On the simpleness of zeros of Stokes multipliers

The aim of this paper is to discuss the simpleness of zeros of Stokes multipliers associated with the differential equation -Φ^″(X)+W(X)Φ(X)=0, where W(X)=X^m+a₁X^m-1+?+a_m is a real monic polynomial. We show that, under a suitable hypothesis on the coefficients a_k, all the zeros of the Stokes multipliers are simple.     

一类无结构三角网上抛物方程的有限差分区域分解算法

本文讨论了一类在无结构三角网上数值求解二维热传导方程的有限差分区域分解算法．在这个算法中,将通过引进两类不同类型的内界点,将求解区域分裂成若干子区域．一旦内界点处的值被计算出来,其余子区域上的计算可完全并行．本文得到了稳定性条件和最大模误差估计,它表明我们的格式有令人满意的稳定性和较高的收敛阶．     

混合中立型方程渐近衰退正解的存在性

该文利用Krasnoselskii不动点定理,讨论了一阶混合中立型微分方程[x(t)-cx(t-h)-c^*x(t+h^*)]'=p(t)x(g(t)),获得了方程在p\leq p(t)<0与0相似文献   

The Hadamard Theorem and Borel–Carathéodory Theorem on Riemann Surfaces

In this paper, we first define a kind of pseudo–distance function and annulus domain on Riemann surfaces, then prove the Hadamard Theorem and the Borel–Carathéodory Theorem on any Riemann surfaces. Supported by NSFC 10501052     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

On CNC commuting contractive tuples

The characteristic function has been an important tool for studying completely non-unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space H. We show that the characteristic function, which is now an operator-valued analytic function on the open Euclidean unit ball in ℂⁿ, is a complete unitary invariant for such a tuple. We prove that the characteristic function satisfies a natural transformation law under biholomorphic mappings of the unit ball. We also characterize all operator-valued analytic functions which arise as characteristic functions of pure commuting contractive tuples.     

Continuation of separately analytic functions defined on part of the domain boundary

Let D ? ? ⁿ be a domain with smooth boundary ?D, let E??D be a subset of positive Lebesgue measure mes(E) > 0, and let F ? G be a nonpluripolar compact set in a strongly pseudoconvex domain D ? ? ^m . We prove that, under an additional condition, each function separately analytic on the set X = (D × F) ∪ (E × G) has a holomorphic contination to the domain $\rlap{--} X = \{ (z,w) \in D \times G:\omega _{in}^ * (z,E,D) + \omega ^ * (w,F,D) < 1\} $ , where ω* is the P-measure and ω*_in is the interior P-measure.     

Dual-primal FETI algorithms for edge finite-element approximations in 3D

^** Email: toselli{at}sam.math.ethz.ch A family of dual-primal finite-element tearing and interconnectingmethods for edge-element approximations in 3D is proposed andanalysed. The key part of this work relies on the observationthat for these finite-element spaces there is a strong couplingbetween degrees of freedom associated with subdomain edges andfaces and a local change of basis is therefore necessary. Theprimal constraints are associated with subdomain edges. We proposethree methods. They ensure a condition number that is independentof the number of substructures and possibly large jumps of oneof the coefficients of the original problem, and only dependson the number of unknowns associated with a single substructure,as for the corresponding methods for continuous nodal elements.A polylogarithmic dependence is shown for two algorithms. Numericalresults validating our theoretical bounds are given.     

Dilation of generalized Toeplitz kernels on ordered groups

We introduce the concept of Toeplitz-Kre?n-Cotlar triplet on ordered groups and we prove a general dilation result and a general representation result for the positive definite case.This general result includes and extends previous generalizations of the Kre?n extension theorem, the Sz.-Nagy and Foias commutant lifting theorem and the generalized Herglotz-Bochner-Weil theorem.