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正规元
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  normal element
     1. If n ≥ 32, then for any prime power q, there exists a primitive normal element ζ of F_(q~n) over F_q such that ζ~(-1) is also a primitive normal element of F_(q~n) over F_q.
     1.若n≥32,则对任意的素数方幂q,存在F_(q~n)在F_q上的互反本原正规元
短句来源
     Let R be a finite von Neumann algebra acting on a complex Hibert space H . In this short note it is shown that every normal element A in R is reductive affiliated with R, and furthermore, the strongly closed subalgebra generated by A and the commutant of R is a von Neumann algebra.
     令 R是作用于 Hilbert空间 H上的有限 von Neumann代数 ,则每个正规元 A∈ R都是关于 R的约化元 ,且 A与其换位 R′生成的强闭子代数是 von Neumann代数
短句来源
     The author proves that if M contains a normal element of order p of the group G,then Cayley graph is edge-Hamitonian.
     作者证明了若M中含有 p阶正规元 ,则Cayley图X(G ,M)是边 Hamilton图 .
短句来源
     Primitive Normal Element and Its Inverse in Finite Fields
     有限域上互反本原正规元的存在性
短句来源
     {(2, 45), (2, 63), (3, 32), (3, 40), (7, 48), (9, 40), (19, 36), (37,36), (41,40)}, then for any a, b ∈ F_q~*, there exists a primitive normal element ζ of F_(q~n) over F_q such that ζ~(-1) is also a primitive normal element of F_(q~n) over F_q, T_(rF_(q~n/f_q))(ζ)= a and T_(rF_(q~n/f_q))(ζ~(-1))= b.
     {(2,45),(2,63),(3,32),(3,40),(7,48),(9,40),(19,36),(37,36),(41,40)},则对任意的a,b∈F_q~*,存在F_(q~n)在F_q上的指定迹(a,b)的互反本原正规元
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  regular element
     A Few Types and Simple Natures of I-Right Regular Element and I-Right Regular Ideal
     I-右正规元、I-正规右理想的几种类型及简单性质
短句来源
     SOME FURTHER DISCUSSION ABOUT I-RIGHT REGULAR ELEMENT AND I-REGULAR RIGHT IDEAL
     对I-右正规元、I-正规右理想的进一步探讨
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  “正规元”译为未确定词的双语例句
     Subnormal Elements in Pro-C~ * -Algebras
     Pro-C~*-代数中的次正规元(英文)
短句来源
     A Property of Normal Elements in Finite von Neumann Algebras
     有限von Neumann代数中正规元的一个性质
短句来源
     In this paper,we point out the problems in "A wide family of nonlinear filter functions with a large linear span",give a counterexample,and get the following conclusions:Let a be a binary m-sequence of degree n with minimal polynomial f(x).
     文章指出了论文“A wide family of nonlinear filter functions with a large linear span”存在的问题,给出一个反例,同时得到如下结论:设a是F2上以f(x)为极小多项式的n级m-序列,α为f(x)的一个根,αδ为F2n在F2上的正规元,1≤δ<2n-1。
短句来源
     On Primitive Normal Elements over Finite Fields
     有限域上本原正规元
短句来源
     (2) both ζ and ζ~(-1) are normal elements of F_(q~n) over F_q, i.e., both {ζ, ζ~q,...,ζ~(q~(n-1))}and{ζ~(-1),ζ~(-q),...,ζ~(-q(n-1))} are basis over F_q.
     (2)ξ和ξ~(-1)都是F_(q~n)在F_q上的正规元,即{ξ,ξ~q,…,ξ~(q~(n-1))和{ξ~(-1),ξ~(-q),…,ξ~(-q~(n-1))}都构成F_(q~n)在F_q上的正规基;
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  normal element
Negative cluster ions MpCn- (M normal element,n>amp;lt;10,p=1-4) produced by various experimental techniques from carbides show in their emission intensities a very strong even-odd effect according to the parity of the carbon atom numbern.
      
Let L denote the lattice of all varieties of monounary algebras (A,f) and let V be a non-trivial non-normal element of L.
      
Indeed, as representative governance spreads, with the conviction by all parties that governments should respond to popular choice, then social movements and protest will also spread, as a normal element of democratic politics.
      
Indeed, as representative governance spreads, with the conviction by all parties that governments should respond to popular choice, then social movements and protest will also spread, as a normal element of democratic politics.
      
The capacity of this soil to adsorb SO42- appeared relatively limited in the absence of normal element cycling.
      
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  regular element
Heating of biological tissues by two-dimensional phased arrays with random and regular element distributions
      
For some special boundary conditions and regular element meshes, the lower and upper bounds for Δt/Δx2can be obtained from those conditions so that reasonable numerical solutions are guaranteed.
      
Our method is based on a solution of a linear algebra problem: the task of finding a locally regular element in a subspace of linear transformations.
      
We prove the following theorem: if a subalgebraB of an algebraG is spanned by root vectors, then ifX is a regular element ofG, the limit {ie160-1} Ad exptX(B) exists and is isomorphic toB, i.e.B "survives" contraction withX.
      
The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible.
      
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Let A be a unital C-algebra and ND(A) the set of all such normal elements x of A with the spectrum. If D is compact, then the C-functional calculus : C(D) is automatically continuous, where . For a unital Banach algebra B, BG denotes the set of all elements x of B with the spectrum . If G is a bounded open subset of complex field C, then the Riesz functional calculus βG: H(G)×BG→ B is automatically continuous, where βG(f,a )=f(α); Especially, the functional calculuses ac and βc are automatically continuous.

研究了泛函演算的自动连续性问题.设A是有单位元的C-代数,ND(A)是A中其谱含于紧集D的所有正规元之集,则泛函演算自动连续.对有单位元的Banach代数B,用BG表示B中其谱含于开集G的元素之集,那么当G有界时,Riesz演算自动连续.作为推论得知与均自动连续.

Let G be a group generated by M. A Chyley graph over G is a graph X(G, M) whose vertex setis G and whose edge set consists of all unordered pairs(a, b) with a, b ∈G and a-1b∈M ∪M-1,Where M-1 denotes the set{x-1|x∈M}. In this paper, if M contains a normal element a of prime or order. then the followins results are proved:(1)If X(G/,M)is hamiltonian, then X(G, M) is hamiltonian.(2)If X(G/,M) is edge-hammiltonian, and a is a generating element, then X(G,M) isedge-hamiltonian.(3) If X(G/,M)is edge-hamiltonian...

Let G be a group generated by M. A Chyley graph over G is a graph X(G, M) whose vertex setis G and whose edge set consists of all unordered pairs(a, b) with a, b ∈G and a-1b∈M ∪M-1,Where M-1 denotes the set{x-1|x∈M}. In this paper, if M contains a normal element a of prime or order. then the followins results are proved:(1)If X(G/,M)is hamiltonian, then X(G, M) is hamiltonian.(2)If X(G/,M) is edge-hammiltonian, and a is a generating element, then X(G,M) isedge-hamiltonian.(3) If X(G/,M)is edge-hamiltonian and there exists x∈M such that ax=xa, then X(G,M) is edge-hamiltonian.

设G是一个有限群,G=<M>.G上的一个Cayley图X(G,M)定义如下:V(X)为G,E(X)是所有无序对(a,b)组成的集合,其中a,b∈G,a-1b∈M∪M-1,M-1={x-1|x∈M}.如果M中含有素数阶正规元a,那么以下结果被证明:(i)若X(G/<a>,M)是Hamilton图,则X(G,M)是Hamilton图.(ii)若X(G/<a>,M)是边-Hamilton图且a为生成元,则X(G,M)是这-Hamilton图.(iii)若X(G/<a>,M)是边-Mamilton图且存在元x∈M,使得xa=ax,则X(G,M)是边-Hamilton图.

In this paper, we present a complete proof of a theorem of submultiplication which claims that a*-algebra A with complete linear space norm such that ||x*x|| ||x||2 for x ∈ A and ||x*x|| = ||x||2 for normal ∈ E A is a C*-algebra. At the same time,a C*-equivalent version of the theorem is given.

本文证明了次可乘定理:设A是一个*代数,A上范数||.||使得(A,||.||)成为完备的赋范线性空间,而且,(I)对于X∈A,||x*x||||x||2;(II)对于正规元x∈A,||x*x||=||x||2,则(A,||.||)是C*-代数.同时,也给出了其对应的C*-等价定理.

 
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