A Stability Estimate for a Solution to a Three-Dimensional Inverse Problem for the Maxwell Equations

We consider the problem of determining dielectric permittivity and conductivity in the Maxwell equations. As additional information we prescribe the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindric domain. We establish a stability estimate for a solution to the inverse problem and a uniqueness theorem.     

厚高阶光学非线性介质Z扫描的变分法分析

利用变分法对具有五阶光学非线性介质的Z扫描特性进行了研究。通过比较，发现当介质在具有较大的五阶非线性系数或较大光强的情况下，五阶非线性项的作用是不可忽略的。这对光限制器的设计和Z扫描实验都具有一定的指导意义。     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.     

On the multidimensional distribution of the subset sum generator of pseudorandom numbers

We show that for a random choice of the parameters, the subset sum pseudorandom number generator produces a sequence of uniformly and independently distributed pseudorandom numbers. The result can be useful for both cryptographic and quasi-Monte Carlo applications and relies on bounds of exponential sums.

     

Lorentz Invariant Decompositions of the State Vector Spaces and the Basis Problem

We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are shown to be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together.     

Capacity Constrained Transit Assignment with Common Lines

This paper proposes the use of absorbing Markov chains to solve the capacity constrained transit network loading problem taking common lines into account. The approach handles congested transit networks, where some passengers will not be able to board because of the absence of sufficient space. The model also handles the common lines problem, where choice of route depends on frequency of arrivals. The mathematical formulation of the problem is presented together with a numerical example. This revised version was published online in July 2006 with corrections to the Cover Date.     

On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

LetB ₁ be a ball of radiusr ₁ inS ⁿ (ℍⁿ), and letB ₀ be a smaller ball of radiusr ₀ such thatB ₀ ⊂B ₁ . ForS ⁿ we considerr ₁ π. Let u be a solution of the problem- δm = 1 in Ω :=B ₁ /B ₀ vanishing on the boundary. It is shown that the associated functionalJ (Ω) is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian on Ω is maximal if and only if the balls are concentric.     

ON THE EQUATION □φ = |vφ|2 IN FOUR SPACE DIMENSIONS

This paper considers the following Cauchy problem for semilinear wave equations in n spacedimensions□φ = F( φ),φ(0, x) = f(x), tφ(0, x) = g(x),The minimal value of s is determined such that the above Cauchy problem is locally well-posed in Hs. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n ≥ 5). The purpose of thispaper is to supplement with a proof in the case n = 2, 4.     

Comment on “A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map“

Comment on a recent paper on Commun. Theor. Phys. (Beijing, China) 38 (2002) pp. 523-528.     

THE COUPLING OF NATURAL BOUNDARY ELEMENT AND FINITE ELEMENT METHOD FOR 2D HYPERBOLIC EQUATIONS

In this paper, we investigate the coupling of natural boundary element and finite element methods of exterior initial boundary value problems for hyperbolic equations. The governing equation is first discretized in time, leading to a time-step scheme, where an exterior elliptic problem has to be solved in each time step. Second, a circular artificial boundary FR consisting of a circle of radius R is introduced, the original problem in an unbounded domain is transformed into the nonlocal boundary value problem in abounded subdomain. And the natural integral equation and the Poisson integral formula are obtained in the infinite domainΩ2 outside circle of radius R. The coupled variational formulation is given. Only the function itself, not its normal derivative at artificial boundary ΓR, appears in the variational equation, so that the unknown numbers are reducedand the boundary element stiffness matrix has a few different elements. Such a coupled method is superior to the one based on direct boundary element method. This paper discusses finite element discretization for variational problem and its corresponding numerical technique, and the convergence for the numerical solutions. Finally, the numerical example is presented to illustrate feasibility and efficiency of this method.