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61.
Vsevolod F. Lev 《Combinatorica》1996,16(4):587-590
In this note the method of [5] and a result from [3] are combined to treat the following classical problem: Given a finite setA and an infinite sequenceS (both inZ), what is the minimal number of elements ofA whose sum lies inS? We obtain an upper bound depending only on the densities ofA andS (but not on their arithmetic nature). 相似文献
62.
Yong Zhang 《Order》1996,13(4):365-367
G. Grätzer, H. Lakser, and E. T. Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a small lattice L, that is, a lattice L with O(n
2
) elements. G. Grätzer, I. Rival, and N. Zaguia proved that, for any <2, O(n
2
) can not be improved to O(n
). In this note we show that the theorem about small representation can be improved further to get a more delicate result. 相似文献
63.
One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed. 相似文献
64.
A perturbation bound for the generalized polar decomposition 总被引:11,自引:0,他引:11
Ren-Cang Li 《BIT Numerical Mathematics》1993,33(2):304-308
LetA be anm×n complex matrix. A decompositionA=QH is termed ageneralized polar decomposition ofA ifQ is anm×n subunitary matrix (sometimes also called a partial isometry) andH a positive semidefinite Hermitian matrix. It was proved that a nonzero matrixA
m×n
has a unique generalized polar decompositionA=QH with the property (Q
H
)=(H), whereQ
H
denotes the conjugate transpose ofQ and (H) the column space ofH. The main result of this note is a perturbation bound forQ whenA is perturbed. 相似文献
65.
Inge Söderkvist 《BIT Numerical Mathematics》1993,33(4):687-694
Given two arbitrary real matricesA andB of the same size, the orthogonal Procrustes problem is to find an orthogonal matrixM such that the Frobenius norm MA – B is minimized. This paper treats the common case when the orthogonal matrixM is required to have a positive determinant. The stability of the problem is studied and supremum results for the perturbation bounds are derived. 相似文献
66.
Richard Steiner 《Applied Categorical Structures》1993,1(3):247-284
The theory of directed complexes is a higher-dimensional generalisation of the theory of directed graphs. In a directed graph, the simple directed paths form a subset of the free category which they generate; if the graph has no directed cycles, then the simple directed paths constitute the entire category. Generalising this, in a directed complex there is a class of split subsets which is contained in and generates a free -category; when a simple loop-freeness condition is satisfied, the split sets constitute the entire -category. The class of directed complexes is closed under the natural product and join constructions. The free -categories generated by directed complexes include the important examples associated to cubes and simplexes. 相似文献
67.
The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.This research was supported in part by the Ministry of Science Grant 3481-1-91 and by the Ministry of Absorption Center for Absorption in Science. 相似文献
68.
Israel Gohberg Naum Krupnik Ilya Spitkovsky 《Integral Equations and Operator Theory》1993,17(3):322-337
The Banach algebra generated by one-dimensional linear singular integral operators with matrix valued piecewise continuous coefficients in the spaceL
p
(,) with an arbitrary weight is studied. The contour consists of a finite number of closed curves and open arcs with satisfy the Carleson condition. The contour may have a finite number of points of selfintersection. The symbol calculus in this algebra is the main result of the paper. 相似文献
69.
Hisahiro Hagiwara Fumihide TakeuchiTakashi Hoshi Toshio SuzukiToshihiro Hashimoto Yoshinori Asakawa 《Tetrahedron letters》2003,44(11):2305-2306
1,9-Dideoxyforskolin 2 has been synthesized starting from ptychantin A 3. 相似文献
70.
LetP be a finite partially ordered set. The lengthl(x) of an elementx ofP is defined by the maximal number of elements, which lie in a chain withx at the top, reduced by one. Letw(P) (d(P)) be the maximal number of elements ofP which have the same length (which form an antichain). Further let
. The numbers
and
as well as all partially ordered sets for which these maxima are attained are determined. 相似文献