Related papers: The torsion log-Minkowski problem
We prove that an approximated version of the Brunn--Minkowski inequality with volume distortion coefficient implies a Gaussian concentration-of-measure phenomenon. Our main theorem is applicable to discrete spaces.
We present an efficient algorithm that computes the Minkowski sum of two polygons, which may have holes. The new algorithm is based on the convolution approach. Its efficiency stems in part from a property for Minkowski sums of polygons…
The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex body. Two types of Minkowski problems in particular are an…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges,…
In this Note, we prepare an $\varepsilon$-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. We prove that the solution to the $\varepsilon$-Stokes problem,…
We consider the small mass asymptotic (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The friction coefficient is assumed to be vanishing within certain region. We introduce a…
We present a theoretical derivation of the homogenous Maxwell equations, based on Stokes theorem for Minkowski space tensors.
In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, which can be seen…
The 100-year-long problem concerning the correct form of the electromagnetic energy-momentum tensor in continuous media (usually called the Abraham-Minkowski problem) continues to attract interest. We provide a critical analysis of…
The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
{We consider alternating minimization procedures for convex optimization problems with variable divided in many block, each block being amenable for minimization with respect to its variable with freezed other variables blocks. In the case…
We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
We study the Dirichlet problem for functions whose graphs are spacelike hypersurfaces with prescribed curvature in the Minkowski space and we obtain some new interior second order estimates for admissible solutions to the corresponding…
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have…
We present a finite-element approximation for the one-sided Stefan problem and the one-sided Mullins--Sekerka problem, respectively. The problems feature a fully anisotropic Gibbs--Thomson law, as well as kinetic undercooling. Our…