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131.
Jong-Shi Pang 《Mathematical Programming》1993,58(1-3):149-160
This paper is concerned with two well-known families of iterative methods for solving the linear and nonlinear complementarity problems. For the linear complementarity problem, we consider the class of matrix splitting methods and establish, under a finiteness assumption on the number of solutions, a necessary and sufficient condition for the convergence of the sequence of iterates produced. A rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution. For the nonlinear complementarity problem, we establish the convergence of the Newton method under the assumption of a pseudo-regular solution which generalizes Robinson's concept of a strongly regular solution. In both instances, the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation.This work was based on research supported by the National Science Foundation under grant ECS-8717968. 相似文献
132.
For lattices with two kinds of points (black and white), distributed according to a translation-invariant joint probability distribution, we study statistical properties of the sequence of consecutive colors encountered by a random walker moving through the lattice. The probability distribution for the single steps of the walk is considered to be independent of the colors of the points. Several exact results are presented which are valid in any number of dimensions and for arbitrary probability distributions for the coloring of the points and the steps of the walk. They are used to derive a few general properties of random walks on lattices containing traps.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982. 相似文献
133.
Masaaki Sibuya 《Annals of the Institute of Statistical Mathematics》1991,43(2):261-285
An elementary majorant-minorant method to construct the most stringent Bonferroni-type inequalities is presented. These are essentially Chebyshev-type inequalities for discrete probability distributions on the set {0, 1,..., n}, where n is the number of concerned events, and polynomials with specific properties on the set lead to the inequalities. All the known results are proved easily by this method. Further, the inequalities in terms of all the lower moments are completely solved by the method. As examples, the most stringent new inequalities of degrees three and four are obtained. Simpler expressions of Mrgritescu's inequality (1987, Stud. Cerc. Mat., 39, 246–251), improving Galambos' inequality, are given. 相似文献
134.
We study facets of the cut coneC
n
, i.e., the cone of dimension 1/2n(n – 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a lifting procedure for constructing facets ofC
n+1 from given facets of the lower dimensional coneC
n
. After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented. 相似文献
135.
Consider a simple random walk on
d
whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn
k
be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let
k
=E(n
k
)–q
–1. Our main result is a proof that (*) lim
k
k
d/2
k
= (1 –q)q
d/2 – 2(d/2)
d/2. Since it is known thatq
– 1
k
=E(n
1
n
k + 1 B) –E(n
1 B)E(n
k + 1 B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of
k
(1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of
k
for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of
k
cannot be faster than (*). 相似文献
136.
本文研究次M矩阵的行列式性质,讨论了对其上的Hadamard-Fischer不等式的改进,得到的主要结果是:对任一非奇异n阶次M矩阵A,都有: 相似文献
137.
Buniakowski-Cauchy积分不等式的新推广 总被引:4,自引:0,他引:4
罗俊丽 《重庆工商大学学报(自然科学版)》2005,22(6):623-624
在研究Buniakowski—Cauchy积分不等式的基础上,给出了其新的积分不等式的推广式,并用构造性方法予以证明.考察了离散型Cauchy不等式,认为只要将所得到的Buniakowski—Cauchy新推广积分不等式作某种特殊赋值,就能够进一步得到离散型Cauchy不等式的新的积分型推广式,从而体现它们之间的内在联系. 相似文献
138.
较为精密的Hardy-Hilbert型不等式 总被引:2,自引:0,他引:2
杨必成 《信阳师范学院学报(自然科学版)》2005,18(2):140-142,158
本文引入参数α,建立一个具有最佳常数因子的较为精密的Hardy Hilbert型不等式 作为应用,建立了一个等价式 相似文献
139.
首先证明了Grushin球不是Grushin平面上等周问题的解,然后得到了Brunn-Minkowski不等式在Grushin平面上是不成立的. 相似文献
140.
对于Post-Widder算子Pn(f,x),证明了当s∈N0=N U{0},wf(s)∈Lp(0,∞)(1<p≤∞)时,存在某一正数m,使得ω2ψ(f(s),1/(∫)n)ω,p≤C(∥ω(P(s)nf-f(s))∥p+∥ω(P(s)mnf-f(s))∥p+1/n∥ωf(s)∥p),其中ψ(x)=x;w(x)=xa(1+x)b;a,6∈R1;C>0;ωψ2(f,t)w,p是带权光滑模. 相似文献