Related papers: Dependence of the layer heat potentials upon suppo…
In this paper we present a self-contained variational theory of the layer potentials for the Stokes problem on Lipschitz boundaries. We use these weak definitions to show how to prove the main theorems about the associated Calder\'on…
In the paper the principal result obtained is the estimate for the heat kernel associated to the Schr\"odinger type operator $(1+|x|^\alpha)\Delta-|x|^\beta$ \[ k(t,x,y)\leq Ct^{-\frac{\theta}{2}}\frac {\varphi(x)\varphi(y)}{1+|x|^\alpha},…
Let M be a compact Riemannian manifold without boundary and let H be a self-adjoint generalized Laplace operator acting on sections in a bundle over M. We give a path integral formula for the solution to the corresponding heat equation.…
The heat capacity of solids at intermediate-to-high temperatures is of fundamental importance to several fields ranging from geology to material science. It depends on a variety of factors, with anharmonicity and, ultimately, melting…
We derive and discuss expressions for the temperature-dependent electrostatic polarizabilities of off-center ions holding good under various experimental conditions. At low temperatures and electric-field strengths, all of them reasonably…
This paper concerns the eigenvalues of the Neumann-Poincar\'e operator, a boundary integral operator associated with the harmonic double-layer potential. Specifically, we examine how the eigenvalues depend on the support of integration and…
We provide estimates for weighted Fourier sums of integrable functions defined on the sphere when the weights originate from a multiplier operator acting on the space where the function belongs. That implies refined estimates for weighted…
We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates…
A hybrid model is presented for hyperon polarization that is based on perturbative QCD subprocesses and the recombination of polarized quarks with scalar diquarks. The updated hybrid model is applied to $p+p\to \Lambda +X$ and successfully…
It is shown that the temperature dependence of Langmuir constants contains all the information needed to determine spherically averaged intermolecular potentials. An analytical ``inversion'' method based on the standard statistical model of…
It is shown that measured heat capacity depends on the rate of the temperature variation and on the initial state of a system. It is calculated here in the framework of two-level model. Fenomenological approach gives the same results.
We calculate holographically three-point functions of scalar operators with large dimensions at finite density and finite temperature. To achieve this, we construct new solutions that involve two isometries of the deformed internal space.…
Let $H=-\Delta+V$ be a Schr\"odinger operator on $\mathbb{R}^n$. We show that gradient estimates for the heat kernel of $H$ with upper Gaussian bounds imply polynomial decay for the kernels of certain smooth dyadic spectral operators. The…
We consider layer potentials associated to elliptic operators $Lu=-{\rm div}(A \nabla u)$ acting in the upper half-space $\mathbb{R}^{n+1}_+$ for $n\geq 2$, or more generally, in a Lipschitz graph domain, where the coefficient matrix $A$ is…
In the present article, we obtain an optimal support function of weighted $L^2$ integrations on superlevel sets of psh weights, which implies the strong openness property of multiplier ideal sheaves.
Temperature dependence of the capacitance of the electrical double layer (EDL) in concentrated electrolytes/ionic liquids has been under debates for decades. To rationalise the capacitance vs temperature dependence, we run molecular…
We prove existence results and lower bounds for the resonances of Schr\"odinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are derived from a combination of heat and wave trace expansions…
We consider a self-adjoint non-negative operator $H$ in a Hilbert space $\mathsf{L}^2(X,{\rm d}\mu)$. We assume that the semigroup $(\mathrm{e}^{-t H})_{t>0}$ is defined by an integral kernel, $p$, which allows an estimate of the form…
This study investigates the stabilization of interlayer temperature in the laser powder bed fusion process through a novel switched layer-to-layer closed-loop feedback controller. The controller architecture aims to measure the interlayer…
We extend the operator preconditioning framework [R. Hiptmair, Comput. Math. with Appl. 52 (2006), pp.~699--706] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their…