Related papers: Complex Langevin: Boundary terms at poles
We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the…
We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrodinger equation for some…
We consider the so called Calder\'on problem which corresponds to the determination of a conductivity appearing in an elliptic equation from boundary measurements. Using several known results we propose a simplified and self contained proof…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
We describe the boundary of linear subvarieties in the moduli space of multi-scale differentials. Linear subvarieties are algebraic subvarieties of strata of (possibly) meromorphic differentials that in local period coordinates are given by…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
Real time evolution of a scalar field theory is investigated. The severe sign problem is circumvented using the Complex Langevin equation. The naive application of the method breaks down for extended real times due to the appearance of…
In this paper we derive quantitative conditions under which a compactly supported drift term depending on the direction of propagation blocks a traveling wave solution or lets it pass almost unchanged. We give explicit conditions on the…
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin…
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…
In this paper, we establish a moderate deviations principle for the Langevin dynamics with strong damping. The weak convergence approach plays an important role in the proof.
Concept drift is a major issue that greatly affects the accuracy and reliability of many real-world applications of machine learning. We argue that to tackle concept drift it is important to develop the capacity to describe and analyze it.…
This paper deals with an optimal control problem related to a phase field system of Caginalp type with a dynamic boundary condition for the temperature. The control placed in the dynamic boundary condition acts on a part of the boundary.…
Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide…
We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.
We present classical and generalized Riemann-Hilbert problem in several contexts arising from $K$-theory and bordism theory. The language of Fredholm pairs turns out to be useful and unavoidable. We propose an abstract formulation of a…