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1 IntroductionLet Ω be the unit disk {z: |z| < 1} in the complex plane C. In this paper, we consider the following boundary value problem: Find out a λ and the analytic function u(z) in the unit disk Ω such that they satisfy the boundary condition 相似文献
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0 Introduetion The Zakharov system,describing the coupling between Langmuir and ion-acoustic waves,is one of the basic plasma models.This system 相似文献
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In this paper, we give the Silov boundary for an analytic family on a bounded strictly pseudoconvex domain or an analytic polyhedron in Cn, and get a necessary and sufficient condition for a generalized Dirichlet problem to be solvable for an analytic family on a bounded holomorphic domain. Especially, we derive that this condition is just that the continuous real boundary value is prescribed on and only on the Silov boundary for an analytic family on a bounded strictly pseudoconvex domain or an analytic polyhedron. 相似文献
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YAO Zheng-an ZHOU Wen-shu LIU Qiang 《数学进展》2005,34(4):503-505
This paper studies a singular diffusion equation in nondivergence form with the Dirichlet boundary value and initial value Here p > 1,Ω(?) RN is a bounded domain with appropriately smooth boundary (?)Ω, and φ(u) satisfies the following condition (1.1) aries some models describing physical phenomenon. For example, if φ(u) = uq with q ∈[0,1), then (1.1) can be written in divergence form after the change of variables (provided 相似文献
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To study the local regularity of solutions to second order elliptic partial differential equations, Morrey in [1] introduced some function spaces, which are called the Morrey spaces todaySince then, many mathematicians have studied regularities of solutions to some kinds of secondorder elliptic equations in Morrey spaces.We give the deceptions of Morrey space and weak Morrey space first.Definition 1 Let TheThesubset of those functions of Lp for which will be called the Morrey space LpDefi… 相似文献
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本文引入了一类强Bazilevic函数,对任意实参数产,讨论了该类函数上的Fekete-Szegoe问题。其结论推广了一些已知的结果. 相似文献
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李书海 《数学的实践与认识》2004,34(7):126-131
引进用 Hλ算子刻画的一族解析函数 Pn(λ,α,β,ρ)并研究族 Pn(λ,α,β,ρ)上算子函数及其导数的α阶组合问题 .得到用α阶组合定义的函数在圆域 |Z|相似文献
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关于某类解析函数的星象性和Ruscheweyh的一个问题 总被引:2,自引:0,他引:2
本文引入了一个涉及Ruscheweyh导数的解析函数子类,应用微分从属方法和Carlson-Shaffer算子讨论了它的从属关系和偏差定理;其次,应用单叶函数的性质和一个微分不等式研究了它的星象性条件和覆盖定理,最后,部分地解决了Ruscheweyh的一个问题。 相似文献
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0 Introduction Signal decomposition is a crucial issue and a key step in signal analysis,which provides the multiscale components for further processing.In many applications related to image and speech/audio processing,it is always necessary to decompose an input signal to extract information such as amplitudes,phases and frequencies.The classical decomposition methods include 相似文献
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TheOctonionalgebra,wedenoteitbyO,asavectorspaceoverF(F=RorC),isanalternative,non-associativedivisionalgebrawiththebasicOctonionicunits:whileeoistheunitelementinO,satisfyingthatandtheconstantstotallyantisymmetricinα,β,γarenon-zeroandequalunityforthesevencombinationsForthemultiplicationtable,see[PY],[J].Now,inwhatfollows,wedenotetheOctonionsbyOwhenF=R,anddenoteitbyOcwhenF=C.Forthereexistsauniqueanti-automorphismofsuchthatwhere"-"denotethecomplexconjugation.Wenowdefinetheinnerproductof… 相似文献
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In the combinatorial geometry of convex sets the question of how efficiently a family of convex sets can be pierced by points has led to various problems which may be regarded as extensions of the Helly-type problems. A family of sets is said to be n-pierceable (abbreviated as Пn) if there exists a set of n points such that each member of the family contains at least one of them. A family of sets is said to be Пnk if every subfamily of size k or less is Пn. The famous Helly theorem in combinatorial geometry asserts that for finite families of convex sets in the plane П13 implies П1. In a recent paper by M. Katchalski and D. Nashtir[a] the following conjecture of Griinbaum[2] was mentioned again: 相似文献
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The paper addresses a nonlinear heat equation (the porous medium equation) in the case of a power-law dependence of the heat conductivity coefficient on temperature. The equation is used for describing high-temperature processes, filtration of gases and fluids, groundwater infiltration, migration of biological populations, etc. The heat waves (waves of filtration) with a finite velocity of propagation over a cold background form an important class of solutions to the equation under consideration. A special boundary value problem having solutions of such type is studied. The boundary condition of the problem is given on a sufficiently smooth closed curve with variable geometry. The new theorem of existence and uniqueness of the analytic solution is proved. 相似文献
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本文引入了一类强Bazilevi函数,对任意实参数μ,讨论了该类函数上的Fekete-Szeg(o)问题,其结论推广了一些已知的结果. 相似文献
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Deng Guantie 《东北数学》1995,(1)
RepresentationFormulasforAnalyticFunctionNon-exponentialinaHalfPlaneDengGuantie(邓冠铁)(DepartmentofMathematics,HuazhongUniversi... 相似文献
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This paper studies the behaviors of the solutions in the vicinity of a given almost periodicsolution of the autonomous systemwhere f ∈E C1(Rn, Rn). Since the periodic solutions of the autonomous system are not Liapunovasymptotic stable, we consider the weak orbitally stability.For the planar autonomous systems (n=2), the classical result of orbitally stability aboutits periodic solution with period w belongs to Poincare, i.e.Theorem A[1,2] A periodic solution p(t) to (1) with period w is o… 相似文献