Given a finite number of moments of an unknown density on a finite measure space, the best entropy estimate-that nonnegative density x with the given moments which minimizes the Boltzmann-Shannon entropy I(x):= x log x-is considered. A direct proof is given that I has the Kadec property in L-if Yn converges weakly to 37 and I(yn) converges to I(37), then yn converges to 37 in norm. As a corolla...

In this paper, we show that if the mean curvature of a closed smooth embedded flow in ${\\mathbb R}^3$ is type-$I$, then rescaled at first finite singular time converges smoothly to self-shrinker with multiplicity one. This result confirms Ilmanen's multiplicity-one conjecture under assumption type-$I$. As corollary, least

This paper considers a decentralized process in many-to-many matching problems. We show that if agents on one side of the market have substitutable preferences and those on the other side have responsive preferences, then, from an arbitrary matching, there exists a finite path of matchings such that each matching on the path is formed by satisfying a blocking individual or a blocking pair for t...

We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter and that with incorrect model parameters converges to zero uniformly over the infinite time interval as the misspecified model converges to the true model, ...

We propose a new method for quickly calculating the probability density function for first passage times in simple Wiener diffusion models, extending an earlier method used by Van Zandt, Colonius and Proctor (2000). The method relies on the observation that there are two distinct infinite series expansions of this probability density, one of which converges quickly for small time values, while ...

The goal of this paper is the analysis of a non-conforming finite element method for convex variational problems in the presence of the Lavrentiev phenomenon for which conforming finite element methods are known to fail. By contrast, it is shown that the Crouzeix–Raviart finite element discretization always converges to the correct minimizer.

In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation (Abraham model) for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is th...

We present a new inversion formula for the classical, finite, and asymptotic Laplace transform f̂ of continuous or generalized functions f . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of f̂ evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sens...