共查询到20条相似文献,搜索用时 15 毫秒
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Mathematical Notes - 相似文献
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Some Simple Estimates for the Singular Values of Matrices 总被引:1,自引:0,他引:1
Chuan-long WANG Guo-jian ZHANGDepartment of Mathematics Normal College of Shanxi University Taiyuan ChinaDepartment of Applied Mathematics Taiyuan University of Technology Taiyuan China 《应用数学学报(英文版)》2002,18(1):117-122
Abstract We first provide a simple estimate for ||A~(-1)||_∞ and ||A~(-1)||_1 of a strictly diagonally dominant matrixA. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scalingwith a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness ofthe new bounds. 相似文献
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M. E. Fernandes Miranda 《Linear and Multilinear Algebra》1981,10(2):155-161
In this paper we prove several inequalities involving the characteristic values, the singular values, the real singular values and the imaginary singular values of a complex matrix. 相似文献
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A direct method is presented for solving a singular integralequation which is a generalization of one occurring in wave-guidetheory and in the theory of dislocations. The present methodavoids elaborate application of the complex variable methodsnormally associated with such singular integral equations. 相似文献
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The Dirichlet problem to a second order differential equation with some singularities is studied. Some existence results are established to the problem which generalize some results recently obtained by D. O‘Regan by eliminating some superfluous constrains to the problem. Also, some new results have been proven which may provide more useful information for the study of the problem. 相似文献
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对简单随机抽样两种定义的关系进行了讨论,澄清了教科书中的一些模糊不清之处;通过反例举证了两种定义在某种意义下的不等价性;给出了变概率抽样与不等概率抽样的定义,指出变概率抽样与不等概率抽样也可以是简单随机抽样;本文最后,给出了简单随机抽样的更具一般性的(广义)定义. 相似文献
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In this paper we consider the thin film equation with prescribed non-zero contact angle condition for a large class of mobility coefficients, in dimension 1. We prove the global in time existence of weak solutions by using a diffuse approximation of the free boundary condition. This approach, which can be physically motivated by the introduction of singular disjoining/conjoining pressure forces had been suggested in particular by Bertsch et al. in [11]. 相似文献
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关于积域上的粗糙奇异积分算子的一点注记 总被引:5,自引:0,他引:5
讨论积域上的奇异积分算子:TΩf(x,y) = p.v.∫Rn×RmΩ(u,v)|u|n|v|m f(x - u,y - v)dudv的Lp 有界性,及相应的Marcinkiew icz积分的L2 有界性. 其中Ω为类似文[4]中引进的函数类. 相似文献
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Ji-Guang Sun 《计算数学(英文版)》1988,6(4):325-335
Some results of the author are used to discuss the sensitivity of zero singular values and multiple singular values of a real matrix analytically dependent on several parameters. 相似文献
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We consider the solvability of the Dirichlet problem in a unit n-ball for the p-Laplacian equation with singular coefficients which are singular not only as |x| tends to 1 but also as |x| tends to 0. The existence and regularity of positive radial solutions are proved under some conditions related to parameters p, r, λ and q. 相似文献
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A simple direct relationship is.established between solutionsof a singular integral equation encountered in wave-guide theoryand in the theory of dislocations and the solutions of the singularCarleman integral equation. 相似文献
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For compact hyperbolic Riemann surfaces, the collar theorem gives a lower bound on the distance between a simple closed geodesic and all other simple closed geodesics that do not intersect the initial geodesic. Here it is shown that there are two possible configurations, and in each configuration there is a natural collar width associated to a simple closed geodesic. If one extends the natural collar of a simple closed geodesic α by ε >0, then the extended collar contains an infinity of simple closed geodesics that do not intersect α.Mathematics Subject Classiffications (2000). primary: 30F45; secondary: 32G07 相似文献
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We deal with weighted inequalities of the type [formula] where: T is either the HardyLittlewood maximal operator or asingular integral operator; G is any measurable subset of Rn; f is any measurable function, vanishing outside G, such thatTf is well-defined; v and w are weights, that is, nonnegativelocally integrable functions on G; p, q(1, ). 1991 Mathematics Subject Classification 42B20, 42B25. 相似文献
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§ 1.IntroductionandStatementsofResults Itiswell knownthatthemaximalsingularintegralonproductdomainsisveryusefullinharmonicanalysis.Herewelisttworesultsrelatedtothispaper.See [1 ] ,[2 ]andthereferencestherein . From [1 ] ,weknowthefollowingfact. SupposethatK(x,y)isl… 相似文献
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Yu WANG Hong YOU 《数学学报(英文版)》2006,22(6):1715-1720
This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that [d(u),u]^n is central, for all u ∈ L, then R must satisfy s4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Filippis's results. 相似文献
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Bounds on Singular Values Revealed by QR Factorizations 总被引:1,自引:0,他引:1
We introduce a pair of dual concepts: pivoted blocks and reverse pivoted blocks. These blocks are the outcome of a special column pivoting strategy in QR factorization. Our main result is that under such a column pivoting strategy, the QR factorization of a given matrix can give tight estimates of any two a priori-chosen consecutive singular values of that matrix. In particular, a rank-revealing QR factorization is guaranteed when the two chosen consecutive singular values straddle a gap in the singular value spectrum that gives rise to the rank degeneracy of the given matrix. The pivoting strategy, called cyclic pivoting, can be viewed as a generalization of Golub's column pivoting and Stewart's reverse column pivoting. Numerical experiments confirm the tight estimates that our theory asserts. 相似文献
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