Search results
- ''of numbers $\alpha_1,\ldots,\alpha_n$'' L(\alpha_1,\ldots,\alpha_n|H) = L(H) = \min |a_1 \alpha_1 + \cdots + a_n \alpha_n|724 bytes (124 words) - 19:48, 20 November 2014
- ...1,\ldots,a_m$, i.e. the number of solutions in non-negative integers $x_1,\ldots,x_m$ of the equation D(z; a_1,\ldots,a_m) = \sum_n D(n;a_1,\ldots,a_m) z^n = \frac{1}{\left({1-z^{a_1}}\right)\cdots\left({1-z^{a_m}}\right)}1 KB (185 words) - 16:46, 23 November 2023
- ...in \mathbb{N}$ ($j = 1,\ldots,k$). The element is also denoted by $x_{n_1 \ldots n_k}$.475 bytes (99 words) - 18:52, 12 October 2014
- ...dots,z_k)$ with integer coefficients such that the $n$-tuple $\langle a_1,\ldots,a_n\rangle$ satisfies the predicate $\mathcal P$ if and only if the Diophan $$P(a_1,\ldots,a_n,z_1,\ldots,z_k)=0\label{*}\tag{*}$$1 KB (165 words) - 16:59, 14 February 2020
- ...associates with a tensor with components $ a^{i_{1} \ldots i_{p}}_{j_{1} \ldots j_{q}} $, $ p,q \geq 1 $, the tensor b^{i_{2} \ldots i_{p}}_{j_{1} \ldots j_{q - 1}}1 KB (237 words) - 02:26, 9 September 2015
- $i,j = 1,2,\ldots$. When $1 \le i,j \le n$, the Kronecker symbol $\delta^i_j$ has $n^2$ compo ...dots j_p}$ (when $p \ge 2$ often denoted by $\epsilon^{i_1\ldots i_p}_{j_1\ldots j_p}$) are called the ''components'' of the Kronecker symbol. An [[affine t2 KB (340 words) - 19:43, 13 January 2016
- ...$n$-th ''continuant'', $K(n)$, of a sequence $\mathbf{a} = a_1,\ldots,a_n,\ldots$ is defined recursively by ...also be obtained by taking the sum of all possible products of the $a_1,\ldots,a_n$ in which any pairs of consecutive terms are deleted.2 KB (265 words) - 13:41, 12 December 2013
- ...ts,a_n$ exists if $a_1 \cdots a_n \neq 0$. It is usually denoted by $[a_1,\ldots,a_n]$. 1) the least common multiple of $a_1,\ldots,a_n$ is a divisor of any other common multiple;2 KB (334 words) - 20:19, 2 November 2016
- $$L=\{P_0,\ldots,P_n,\ldots,F_0,\ldots,F_m,\ldots\}$$ where $P_0,\ldots,P_n,\ldots,$ are [[predicate symbol]]s and $F_0,\ldots,F_m,\ldots,$ are function symbols for each of which a number of argument places is giv1 KB (219 words) - 10:43, 18 October 2016
- ...$, $(x_i)_1^n$, $(x_i)_{i\in\{1,\ldots,n\}}$, $(x_1,\ldots,x_n)$, or $x_1,\ldots,x_n$. The number $n$ is called its length ($n\geq0$), $x_i$ is called the $ ...\ldots,x_n)$ is the empty set for $n=0$, and $(x_1,\ldots,x_{n+1})=\{(x_1,\ldots,x_n),\{x_{n+1}\}\}$.1 KB (251 words) - 21:18, 12 January 2016
- ...he number $0,\pm1,\ldots,\pm(m-1)/2$ if $m$ is odd or the numbers $0,\pm1,\ldots,\pm(m-2)/2,m/2$ if $m$ is even.428 bytes (69 words) - 12:43, 23 November 2014
- ...\ldots,y_n)$ then the concatenation $xy$ is the word $(x_1,\ldots,x_m,y_1,\ldots,y_n)$: the notations $x|y$, $x \cdot y$ are also used. Denoting the empty653 bytes (113 words) - 21:39, 12 January 2016
- (-1)^{s+t} \det A_{i_1\ldots i_k}^{j_1\ldots j_k} ...j_k$, of some square matrix $A$ of order $n$; $\det A_{i_1\ldots i_k}^{j_1\ldots j_k}$ is the determinant of the matrix of order $n-k$ obtained from $A$ by1 KB (182 words) - 11:43, 9 February 2021
- a_1 & b_1 & 0 & 0 & \ldots & 0 & 0 \\ c_1 & a_2 & b_2 & 0 & \ldots & 0 & 0 \\897 bytes (116 words) - 18:31, 14 April 2018
- (\forall x_1,\ldots,x_n)\,(A_1 \wedge \cdots \wedge A_p \rightarrow A) where $A_1,\ldots,A_p$ and $A$ denote atomic formulae of the form1 KB (193 words) - 07:40, 21 October 2016
- \phi : x \mapsto F(a_1,\ldots,a_{k-1},x,a_{k+1},\ldots,a_n) where $F$ is the symbol of a basic operation in $\Omega$ and $a_1,\ldots,a_n$ are fixed elements of the set $A$.557 bytes (88 words) - 16:59, 23 November 2023
- ...e propositions such that the truth value of $P_i$ is equal to $V_i$, $i=1,\ldots,n$.806 bytes (143 words) - 16:55, 2 November 2014
- ...x_{2n-1} \omega = x_1 \ldots x_i (x_{i+1} \ldots x_{i+n})\omega x_{i+n+1} \ldots x_{i+2n-1} \omega for all $i=1,\ldots,n$.1 KB (190 words) - 20:52, 7 January 2016
- f_2(x) = f[f_1(x)] \,,\ \ldots\ ,\,f_n(x) = f[f_{n-1}(x)] are called the second, $\ldots$, $n$-th iterates of $f(x)$. E.g., putting $f(x) = x^\alpha$ one obtains994 bytes (158 words) - 17:21, 8 September 2017
- ...s that are often used (next to the operators $\int \ldots dx$ and $\{ x : \ldots \}$), in which $x$ is an operator variable: $\forall x (\ldots)$, $\exists x (\ldots)$, that is, the universal and existential quantifiers;2 KB (315 words) - 19:45, 2 March 2018