On the principles of limiting absorption and limit amplitude for a class of locally perturbed waveguides. Part 1: Time-independent theory

Let Ω be a local perturbation of the n-dimensional domain Ω₀ = Ropf;^{n ? 1} × (0, π). In a previous paper⁸ we have introduced the notion of an admissible standing wave. We shall prove that the principle of limiting absorption holds for the Dirichlet problem of the reduced wave equation in Ω at ω ≥ 0 if Ω does not allow admissible standing waves with frequency ω. From Reference 8, this condition is satisfied for every ω ≥ 0 if Ω ≠ Ω₀, and v · x ′ ≤ 0 on δΩ, where x′ = ( x ₁,…, x_{n ? 1}, 0) and v is the normal unit vector on δΩ pointing into the complement of Ω. In contrast to this, the principle of limiting absorption is violated in the case of the unperturbed domain Ω₀ at the frequencies ω = 1,2,… if n ≤ 3. The second part of our investigation, which will appear in a subsequent paper, is devoted to the principle of limit amplitude.     

与线性变换的完全环同构的环理论(Ⅱ)

<正> 为了进一步对本原环结构的研究,本文引进规范环的概念,我们说环R是规范的,若R是一个线性变换完全环并且及的基座对于任一对应基{E_i}皆有=∑RE_i=∑E_iR.容易知道,满足单侧理想极小条件的单纯环必是规范的.     

A new approach to the stability theory of functional differential systems

In this article we study the behaviour of dominant Fredholm eigenvalues for the Helmholtz operator in a regular bounded open set Ω in R^m relative to some larger set Ω′ if the latter is altered. It is shown that if the frequency is suitably chosen, then the dominant Fredholm eigenvalues decrease when Ω′ is decreased. This property was so far merely established for the Fredholm eigenvalues for the Laplacian (Kress and Roach, J. Math. Anal. Appl.55 (1976), 102–111). The results obtained will be applied to improve the convergence of a Neumann-Liouville bounded integral operator series, which serves as a tool in determining the solution of the Dirichlet problem.     

算子群的容许子群链

<正> 本文的目的是把作者(1956)最近所得到的一些有关链条件四条件的强果推广到算子群中去.在第一节里的主要结果是定理3,将其用于非结合环即得作者(1956)定理6之推广结果.在§2中讨论算子群的直接乘积的容许子群链,其主要结果为:若诸算子群均各     

Cauchy integral decomposition for harmonic forms

Let ann-dimensional differential form Ω be defined at points of aC ¹-smooth boundary π of a domainG ? ? ⁿ . Under what condition can Ω be represented as Ω = Ω₊ + Ω₊ + Ω_-, where Ω_± are forms insideG and outsideG, harmonic in the sense of Hodge? A necessary condition is that both restrictions Ω{inπ and *Ω{inπ be closed in the sense of currents. This condition, with an additional smoothness assumption, turns out to be sufficient as well. This is an analogue of the Cauchy integral decomposition of functions in the plane.     

有限维中心代数上矩阵方程组的广对称解与斜广对称解

设Ω是一个具有对合反自同构的有限维中心代数且charΩ≠2.本文在Ω上定义了广对称矩阵和斜广对称矩阵,在Ω[λ]上考虑了三个矩阵方程组,分别给出了其有广对称解和斜广对称的充要条件.作为特例,得到了某些矩阵方程相应的结果.     

半线性椭圆型问题爆炸解的存在性与渐近行为

设Ω是RN（N≥3）中的C2有界区域,f是单调非减的非负连续可微函数满足f＇（a）∫a∞1/f（s）ds≤C0,　a>0.应用一种新型的非线性变换w（x）=∫u（x）∞　ds/f（s）将爆炸解问题△u=k（x）f（u）,u>0,x∈Ω,u|　Ω=∞转化成等价的带奇异项的Dirichlet问题,不仅得到了爆炸解问题解的最小爆炸速度,而且揭示了两类典型非线性爆炸解问题基本上是相同的.应用摄动方法,上下解方法得到了爆炸解的存在性.特别允许非线性项的系数不仅在Ω的内部子区域恒为零而且在Ω上可适当无界.随后再应用摄动方法,将所得结果推广到无界区域,得到了整体爆炸解的存在性以及在无穷远附近的最小爆炸速度（有关文献参见[1-33]）.     

Base subsets in symplectic Grassmannians of small indices

Let V and V′ be n-dimensional vector spaces. Let also Ω and Ω′ be non-degenerate symplectic forms defined on V and V′, respectively. Denote by Π and Π′ the projective spaces associated with V and V′. We put for the sets of k-dimensional totally isotropic subspaces of Π and Π′. We study mappings of BF03322901 which transfer base subsets to base subsets and show that such mappings are induced by strong embeddings of Π to Π′ if 3k + 3 ≤ n.     

中心代数上一矩阵方程的中心对称与中心斜对称解

Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.     

A note on plurisubharmonic defining functions in$$\mathbb{C}^2$$

Let Ω ?? \(\mathbb{C}^2\) be a smoothly bounded domain. Suppose that Ω admits a smooth defining function which is plurisubharmonic on the boundary of Ω. Then the Diederich-Fornæss exponent can be chosen arbitrarily close to 1, and the closure of Ω admits a Stein neighborhood basis.     

Monoids of injective maps closed under conjugation by permutations

Let Ω be a countably infinite set, Inj(Ω) the monoid of all injective endomaps of Ω, and Sym(Ω) the group of all permutations of Ω. We classify all submonoids of Inj(Ω) that are closed under conjugation by elements of Sym(Ω).     

The Suzuki Groups Sz(q) and 2-(v,k,1) Designs

A 2-(v,k,1) design D=(Ω, B) is a systemconsisting of a finite set Ω of vpoints and a collection B of k-subsets of Ω, calledblocks,such that any 2-subset of Ω is contained in exactly one block.We shall always assume that 2相似文献   

An anisotropic inverse boundary value problem

We consider the impedance tomography problem for anisotropic conductivities. Given a bounded region Ω in space, a diffeomorphism Ψ from Ω to itself which restricts to the identity on ? Ω, and a conductivity γ on Ω, it is easy to construct a new conductivity Ψ_*γ which will produce the same voltage and current measurements on ? Ω. We prove the converse in two dimensions (i.e., if γ₁ and γ₂ produce the same boundary measurements, then γ₁, = Ψ_*γ₂ for an appropriate Ψ) for conductivities which are near a constant.     

On the solvability of the jump problem in clifford analysis

Let Ω be a bounded open and oriented connected subset of ? ⁿ which has a compact topological boundary Γ, let C be the Dirac operator in ? ⁿ , and let ?_0,n be the Clifford algebra constructed over the quadratic space ? ⁿ . An ?_0,n -valued smooth function f : Ω → ?_0,n in Ω is called monogenic in Ω if Df = 0 in Ω. The aim of this paper is to present the most general condition on Γ obtained so far for which a Hölder continuous function f can be decomposed as F ⁺ ? F ^? = f on Γ, where the components F ^± are extendable to monogenic functions in Ω^± with Ω⁺ := Ω, and Ω^? := ? ⁿ \ (Ω ? Γ), respectively.     

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF INHOMOGENEOUS p-LAPLACE EQUATION

LetΩbe a smooth bounded domain in Rn. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation -△pu=|u|q-1u λf(x) onΩ, and identify necessary and sufficient conditions onΩand f(x) which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.     

Lukasiewicz语义集上的紧Hausdorff拓扑

以Ω记从全体命题之集F（S）到单位区间的全体Lukasiewicz赋值之集.本文通过一种自然的方法在Ω上引入了Fuzzy拓扑δ,证明了其为第二可数的零维良紧空间,并证明了δ在Ω上生成的截拓扑空间是第二可数的紧Hausdorff空间,从而是可度量化的空间.     

The vetoers in a simple game with ordinal preferences

We consider a core of a simple game with ordinal preferences on a set of alternative outcomes Ω. When a player's strict preference relation takes any logically possible form of acyclic binary relation on Ω, necessary conditions for a simple game to have a nonempty core are given. If Ω is a finite set, the conditions are also sufficient. Further some related results are obtained.     

Stationary solutions to an energy model for semiconductor devices where the equations are defined on different domains

We discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain Ω₀ of the domain of definition Ω of the energy balance equation and of the Poisson equation. Here Ω₀ corresponds to the region of semiconducting material, Ω \ Ω₀ represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two‐dimensional stationary energy model. For this purpose we derive a W^1,p ‐regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set

Mathematical Notes - We consider a model nilpotent convex problem with two-dimensional control from an arbitrary convex set Ω. For the case in which Ω is a polygon, the problem is solved...