A Stability Estimate for a Solution of the Problem of Determining the Dielectric Permittivity

We consider the problem of determining the dielectric permittivity for a nonconducting and nonmagnetic medium. As information we take the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindrical domain. These traces correspond to a solution to some direct problem for the Maxwell system. The impulse source of the current flux lies outside the domain in which the coefficient is sought. The main result of the article is a stability estimate for a solution to the inverse problem in question.     

Eigenvalue and stability of singular differential delay systems

The eigenvalue and the stability of singular differential systems with delay are considered. Firstly we investigate some properties of the eigenvalue, then give the exact exponential estimation for the fundamental solution, and finally discuss the necessary and sufficient condition of uniform asymptotic stability.     

Annealing behavior of gel‐spun polyethylene fibers at temperatures lower than needed for significant shrinkage

The annealing at 373 K of ultrastrong, gel‐spun polyethylene (PE) has been studied. At this temperature, the fibers show no significant shrinkage. Still, a significant decrease in the mechanical properties is observed. The fibers have been analyzed with differential scanning calorimetry (DSC), temperature‐modulated differential scanning calorimetry (TMDSC), atomic force microscopy (AFM), and small‐angle X‐ray scattering (SAXS). During the annealing, the glass transition of the intermediate phase is exceeded, as shown by DSC. When split for structure analysis by AFM, the annealed fibers undergo plastic deformation around the base fibrils instead of brittle fracture. The quasi‐isothermal TMDSC experiments are compared to the minor structural changes seen with SAXS and AFM. The loss of performance of the PE fibers at 373 K is suggested to be caused by the oriented intermediate phase, and not by major changes in the structure or morphology. The overall metastable, semicrystalline structure is shown by TMDSC to posses local regions that can melt reversibly. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 403–417, 2003     

Periodic solutions of nonlinear impulsive differential inclusions with constraints

In this paper we obtain the existence of periodic solutions for nonlinear ``invariance' problems monitored by impulsive differential inclusions subject to impulse effects.

     

Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ². A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Online publication 23 January 2004.     

Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

On Covariant Phase Space and the Variational Bicomplex

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation.     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

Commuting Rank 2 Differential Operators Corresponding to a Curve of Genus 2

We construct commuting rank 2 formally self-adjoint ordinary differential operators corresponding to a curve of genus 2.     

具有无限时滞的二阶微分方程解的存在性

§ 1.　IntroductionRecently ,thedifferentialequationswithdeviatingargumentswereusuallydiscussed(see[1 ],[4],[5 ]) .In [1 ],AGARWALRPandO’REGANDconsideredequationy″(t) =f(t,y(t) ,y(σ(t) ) ) ,　a.e .t∈ [0 ,1 ]y(t) =ψ(t) ,　　　　　　　　t∈ [-r ,0 ]y( 1 ) =a ,( )andtheydiscussedtheexistenceofatleastonesolutionforequation ( ) .Inthispaper ,weconsideramoregeneralequation-x″(t) =f(t ,xt) ,　t∈ [0 ,1 ]x(t) =ψ(t) ,　　　　t∈ ( -∞ ,0 ]x( 0 ) =x( 1 ) =0 ,( 1 .1 )andsomeexistencetheor…