相关论文: Solving moment problems by dimensional extension

This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…

In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…

Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance one may include…

The trigonometric moment problem arises from the study of one-parameter families of centers in polynomial vector fields. It asks for the classification of the trigonometric polynomials $Q$ which are orthogonal to all powers of a…

The analysis of many physical phenomena can be reduced to the study of solutions of differential equations with polynomial coefficients. In the present work, we establish the necessary and sufficient conditions for the existence of…

This paper is a complement of our recent works on the semilinear Tricomi equations in [8] and[9].

We propose a computationally tractable method for the identification of stable canonical discrete-time rational transfer function models, using frequency domain data. The problem is formulated as a global non-convex optimization problem…

In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with $\ell_\tau$-norms proposing two different methodologies: 1) by a new second order cone mixed…

This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…

Our overall goal is to unify and extend some results in the literature related to the approximation of generating functions of finite and infinite sequences over a field by rational functions. In our approach, numerators play a significant…

Generalized moment problems optimize functional expectation over a class of distributions with generalized moment constraints, i.e., the function in the moment can be any measurable function. These problems have recently attracted growing…

Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of squares of rational functions modulo the vanishing ideal I(X). From the point of view of applications, such as polynomial optimization, we…

We introduce a large class of Sobolev bi-orthogonal polynomial sequences arising from a $LU$-factorizable moment matrix and associated with a suitable measure matrix that characterizes the Sobolev bilinear form. A theory of deformations of…

We define a function of two real vectors by a certain homogeneous quotient involving power sums, and show that its supremum grows asymptotically linearly w.r.t. the dimension. From this, we deduce a condition under which a parametric set of…

We consider the set of the power non-negative polynomials of several variables and its subset that consists of polynomials which can be represented as a sum of squares. It is shown in the classic work by D.Hilbert that it is a proper…

In this article, we study the higher-power moments of restricted divisor functions. In order to establish our main results, we prove a more general result pertaining to the distribution of solutions to certain multiplicative Diophantine…

The asymptotic behavior (such as convergence to an equilibrium, convergence to a 2-cycle, and divergence to infinity) of solutions of the following multi-parameter, rational, second order difference equation x_{n+1} =(ax_{n}^3+…

The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…

We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…

The solution to systems of moment differential equations of the form $z\partial_my=(zA+B)y$ are provided, for a matrix $B$ with general good spectrum. Existence and convergence of Floquet-type solutions is studied. A generalized definition…