Related papers: Gauss-Type Quadrature Rules Based on Identity-Type…
We consider a generalized Gauss sum supported on matrices over a number field. We evaluate this Gauss sum and relate it to the number of totally isotropic subspaces of related quadratic spaces. Then we consider a further generalization of…
Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…
A quadrature rule of a measure $\mu$ on the real line represents a convex combination of finitely many evaluations at points, called nodes, that agrees with integration against $\mu$ for all polynomials up to some fixed degree. In this…
In this paper we define and study properties and applications of a, b, x0, x1 elements in some special cases.
Stieltjes, Perron, and Markov in analysis of the moment problem, for absolutely continuous measures, constructed the underlying measure as the discontinuity across the cut of a Cauchy representation of an otherwise real-analytic function.…
Given an isotropic quadratic form over a number field which assumes a value $t$, we investigate the distribution of points at which this value is assumed. Building on the previous work about the distribution of small-height zeros of…
In this work, an expansion of Guessab-Schmeisser two points formula for n-times differentiable functions via Fink type identity is established. Generalization of the main result for harmonic sequence of polynomials is established. Several…
A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and…
Despite extensive research on symmetric polynomial quadrature rules for triangles, as well as approaches to their calculation, few studies have focused on non-polynomial functions, particularly on their integration using symmetric triangle…
In this paper, we introduce and analyze arbitrarily high-order quadrature rules for evaluating the two-dimensional singular integrals of the forms \begin{align} I_{i,j} = \int_{\mathbb{R}^2}\phi(x)\frac{x_ix_j}{|x|^{2+\alpha}} \d x, \quad…
We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extension of that field. Some generalized notions of isotropy,…
In this paper we describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable…
An analysis of the characteristic function of Gaussian quadratic forms is presented in [1] to study the performance of multichannel communication systems. This technical report reviews this analysis, obtaining alternative expressions to…
We study integrals over the triangle with vertices (1,0), (0,1), (1,1) that give linear combinations of multiple zeta values.
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
In this work, we consider the singular integrals of Cauchy type of the forms $$\ds J(f,x)= \frac{\sqrt{1-x^2}}{\pi}\int_{-1}^1\frac{f(t)}{\sqrt{1-t^2}(t-x)}\,dt, -1<x<1 and $$\ds \Phi(f,z)=…
In this paper we initiate a study on Gauss factorials of polynomials over finite fields, which are the analogues of Gauss factorials of positive integers.
The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…
Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the…