相关论文: A Parametric Interpolation Framework for 1D Scalar…
The equivalence of inertial and gravitational masses is a defining feature of general relativity. Here, we clarify the status of the equivalence principle for interactions mediated by a universally coupled scalar, motivated partly by recent…
We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…
In this contribution, we present a novel approach for solving the obstacle problem for (linear) conservation laws. Usually, given a conservation law with an initial datum, the solution is uniquely determined. How to incorporate obstacles,…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
We find, in an intrinsic form, a generalized Rankine-Hugoniot condition with respect to an entropy density that allows to give the proper interpretation to a formula of Vol'pert reducing the entropy condition on a function with bounded…
In this article, we propose a novel front tracking scheme for scalar conservation laws with spatially heterogeneous, uniformly convex flux and prove that approximations converge to the unique entropy solution. The main tools are Dafermos'…
We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in $L^2$, we show the existence and uniqueness of the solution by using a…
We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random $N (\gg 1)$-dimensional Gaussian landscape and confined by a…
Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
Spectral and spectral element methods using Galerkin type formulations are efficient for solving linear fractional PDEs (FPDEs) of constant order but are not efficient in solving nonlinear FPDEs and cannot handle FPDEs with variable-order.…
We investigate the properties of the high-order discontinuous Galerkin spectral element method (DGSEM) with implicit backward-Euler time stepping for the approximation of hyperbolic linear scalar conservation equation in multiple space…
Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…
The paper is concerned with locally stabilized space-time IgA approximations to initial boundary value problems of the parabolic type. Originally, similar schemes (but weighted with a global mesh parameter) was presented and studied by U.…
Many authors studied the problem that rational triangle pairs (triangle-parallelogram pairs) with the same area and the same perimeter. They investigated this problem by solving the rational solutions of the corresponding Diophantine…
The carr\'e du champ method is a powerful technique for proving interpolation inequalities with explicit constants in presence of a non-trivial metric on a manifold. The method applies to some classical Gagliardo-Nirenberg-Sobolev…
Laws of large numbers establish asymptotic guarantees for recovering features of a probability distribution using independent samples. We introduce a framework for proving analogous results for recovery of the $\sigma$-field of a…
Evolution equations which describe the changes in a velocity field over time have been classically studied within the Eulerian or Lagrangian frame of reference. Classically, these frameworks are equivalent descriptions of the same problem,…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…