in this paper we consider a petrovsky viscoelastic inverse source problem with memory term in the boundary condition. we obtain sufficient conditions on relaxation function and initial data for which the solutions of problem are asymptotically stable when the integral overdetermination tends to zero as time goes to infinity.

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

We give a survey of some results, mainly obtained by the authors and their collaborators, on spectral properties of the magnetic Schrödinger operators in the semiclassical limit. We focus our discussion on asymptotic behavior of the individual eigenvalues for operators on closed manifolds and existence of gaps in intervals close to the bottom of the spectrum of periodic operators.

We study three internally connected Sturm-Liouville problems for nonlinear ordinary differential equations that are motivated by the problem of aeroelastic instability. Solutions are analyzed and asymptotic results are presented. A numerical study using a development of simple shooting reveals the spectrum and corresponding eigenfunctions.

We present a novel, simple asymptotic expansion for the spectrum of radiation that is backscattered from a laser by a counterpropagating (or copropagating) electron. The solutions are presented in such a way that they explicitly show the relative merit of using an intense laser and of an energetic electron beam in x-ray production in the single particle regime. Simple scaling laws are given.

In this note we show that the length spectrum for metric graphs exhibits a very high degree of degeneracy. More precisely, we obtain an asymptotic for the number of pairs of closed geodesics (or closed cycles) with the same metric length.

The purpose of this paper is to describe asymptotic formulas for determinants of certain operators that are analogues of Wiener-Hopf operators. The determinant formulas yield information about the distribution functions for certain random variables that arise in random matrix theory when one rescales at “the edge of the spectrum”.

The classical second order Lamé equation contains a so-called accessory parameter B. In this paper we study for which values of B the Lamé equation has a monodromy group which is conjugate to a subgroup of SL(2,R) (unitary monodromy with indefinite hermitian form). We refomulate the problem as a spectral problem and give an asymptotic expansion for the spectrum.

It is shown that when the dimension of gauge group exceeds a critical value NC, the only types of asymptotic-freedom-allowed representations for ._ fermions are vector and second rank tensors. A possible connection between this observation and quark-lepton spectrum is discussed.

We study asymptotic behavior of the spectrum of a Schrödinger type operator LV = L− λV on the Wiener space as λ→∞. Here L denotes the Ornstein-Uhlenbeck operator and V is a nonnegative potential function which has finitely many zero points. For some classes of potential functions, we determine the divergence order of the lowest eigenvalue. Also tunneling effect is studied.