相关论文: The Matrix-Valued $H^{p}$ Corona Problem in the Di…

This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calder\'on calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density…

Given a set of disks in the plane, the goal of the problem studied in this paper is to choose a subset of these disks such that none of its members contains the centre of any other. Each disk not in this subset must be merged with one of…

In the paper arXiv:1708.02289 we have introduced new solvability methods for strongly elliptic second order systems in divergence form on a domains above a Lipschitz graph, satisfying $L^p$-boundary data for $p$ near $2$. The main novel…

The $p$-center problem (pCP) is a fundamental problem in location science, where we are given customer demand points and possible facility locations, and we want to choose $p$ of these locations to open a facility such that the maximum…

We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We…

In this work we describe our implementation of a thermodynamic energy equation into the global corona model of the Space Weather Modeling Framework (SWMF), and its development into the new Lower Corona (LC) model. This work includes the…

We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…

We present a code for solving the nonlinear force-free equations in spherical polar geometry, with the motivation of modeling the magnetic field in the corona. The code is an implementation of the Grad-Rubin method. Our method is applicable…

The canonical polyadic decomposition (CPD) of a low rank tensor plays a major role in data analysis and signal processing by allowing for unique recovery of underlying factors. However, it is well known that the low rank CPD approximation…

This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mathcal{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of…

We present results of radiative transfer calculations of Compton scattering of polarized radiation in a corona above an accretion disk. The corona has a plane-parallel geometry and is assumed to be homogeneous with a fixed temperature. We…

The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…

We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…

We establish sharp $L^p$ integral mean estimates for $(\alpha,\beta)$-harmonic functions on the unit disk. Explicit bounds for the functions and their partial derivatives are obtained in terms of boundary data, by means of the associated…

In 2013, Marcus, Spielman, and Srivastava resolved the famous Kadison-Singer conjecture. It states that for $n$ independent random vectors $v_1,\cdots, v_n$ that have expected squared norm bounded by $\epsilon$ and are in the isotropic…

Let $p$ be a prime. Given a polynomial in $\F_{p^m}[x]$ of degree $d$ over the finite field $\F_{p^m}$, one can view it as a map from $\F_{p^m}$ to $\F_{p^m}$, and examine the image of this map, also known as the value set. In this paper,…

The complexity of computing the solutions of a system of multivariate polynomial equations by means of Groebner bases computations is upper bounded by a function of the solving degree. In this paper, we discuss how to rigorously estimate…

Let $E \subset \mathbb R^{n+1}$ be a parabolic uniformly rectifiable set. We prove that every bounded solution $u$ to $$\partial_tu- \Delta u=0, \quad \text{in} \quad \mathbb R^{n+1}\setminus E$$ satisfies a Carleson measure estimate…

We propose that the LP-Newton method can be used to solve conic LPs over a conic box, whenever linear optimization over an otherwise unconstrained conic box is easy. In particular, if $\leq_\mathcal{K}$ is the partial order induced by a…

In this paper, we study the $L^{p}$-estimates for the solution to the $2\mathrm{D}$-wave equation with a scaling-critical magnetic potential. Inspired by the work of \cite{FZZ}, we show that the operators…