Related papers: Riemann-Schwarz Reflection Principle and Asymptoti…
We study the asymptotic behavior of a diffusion process with small diffusion in a domain $D$. This process is reflected at $\partial D$ with respect to a co-normal direction pointing inside $D$. Our asymptotic result is used to study the…
Let $R$ and $S$ be rings and $_R\omega_S$ a semidualizing bimodule. We prove that there exists a Morita equivalence between the class of $\infty$-$\omega$-cotorsionfree modules and a subclass of the class of $\omega$-adstatic modules. Also…
We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is…
We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness…
We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator…
We study the asymptotic behaviour of convolution-type functionals defined on general periodic domains by proving an extension theorem
In this note, I discuss in some detail the dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in math.AG/0402015, and used in math.QA/0412149 to…
The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…
We consider conformal defects joining two conformal field theories along a line. We define two new quantities associated to such defects in terms of expectation values of the stress tensors and we propose them as measures of the…
The composite systems can be non-uniquely decomposed into parts (subsystems). Not all decompositions (structures) of a composite system are equally physically relevant. In this paper we answer on theoretical ground why it may be so. We…
We reexamine the proofs of isospectrality of the counterexample domains to Kac' question `Can one hear the shape of a drum?' from an analytical viewpoint. We reformulate isospectrality in a more abstract setting as the existence of a…
We report a unified representation of the spatial and angular Goos-Hanchen and Imbert-Fedorov shifts that occur when a light beam reflects from a plane interface. We thus reveal the dual nature of spatial and angular shifts in optical beam…
We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Gamma-convergence. In contrast to what one naturally would expect, our result shows that the limiting…
The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or super-attracting fixed point with…
While the existence of conformal mappings between doubly connected domains is characterized by their conformal moduli, no such characterization is available for harmonic diffeomorphisms. Intuitively, one expects their existence if the…
Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, labyrinths, cells and mixed states of stripes and cells. These patterns do change in a reversible way when the intensity of an…
We study solutions of three-term recurrence relations whose $N$-step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics. For orthonormal polynomials we show more.…
In this paper, considering the difference between the finiteness dimension and cohomological dimension for a finitely generated module, we investigate the asymptotic behavior of grades of components of graded local cohomology modules with…
We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity…
I show that a model for the interaction of magnetic domains that includes a short range ferromagnetic and a long range dipolar anti-ferromagnetic interaction reproduces very well many characteristic features of two-dimensional magnetic…