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921.
Abstract
We give a linear symmetric differential operator L defined by
in the 2π-periodic function space, and study the inverse-definiteness property of L. We obtain a complete result about the inverse-definiteness property of L with real constants a and b when b
2-4a > 0 and a - bk
2 + k
4 ≠ 0 for any k ∈? {1, 2, 3, . . . }.
Supported by GNAFACNR and the Natural Science Foundation of China and Jiangsu Provincial Education Commission 相似文献
922.
XinRongMA 《数学学报(英文版)》2004,20(1):157-162
In two centuries ago,Ming Autu discovered the famous Catalan numbers while he tried to expand the function sin(2px) as power series of sin(x) for the case p=1,2,3.Very recently,P.J.Larcombe shows that for any p,sin(2px) can always be expressed as an infinite power series of sin(x) involving precise combinations of Catalan numbers as part of all but the initial p terms and gave all expansions for the case p=4,5.The present paper presents the desired expansion for arbitrary integer p. 相似文献
923.
ZhiXiangWU 《数学学报(英文版)》2004,20(1):125-134
In this paper.we study the ring #(D.B)and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules and the category of all(B.D)-Hopf modules BM^D.Cai and Chen have proved this result in the case B=D=A.Secondly they have proved that if A has a nonzero left integral then A#A^*rat is a dense subring of Endk(A).We prove that #(A,A) is a dense subring of Endk(Q),where Q is a certain subspace of #(A.A)under the condition that the antipode is bijective(see Theorem18).This condition is weaker than the condition that A has a nonzero integral.It is well known the antipode is bijective in case A has a nonzero integral.Furthermore if A has nonzero left integral,Q can be chosen to be A(see Corollary 19)and #(A,A)is both left and right primitive.Thus A#A^*rat #(A,A)-Endk(A).Moreover we prove that the left singular ideal of the ring #(A,A)is zero.A corollary of this is a criterion for A with nonzero left integral to be finite-dimensional,namely the ring #(A,A)has a finite uniform dimension. 相似文献
924.
Cauchy Problem of Some Doubly Degenerate Parabolic Equations with Initial Datum a Measure 总被引:1,自引:0,他引:1
This paper discusses the Cauchy problem of the equation
with initial datum a measure. Under the assumption of the parameters, one proves the existence and non-existence of the non-negative
generalized solution.
Member in Partner Group of MPI for Math. in Leipzig at AMSS.
Supported by the Research Fund for Returned Overseas Chinese Scholars 20010107 相似文献
(1) |
925.
WeiJieFENG 《数学学报(英文版)》2004,20(6):983-988
In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang‘s paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems. 相似文献
926.
LuisVazauez 《计算数学(英文版)》2003,21(4):491-494
We present a generalization of the linear one-dimensional diffusion equation by com-bining the fractional derivatives and the internal degrees of freedom. The solutions areconstructed from those of the scalar fractional diffusion equation. We analyze the in-terpolation between the standard diffusion and wave equations defined by the fractionalderivatives. Our main result is that we can define a diffusion process depending on theinternal degrees of freedom associated to the system. 相似文献
927.
A Global Solution to a
Two-dimensional Riemann Problem Involving Shocks as Free
Boundaries 总被引:4,自引:0,他引:4
YuxiZheng 《应用数学学报(英文版)》2003,19(4):559-572
We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values. 相似文献
928.
On the Upper Bound of Second Eigenvalues for Uniformly Elliptic Operators of any Orders 总被引:1,自引:0,他引:1
Gao Jia Xiao-ping Yang Chun-lin QianBengbu Tank Institute Bengbu China & School of Science Nanjing University of Science Technology Nanjing ChinaSchool of Science Nanjing University of Science Technology Nanjing China Suzhou Television & Radio Broadcasting University Suzhou China 《应用数学学报(英文版)》2003,19(1):107-116
Abstract Let Ω R~m(m≥1)be a bounded domain with piecewise smooth boundary Ω.Let t and r bepositive integers with t>r+1. We consider the eigenvalue problems(1.1)and(12),and obtain Theorem 1and Theorem 2, which generalize the results in[1,2.5]. 相似文献
929.
Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models 总被引:3,自引:0,他引:3
Song-guiWang Mi-xiaWu Wei-qingMa 《应用数学学报(英文版)》2003,19(1):13-18
Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the nean square errors criterion,where the model matrix need not have full rank and the dispersion matrix can be singular.Our results show that any one of both estimates cannot be always superior to the other.Some sufficient criteria for any one of them to be better than the other are established.Some interesting relations between these two estimates are also given. 相似文献
930.
“调配问题”的动态规划模型与计算 总被引:1,自引:0,他引:1
本给出了调配问题的动态规划模型与计算,该表征更具一般化,且便于计算机计算。 相似文献