Related papers: Tracial moment problems on hypercubes
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear…
The main result of the paper is an interesting relation between the solution of the truncated Exponential Moment problem and truncated Classical Moment problem, considered on the half-line or on a compact interval.
In this paper, we compute the Stokes matrices of a special quantum confluent hypergeometric system with Poincar\'e rank one. The sources of the interests in the Stokes phenomenon of such system are from representation theory and the theory…
Klee's Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known for several…
This work explores the solvability of a sixth-order Cahn--Hilliard equation with an inertial term, which serves as a relaxation of a higher-order variant of the classical Cahn--Hilliard equation. The equation includes a source term that…
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…
A successful computational approach for solving large-scale positive semidefinite (PSD) programs is to enforce PSD-ness on only a collection of submatrices. For our study, we let $\mathcal{S}^{n,k}$ be the convex cone of $n\times n$…
We consider the following variant of the Mortality Problem: given $k\times k$ matrices $A_1, A_2, \dots,A_{t}$, does there exist nonnegative integers $m_1, m_2, \dots,m_t$ such that the product $A_1^{m_1} A_2^{m_2} \cdots A_{t}^{m_{t}}$ is…
Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related…
We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. A way to construct atomic solutions of the moment problem is indicated.
A quaternionic version of the Calabi problem on Monge-Ampere equation is introduced. It is a quaternionic Monge-Ampere equation on a compact hypercomplex manifold with an HKT-metric. The equation is non-linear elliptic of second order. For…
We focus on computing certified upper bounds for the positive maximal singular value (PMSV) of a given matrix. The PMSV problem boils down to maximizing a quadratic polynomial on the intersection of the unit sphere and the nonnegative…
We solve the infinite potential well problem using the methods of Heisenberg's matrix mechanics. In addition to being of educational value, the matrix mechanics allows us to deal with various unphysical issues caused by this potential in a…
In this paper, we develop a constructive solution for the pure truncated moment problem on cubic curves in Weierstrass form, establishing the existence of a representing measure whose number of atoms equals the rank of the associated moment…
We address the existence of solutions for the inviscid version of the Hall-Vinen-Bekharevich-Khalatnikov equations in 3D, a macro-scale model of superfluidity. This system couples the incompressible Euler equations for the normal fluid and…
We introduce the "moment rank" and "unitary rank" of numerical sequences, close relatives of linear-recursive order. We show that both parameters can be characterized by a broad set of criteria involving moments of measures, types of…
Mixed-moment models, introduced before for one space dimension, are a modification of the method of moments applied to a (linear) kinetic equation, by choosing mixtures of different partial moments. They are well-suited to handle such…
We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring…
The polynomial-time computability of the permanent over fields of characteristic 3 for k-semi-unitary matrices (i.e. square matrices such that the differences of their Gram matrices and the corresponding identity matrices are of rank k) in…
In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube $[0, 1]^d$ and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its…