相关论文: Nearly optimal codebooks based on generalized Jaco…

From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…

This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…

A basic problem for constant dimension codes is to determine the maximum possible size $A_q(n,d;k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$, called codewords, such that the subspace distance satisfies…

In this paper we investigate known Singleton-like bounds in the Lee metric and characterize optimal codes, which turn out to be very few. We then focus on Plotkin-like bounds in the Lee metric and present a new bound that extends and…

We provide a simple algorithm for finding the optimal upper bound for sums of products of matrix entries of the form S_pi(N) := sum_{j_1, ..., j_2m = 1}^N t^1_{j_1 j_2} t^2_{j_3 j_4} ... t^m_{j_2m-1 j_2m} where some of the summation indices…

We study the structure of the zeros of optimal polynomial approximants to reciprocals of functions in Hilbert spaces of analytic functions in the unit disk. In many instances, we find the minimum possible modulus of occurring zeros via a…

In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…

Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…

This paper considers efficient spectral solutions for weakly singular nonlocal diffusion equations with Dirichlet-type volume constraints. The equation we consider contains an integral operator that typically has a singularity at the…

Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it…

We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights $w$ having finitely many zeros and singularities (i.e., points where $w$ becomes infinite) on an interval and not too ``rapidly…

We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…

We classify all post-critically finite unicritical polynomials defined over the maximal totally real algebraic extension of ${\mathbb Q}$. Two auxiliary results used in the proof of this result may be of some independent interest. The first…

Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived, by applying van der Corput type lemmas, for functions of logarithmatic singularities, which…

Low correlation (finite length) sequences are used in communications and remote sensing. One seeks codebooks of sequences in which each sequence has low aperiodic autocorrelation at all nonzero shifts, and each pair of distinct sequences…

Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…

This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled…

Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to…

For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$, where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a…

Let $\lambda_{1},\ldots,\lambda_{n}$ be real numbers in $(0,1)$ and $p_{1},\ldots,p_{n}$ be points in $\mathbb{R}^{d}$. Consider the collection of maps $f_{j}:\mathbb{R}^{d}\to\mathbb{R}^{d} $ given by $$f_{j}(x)=\lambda_{j} x…