一类非线性抛物方程组解的爆破时间上下界估计

本文研究了一类非线性抛物方程组uj/t=△uj+fj(u)解的爆破时间的估计问题.通过构造恰当的辅助函数和建立一系列微分不等式,获得了此类非线性抛物方程组解的爆破时间上下界的估计.从而将单个方程的结论推广到了方程组的情形.     

ON THE METRIZATION LEMMA FOR UNIFORM SPACES

Abstract

We show a numeric generalization of the well-known metrization lemma for uniform spaces, thereby answering a question left open in [2] to the affirmative. An application of the new lemma in the setting of approach theory yields the conclusion that every approach uniformity has a basis of pseudo-metrics.     

关于一些矩阵分解因子的扰动分析

关于一些矩阵分解因子的扰动分析刘新国（青岛海洋大学）ＯＮＴＨＥＰＥＲＴＵＲＢＡＴＩＯＮＢＯＵＮＤＳＦＯＲＳＯＭＥＭＡＴＲＩＸＦＡＣＴＯＲＩＺＡＴＩＯＮＳ￥ＬｉｕＸｉｎ－ｇｕｏ（ＱｃｅａｎＵｎｉｖｅｒｓｉｔｙｏｆＱｉｎｇｄａｏ，Ｑｉｎｇｄａｏ）Ａｂｓｔ...     

关于矩阵二次型极值的若干结果

本文出于统计研究的需要，系统地讨论了Ｒａｙｌｅｉｇｈ－Ｒｉｔｚ定理在矩阵形式下的推广，给出了若干新结果，完善了现有文献中这方面的研究。     

SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)

We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_g on F(p,pα-2,s),which generalizes the existing results and answers a question raised in [A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_g,we show that,for 0 <α≤1,J_g never has a closed range on F(p,pα-2,s).We...     

多角形区域上的数值积分的龙贝算法与积分方程的分裂外推解法

本文分两部分,前一部分论述多角形区域上数值积分的龙贝方法;后一部分提供多角形区域上积分方程 Nystr(?)m 解的分裂外推方法.由于多角形总可以分成有限个三角形,故仅需要研究三角形区域上数值积分方法.设Δ是给定的三角形,考虑其上积分J=integral from Δ f(y)dy,(1)这里,y=(y_1,y_2),f(y)=f(y_1,y_2),并且下文总是用希腊字母 α,β 等表示二重指标集.为了建立(1)的求积公式,我们采用逐次加密剖分Δ,即 k 次加密是连接第 k-1 次加密剖分的诸三角形每边中点得到.由此经过 s 次加密后Δ被分成4~s 个全等三角形:Δ=sum from i=1 to 4~s Δ_i.又令Δ~h=1/(4~s)measΔ.我们来构造两种数值积分公式:类矩形公式     

SOME REMARKS ON THE NULL CONDITION FOR NONLINEAR ELASTODYNAMIC SYSTEM

The author derives the same null condition as in[1]for the nonlinear elastodynamic systemin a simpler way and proves the equivalence of the null conditions introduced in[1]and[7]respectively.     

SOME LIOUVILLE TYPE THEOREMS FOR THE P-SUB-LAPLACIAN ON THE GROUP OF HEISENBERG TYPE

In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.     

映象方程多解问题的某些研究

本文用ｆｐ－同伦方法，在一定的技巧和变换的配合下，在紧性条件支持下，研究了赋范线性空间中一类集值映象方程的多解问题。还给出所得理论结果的一个应用。     

INTERGRATION BBBBY PARTS FOR THE APPROXIMATELY CONTINUOUS FORAN INTERGRAL

This note gives an integration by parts fomula for the approximately continuous Foran integral.     

ON SOME TESTS FOR ELLIPTICAL SYMMETRY

In this paper, some test statistics of Kolmogorov type and Cramer-von Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and any fixed alternative. The asymptotic properties of Bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on number theoretic method, is suggested.     

关于B-值迭对数律的一些结论

本文讨论小球条件在B－值独立同分布随机元迭对数律中的应用，并给出了B－值随机元迭对数律的一些结论。     

SOME PATH PROPERTIES OF BROWNIAN MOTION AND SUPER-BROWNIAN MOTION ON THE SIERPINSKI GASKET

1SomeNotationsLetB(t)betheBrownianmotionontheSierpinskigasket.ThisprocesswasfirstconstructedbyM.T.BallotandE.A.Perkins[2],sowewillsdoptthenotationstherein.Forpurposeofsyste~izationsomeboortantnotationswillbereviewedbriefly.LetaO=(0,0),al=(1,0)andaZ==(i,4),letFO={ac,al,a2}bethevenicesOfanequilateraltriangleintheplaneofsideone.DefineinductivelyLetG6=U7=.Fi'GObeGStogetherwithitsreflectioninthey-axis.LetthenG=of(Goo),theclosureOfG.,isnamedtheSierpinskigasket.NowweintroduceG(u):LetG(o…     

Banach 空间微分包含在闭集上的生存性

本文在抽象Banach空间中研究非自治微分包含系统x（t）∈A（t,x）;x（0）＝x0在闭集上的生存性．在假定A是上半连续,满足一定的模条件与紧性条件之下,获得微分包含初值问题在闭集上的生存定理．     

Heisenberg群上热核及Green核的渐近性

本文讨论Heisenberg群上热核及Green核的渐近性，给出了当群中元素靠近中心和远离中心时的渐近行为     

Sierpinski Gasket上Brownian运动的局部时

本文证明了Ｓｉｅｒｐｉｎｓｋｉｇａｓｋｅｔ上Ｂｒｏｗｎ运动局部时的联合连续性。     

QUANTUM COMPLEXITY OF THE INTEGRATION PROBLEM FOR ANISOTROPIC CLASSES

We obtain the optimal order of high-dimensional integration complexity in the quantumcomputation model in anisotropic Sobolev classes W∞^r ([0, 1]^d) and Hǒlder Nikolskii classes H∞^r([0, 1]^d). It is proved that for these classes of functions there is a speed-up of quantum algorithms over deterministic classical algorithms due to factor n^-1 and over randomized classical methods due to factor n^-1/2. Moreover, we give an estimation for optimal query complexity in the class H∞^∧ (D) whose smoothness index is the boundary of some complete set in Z ^d.     

关于随机变量加权和的强收敛性注记

设{X,;n≥1}为独立同分布随机序列,{a_(xi);1≤i≤K_n,↑~∞,n≥1}为权系数序列。本文给出三组sum from i=1 to K_n(a_(ai)X_i→0a.s.充分条件。同时,还讨论加权和的完全收敛性,我们的条件比[3]弱。