Boundary conditions for the volume potential for the polyharmonic equation

In a bounded connected domain, we obtain boundary conditions for the volume potential for the polyharmonic equation.     

Estimates for the classical parametrix for the Laplacian

We consider the integral operators which were used classically to give a parametrix and remainder for the Laplacian on a Riemannian manifold. Their kernels are defined in terms of the distance function. These operators are shown to be bounded operators on the L₂ Hilbert spaces of differential forms, under the hypotheses that the manifold be complete and of finite volume, and that it satisfy curvature bounds. Furthermore, the remainder is shown to be compact.     

正态变差系数的经典限

本文推导了正态变差系数的经典精确限.为了满足工程实践的需要,利用Odeh和Owen的计算方法及Brent算法,给出了高精度的可手算的近似限.对不同的置信度γ及样本大小n=1(1)30,40,60,120,样本变差系数ε=0.01(0.01)0.20,计算了正态变差系数的经典精确限表.本文指出,当n≤8,ε≤0.20时,经典精确限C_u略大于Fiducial精确限C_u,F.当n>8.ε≤0.20时.C_u-C_u,F<5×10-6.     

行业对电子商务综合规范需求分析研究

通过对中国各大城市不同类型的企业调查分析,运用多变量统计分析模型,对各行业的电子商务综合规范需求及差异进行了对比分析,利用统计分析结果剖析其原因与关键问题,最后提出若干合理化建议.     

Integral equations for the Fourier-transformed boundary values for the transmission problems for right-angled wedges and octants

A 4×4-system of integral equations for the Fourier transformed boundary values of the normal derivatives of the wave functions defined in the four quadrants of R ²-space is derived. This system results from the scalar transmission problem with continuous passage of the boundary values of the total wave-fields and of the weighted normal derivatives corresponding to the case of magnetically polarized fields. Several equivalent systems of integral equations are deduced then which show that Banach's fixed point principle may be applied at least for slightly differing media in the four quadrants. The method, which is equivalent to a compatibility condition for holomorphic functions, may be generalized to the case of the scalar transmission problem for octants in R ³-space. There a 12 × 12-system of integral equations for the Fourier transformed normal derivatives on the quarter-plane faces is established.     

Solvability Conditions for the Second Boundary Value Problem for the Navier System

Under consideration is the second boundary value problem in a half-space for the Navier system.We provide some necessary conditions for unique solvability in Sobolev spaces.     

Wavelet moment method for the Cauchy problem for the Helmholtz equation

The paper is concerned with the problem of reconstruction of acoustic or electromagnetic field from inexact data given on an open part of the boundary of a given domain. A regularization concept is presented for the moment problem that is equivalent to a Cauchy problem for the Helmholtz equation. A method of regularization by projection with application of the Meyer wavelet subspaces is introduced and analyzed. The derived formula, describing the projection level in terms of the error bound of the inexact Cauchy data, allows us to prove the convergence and stability of the method.     

Criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation

In the present paper, we prove a necessary and sufficient condition for the well-posedness of the problem indicated in the title in the space L ₂(Ω). To this end, we use expansions in the eigenfunctions of the mixed Cauchy problem for the Laplace equation with a deviating argument.     

Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation

The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined.     

Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus

In this note, we report on the formulation and mathematical analysis of single and multiple group models for the spread of the human immuno-deficiency virus (HIV), which is the etiological agent for the acquired immunodeficiency syndrome (AIDS). Results on the robustness of a single group model are stated for specific and arbitrary survivorship functions. In addition, we provide results that show that multiple group models can have multiple endemic equilibria.     

On the domino-parity inequalities for the STSP

One method which has been used very successfully for finding optimal and provably good solutions for large instances of the symmetric travelling salesman problem (STSP) is the branch and cut method. This method requires knowledge of classes of useful valid inequalities for the polytope associated with the STSP, as well as efficient separation routines for these classes of inequalities. Recently a new class of valid inequalities called the domino-parity inequalites were introduced for the STSP. An efficient separation routine is known for these constraints if certain conditions are satisfied by the point to be separated. This separation routine has never been implemented or tested. We present several performance enhancements for this separation routine, and discuss our implementation of this improved algorithm. We test our implementation and provide results which we believe demonstrate the practical usefulness of these constraints and the separation routine for the STSP within a branch and cut framework. This research was partially supported by grants from the Natural Sciences and Engineering Research Council of Canada     

A new approach for the derivation of bounds for the Jensen difference

There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.     

Conditions for Optimal Scheduling for the Three-machine Problem

This note proposes a simpler formulation for the conditionssuggested by Eltman & Townsend for the three-machine problem,which if satisfied must result in one job preceding anotherin an optimal sequence. These are compared with Johnson's conditions.     

On the convergence condition for the Schwarz alternating method for the two-dimensional Laplace equation

The Schwarz alternating method makes it possible to construct a solution of the Dirichlet problem for the two-dimensional Laplace equation in a finite union of overlapping domains, provided that this problem has a solution in each domain. The existing proof of the method convergence and estimation of the convergence rate use the condition that the normals to the boundaries of the domains at the intersection points are different. In the paper, it is proved that this constraint can be removed for domains with Hölder continuous normals. Removing the constraint does not affect the rate of convergence.

     

Stability estimates for the solutions of control problems for the stationary magnetohydrodynamic equations

We study control problems for the stationary magnetohydrodynamic equations. In these problems, one has to find an unknown vector function occurring in the boundary condition for the magnetic field and the solution of the boundary value problem in question by minimizing a performance functional depending on the velocity and pressure. We derive new a priori estimates for the solutions of the original boundary value problem and the extremal problem and prove theorems on the local uniqueness and stability of solutions for specific performance functionals.     

On Li's criterion for the Riemann hypothesis for the Selberg class

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In this paper, we shall prove a generalization of Li's positivity criterion for the Riemann hypothesis for the extended Selberg class with an Euler sum. We shall also obtain two arithmetic expressions for Li's constants , where the sum is taken over all non-trivial zeros of the function F and the indicates that the sum is taken in the sense of the limit as T→∞ of the sum over ρ with |Imρ|?T. The first expression of λF(n), for functions in the extended Selberg class, having an Euler sum is given terms of analogues of Stieltjes constants (up to some gamma factors). The second expression, for functions in the Selberg class, non-vanishing on the line , is given in terms of a certain limit of the sum over primes.

Video

For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=EwDtXrkuwxA.     

On the search for weighted inequalities for operators related to the Ornstein-Uhlenbeck semigroup

In this paper, for each given $ we characterize the weights v for which the centered maximal function with respect to the gaussian measure and the Ornstein-Uhlenbeck maximal operator are well defined for every function in and their means converge almost everywhere. In doing so, we find that this condition is also necessary and sufficient for the existence of a weight u such that the operators are bounded from into We approach the poblem by proving some vector valued inequalities. As a byproduct we obtain the strong type (1,1) for the “global” part of the centered maximal function. Received May 18, 1999 / Revised December 9, 1999 Published online July 20, 2000     

Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary.     

A functional form for the lower Lipschitz condition for the stable subordinator

Summary Consider a completely asymmetric stable process with characteristic exponent less than one. J. Hawkes (1971, Z. Wahrscheinlichkeitstheor. Verw. Geb.17, 23–32) proved a result for the lower Lipschitz condition. In the present paper a functional form for this result is proved.