2022
Both Boole and Jevons understood logic to be an expression of “the laws of thought.” Yet Boole had more of an algebraic concept of
...d by G. Boole and W. S. Jevons, but which greatly exceeds it in richness of expression.”
189 KB (29,059 words) - 14:31, 19 March 2023
An alternate expression of the Archimedean axiom or property with respect to the theory of ordered
91 KB (14,186 words) - 16:58, 23 November 2023