Related papers: Exact sum rules for inhomogeneous drums
We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j \pm 1| and…
In this article, we derive a congruence property of particular sum rules involving prime numbers. The resulting expression involves Bernoulli numbers and polynomials, for which we obtain, as a consequence, a general congruence relation as…
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if…
New bounds are derived for the eigenvalues of sums of Kronecker products of square matrices by relating the corresponding matrix expressions to the covariance structure of suitable bi-linear stochastic systems in discrete and continuous…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a…
In the paper we develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of first-order ordinary differential equations in spaces of smooth functions on a finite interval. This problems are set…
We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
We consider the crossing and non-crossing O(1) dense loop models on a semi-infinite strip, with inhomogeneities (spectral parameters) that preserve the integrability. We compute the components of the ground state vector and obtain a closed…
An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
Higher degree forms are homogeneous polynomials of degree $d > 2,$ or equivalently symmetric $d$-linear spaces. This paper is mainly concerned about the algebraic structure of the centers of higher degree forms with applications…
We consider the problem of deriving upper bounds on the parameters of sum-rank-metric codes, with focus on their dimension and block length. The sum-rank metric is a combination of the Hamming and the rank metric, and most of the available…
In this thesis I demonstrate that isospectral domains, that is domains of differing geometric shapes that possess identical spectra, do not remain isospectral when subject to uniform rotation. One thus *can* hear the shape of a rotating…
We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words Ewald sums for one dimension. We also provide a set of tools for exploring the…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often…
The moduli associated with boundaries in a Riemann surface are parametrized by the positions and strengths of electric charges. This suggests a method for summing over orientable Riemann surfaces with Dirichlet boundary conditions on the…
We show that eigenvalue correlations in unitary-invariant ensembles of large random matrices adhere to novel universal laws that only depend on a multicriticality of the bulk density of states near the soft edge of the spectrum. Our…