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We study integro-differential inclusions in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations and inclusions are covered by the…
In collisional ionization equilibrium (CIE), the X-ray spectrum from a plasma depends on the distribution of emission measure over temperature (DEM). Due to the well-known ill conditioning problem, no precisely resolved DEM can be inverted…
We show that some previous results concerning the boundedness of differentiation and integration operators on weighted spaces given by radial weights in the unit disk or the complex plane might fail without some natural additional…
While an integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions is available in the literature, a proof of this formula seems to be…
The process of deriving an interatomic potentials represents an attempt to integrate out the electronic degrees of freedom from the full quantum description of a condensed matter system. In practice it is the derivatives of the interatomic…
I discuss in this paper the behaviour of the solutions of the so-called q-hyperbolic potentials, i.e. P"oschl-Teller-like and conditionally solvable potentials, in terms of the path integral formalism. The differences in comparison to the…
At low temperature using thermodynamics of irreversible processes the general expressions for the temperature dependence of the thermopower in the case of the hopping conductivity for disordered materials are found. The account of influence…
We study the correct solvability of an abstract functional differential equations in Hilbert space, which includes integro-differential equations describing evolution of thermal phenomena, heat transfer in materials with memory or sound…
In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be symplectic. This…
An implementation of an electron temperature-dependent interaction potential for copper in a two-temperature model-molecular dynamics framework is presented. An algorithm for enforcing energy conservation when using such an interaction is…
The aging phenomena occurring in the course of cycling processes in the insertion host-guest compounds are discussed in the framework of a simple model. It takes into account two types of effects. One can be attributed to modifications of…
Using the modified factorization method employed by Mielnik for the harmonic oscillator, we show that isospectral structures associated with a second order operator $H$, can always be constructed whenever $H$ could be factored, or exist…
In this article we prove a sharp decay estimate for certain multilinear oscillatory integral operators of a form inspired by the general framework of Christ, Li, Tao, and Thiele [6]. A key purpose of this work is to determine when such…
We prove H\"older regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also…
Based on the work of Heemskerk, Marolf, Polchinski and Sully (HMPS), we study the reconstruction of operators behind causal horizons in time dependent geometries obtained by acting with shockwaves on pure states or thermal states. These…
Providing students of introductory thermal physics with a plot of the heat capacities of many low density gases as a function of temperature allows them to look for systematic trends. Specifically, large amounts of heat capacity data allow…
The present work is devoted to the problem of boundary stabilization of the semilinear 1-D heat equation with nonlocal boundary conditions. The stabilizing controller is finite-dimensional, linear, given in an explicit form, involving only…
The extended Hubbard model can host s-wave, d-wave and p-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. Upon detailed examination of the free energy functional of the gap in this…
In this paper we study left-invariant Laplacians on compact connected groups that are form-comparable perturbations of bi-invariant Laplacians. Our results show that Gaussian bounds for derivatives of heat kernels enjoyed by certain…
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…