Related papers: Completeness of generalized transmission eigenstat…
Ordinary Boltzmann-Gibbs entropy is inadequate to be used in systems depending on a control parameter that yield different mean energy values. Such systems fail to give the correct comparison between the off-equilibrium and equilibrium…
We prove inequalities relating the measures of maximal entropy of two patterns u,v where the extender set of u is contained in the extender set of v. Our main results are two generalizations of a Theorem of Meyerovitch; the first applies to…
Several integral identities related to acoustic scattering are presented. In each case the identity involves the integral over frequency of a physical quantity. For instance, the integrated transmission loss, a measure of the transmitted…
After introducing the fundamental properties of self-gravitating systems, we present an application of Tsallis' generalized entropy to the analysis of their thermodynamic nature. By extremizing the Tsallis entropy, we obtain an equation of…
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder equipped with an incomplete Riemannian metric of Grushin type, in the class of metrics yielding an infinite deficiency…
Given $\Omega\subset \mathbb{R}^n$ with $n\geq 2$, $D\subset \Omega$ open, and $u:\Omega \to \mathbb{R}^m$, we study elliptic systems of the type $$ {\rm div} \big( ( A + (B- A)\chi_D)\nabla u\big) = 0 \quad \text{in $\Omega\cap B_1$,} $$…
We study Schwinger-Keldysh effective field theories (EFTs) for systems with non-Abelian internal symmetries near thermal equilibrium. We consider two approaches that were put forward in the literature -- one using a redundant Goldstone…
We consider the scattering transform for the Schr\"odinger equation with a singular potential and no bound states. Using the Riccati representation for real-valued potentials on the line, we obtain invertibility and Lipschitz continuity of…
In this paper, we have obtained a generalization of the Grothendieck's theorem for the space of continuous mappings $C_{\lambda,\mu}(X,Y)$ where $Y$ is a complete uniform space with the uniformity $\mu$ endowed with the topology of uniform…
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the hamiltonian structure of system following Dirac's methodology and, then, we…
On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive…
We consider ergodic random magnetic Schr\"odinger operators on the metric graph $\mathbb{Z}^d$ with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting…
We prove the optimal endpoint Strichartz estimates for Schr\"{o}dinger equation with charge transfer potentials and a general source term in $\mathbb{R}^n$ for $n\geq3$. The proof is based on using the projection on the scattering states…
A novel variational formulation of layer potentials and boundary integral operators generalizes their classical construction by Green's functions, which are not explicitly available for Helmholtz problems with variable coefficients.…
For the generalized oscillator, we prove a Rellich type theorem, or characterize the order of growth of eigenfunctions. The proofs are given by an extensive use of commutator arguments invented recently by Ito and Skibsted. These arguments…
In this note, we study some properties of threshold resonant states or threshold eigenfunctions for discrete Schr\"odinger operators. We mainly prove two theorems. First, we prove that resonant states at the elliptic threshold have the same…
In this work we investigate the transfer of fundamental order and completeness properties between truncated Riesz spaces and their unitizations. Specifically, we provide characterizations and equivalences for several notions of…
The generalized symmetry method is applied to a class of completely discrete equations including the Adler-Bobenko-Suris list. Assuming the existence of a generalized symmetry, we derive a few integrability conditions suitable for testing…
We will study solvability of nonlinear second-order elliptic system of partial differential equations with nonlinear boundary conditions. We study the generalized Steklov Robin eigensystem (with possibly matrices weights) in which the…
In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.