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111.
Dao-sheng Zheng 《计算数学(英文版)》1998,(2)
1.IntroductionSince1984,severalchinesemathematicianshaveobtailledmanyresultsboutmatrixoperatornormcondition.umbe.[ll'12'18].Twokindsmatrixconditionnllmbers[9]are:(1)IfAECoxsisnonsingular,thellunlberK.(A)~IIAll.llA--'if.iscalledtheor--normconditionnumberof… 相似文献
113.
We develop structural formulas
satisfied by some families of
orthogonal matrix polynomials of size $2\times 2$ satisfying
second-order differential equations with polynomial coefficients. We consider
here two one-parametric families of weight matrices,
namely
\[
H_{a,1}(t)\;=\;e^{-t^2} \left( \begin{array}{@{}cc@{}}
1+\vert a\vert ^2t^2 & at \\bar at & 1 \end{array} \right) \quad {\rm and} \quad H_{a,2}(t)\;=\;e^{-t^2} \left( \begin{array} {@{}cc@{}}
1+\vert a\vert ^2t^4 & at^2 \\bar at^2 & 1
\end{array} \right),
\]
$a\in \mbox{\bf C} $ and $t\in \mbox{\bf R} $, and their corresponding orthogonal
polynomials. 相似文献
114.
Eric J. Beh 《Computational Statistics》2005,20(3):415-438
An exploration of the application of S-PLUS code designed to perform classical correspondence analysis is made in this paper.
This code allows for the “classical” analysis to be performed on categorical data consisting of two or more variables. For
multi-way contingency tables, correspondence analysis can be performed by considering either the indicator matrix or the Burt
matrix. The code also allows the user to incorporate into the analysis confidence circles (to identify categorical responses
that deviate from the hypothesis of independence) and for an asymmetrical analysis to be performed. The function includes
various warnings and stoppages to help the user properly analyse their data. 相似文献
115.
Redouane Kara Mourad Ahmane Jean Jacques Loiseau Said Djennoune 《Nonlinear Analysis: Hybrid Systems》2009,3(4):738-748
This paper deals with constrained regulation of continuous Petri nets under the so-called infinite servers semantics. Our aim is to design feedback gains that permit us to reach both desired stationary marking vector and desired asymptotic firing rate vector. The proposed approach takes into account constraints on the control, the marking of the Petri net, and the stability of the closed-loop system. The existence of a solution is first expressed geometrically, in terms of the inclusion of two polyhedral sets. They are reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem. Finally, an application to an assembly production system is given. 相似文献
116.
《Linear algebra and its applications》2009,430(4):1313-1327
Let C={1,2,…,m} and f be a multiplicative function such that (f∗μ)(k)>0 for every positive integer k and the Euler product converges. Let (Cf)=(f(i,j)) be the m×m matrix defined on the set C having f evaluated at the greatest common divisor (i,j) of i and j as its ij-entry. In the present paper, we first obtain the least upper bounds for the ij-entry and the absolute row sum of any row of (Cf)-1, the inverse of (Cf), in terms of ζf. Specializing these bounds for the arithmetical functions f=Nε,Jε and σε we examine the asymptotic behavior the smallest eigenvalue of each of matrices (CNε),(CJε) and (Cσε) depending on ε when m tends to infinity. We conclude our paper with a proof of a conjecture posed by Hong and Loewy [S. Hong, R. Loewy, Asymptotic behavior of eigenvalues of greatest common divisor matrices, Glasg. Math. J. 46 (2004) 551-569]. 相似文献
117.
The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all noncentral elements of R, and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this article we investigate some graph-theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields F and E and integers n, m ≥ 2, if Γ(M n (F))?Γ(M m (E)), then n = m and |F|=|E|. 相似文献
118.
Huanyin Chen 《代数通讯》2013,41(10):3790-3804
An element of a ring is called strongly J-clean provided that it can be written as the sum of an idempotent and an element in its Jacobson radical that commute. A ring is strongly J-clean in case each of its elements is strongly J-clean. We investigate, in this article, strongly J-clean rings and ultimately deduce strong J-cleanness of T n (R) for a large class of local rings R. Further, we prove that the ring of all 2 × 2 matrices over commutative local rings is not strongly J-clean. For local rings, we get criteria on strong J-cleanness of 2 × 2 matrices in terms of similarity of matrices. The strong J-cleanness of a 2 × 2 matrix over commutative local rings is completely characterized by means of a quadratic equation. 相似文献
119.
Lambek extended the usual commutative ideal theory to ideals in noncommutative rings, calling an ideal A of a ring R symmetric if rst ∈ A implies rts ∈ A for r, s, t ∈ R. R is usually called symmetric if 0 is a symmetric ideal. This naturally gives rise to extending the study of symmetric ring property to the lattice of ideals. In the process, we introduce the concept of an ideal-symmetric ring. We first characterize the class of ideal-symmetric rings and show that this ideal-symmetric property is Morita invariant. We provide a method of constructing an ideal-symmetric ring (but not semiprime) from any given semiprime ring, noting that semiprime rings are ideal-symmetric. We investigate the structure of minimal ideal-symmetric rings completely, finding two kinds of basic forms of finite ideal-symmetric rings. It is also shown that the ideal-symmetric property can go up to right quotient rings in relation with regular elements. The polynomial ring R[x] over an ideal-symmetric ring R need not be ideal-symmetric, but it is shown that the factor ring R[x]/xnR[x] is ideal-symmetric over a semiprime ring R. 相似文献
120.
Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms. 相似文献