Related papers: A necessary condition for the logarithmic Minkowks…

We begin a systematic study of the region of possible values of the volumes of Minkowski subset sums of a collection of $M$ compact sets in $\mathbb{R}^d$, which we call the Lyusternik region, and make some first steps towards describing…

The classical Minkowski problem for convex bodies has deeply influenced the development of differential geometry. During the past several decades, abundant mathematical theories have been developed for studying the solutions of the…

We present a unified study of first and second order necessary and sufficient optimality conditions for minimax and Chebyshev optimisation problems with cone constraints. First order optimality conditions for such problems can be formulated…

We develop a new discrete mathematical model which includes the classical Sudoku puzzle, Latin Squares and gerechte designs. This problem is described by integer equations and a special type of inequality constraint. We consider solutions…

In this paper we prove the necessity of the main sufficient condition of Meinardus for sub exponential rate of growth of the number of structures, having multiplicative generating functions of a general form and establish a new necessary…

We prove an extension of Yuan's Lemma to more than two matrices, as long as the set of matrices has rank at most 2. This is used to generalize the main result of [A. Baccari and A. Trad. On the classical necessary second-order optimality…

We give necessary and sufficient conditions for a pair of (generalized) functions $\rho_1(\mathbf{r}_1)$ and $\rho_2(\mathbf{r}_1,\mathbf{r}_2)$, $\mathbf{r}_i\in X$, to be the density and pair correlations of some point process in a…

In this paper, we derive the existence of solutions with small volume to the $L_p$-Gaussian Minkowski problem for $1\leq p<n$, which implies that there are at least two solutions for the $L_p$-Gaussian Minkowski problem.

We prove the EXPTIME-hardness of the validity problem for the basic temporal logic on Minkowski spacetime with more than one space dimension. We prove this result for both the lightspeed-or-slower and the slower-than-light accessibility…

In this paper, we obtain the classification theorem for three-dimensional complete space-like $\lambda$-translators $x:M^{3} \rightarrow \mathbb R^{4}_{1}$ with constant norm of the second fundamental form and constant $f_{4}$ in the…

We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of…

In this paper, we propose necessary and sufficient conditions for a scalar function to be nonincreasing along solutions to general differential inclusions with state constraints. The problem of determining if a function is nonincreasing…

We give a necessary condition for a domain to have a bounded extension operator from $L^{1,p}(\Omega)$ to $L^{1,p}(\mathbb R^n)$ for the range $1 < p < 2$. The condition is given in terms of a power of the distance to the boundary of…

This work is concerned with an optimal control problem on a Riemannian manifold, for which two typical cases are considered. The first case is when the endpoint is free. For this case, the control set is assumed to be a separable metric…

This article is concerned with the question of whether Marcinkiewicz multipliers on $\mathbb R^{2n}$ give rise to bilinear multipliers on $\mathbb R^n\times \mathbb R^n$. We show that this is not always the case. Moreover we find necessary…

We consider the Einstein-Maxwell equations in space-dimension $n$. We point out that the Lindblad-Rodnianski stability proof applies to those equations whatever the space-dimension $n\ge 3$. In even space-time dimension $n+1\ge 6$ we use…

Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…

We provide a necessary condition on the regularity of domains for the optimal embeddings of first order (and higher order) Orlicz-Sobolev spaces into Orlicz spaces in the sense of \cite{Cia96} (and \cite{Cia06}).

We use a matrix approach to study the concept of Morita context in the bicategory $\mathcal{LG}_{K}$ of Landau-Ginzburg models on a particular class of objects. In fact, we first use properties of matrix factorizations to state and prove…

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…