1,720,964 research outputs found
Frankl-type problem for a mixed type equation associated hyper-Bessel differential operator
No full textThe main target of the present research is the Frankl-type problem for mixed type equation with the Caputo-like counterpart
hyper-Bessel fractional derivative. We prove a unique solvability of this problem under certain conditions on given data. For this aim, we use energy integrals (for the uniqueness) and method of integral equations (for the existence)
Properties of Some of Two-Variable Orthogonal Polynomials
No full textThe present paper deals with various recurrence relations, generating functions and series expansion formulas for two families of orthogonal polynomials in two variables, given Laguerre–Laguerre Koornwinder polynomials and Laguerre–Jacobi Koornwinder polynomials in the limit cases. Several families of bilinear and bilateral generating functions are derived. Furthermore, some special cases of the results presented in this study are indicated. © 2019, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.Ministarstvo Prosvete, Nauke i TehnoloÅ¡kog RazvojaThe authors are deeply grateful to the anonymous referees for their comments and constructive suggestions for improvements of this paper. The first author was supported in part by the Serbian Academy of Sciences and Arts (No. ? \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} -96) and by the Serbian Ministry of Education, Science and Technological Development (No. #OI 174015)
S-orthogonality and construction of Gauss-Turán-type quadrature formulae
No full textAbstractUsing the theory of s-orthogonality and reinterpreting it in terms of the standard orthogonal polynomials on the real line, we develop a method for constructing Gauss-Turán-type quadrature formulae. The determination of nodes and weights is very stable. For finding all weights, our method uses an upper triangular system of linear equations for the weights associated with each node. Numerical examples are included
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Monotonicity of the error term in Gauss-Turán quadratures for analytic functions
No full textFor Gauss¿Tur¿an quadrature formulae with an even weight function on the interval [-1; 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than 1, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some `2-error estimates are considered
A FRACTIONAL INTEGRAL OPERATOR INVOLVING THE MITTAG-LEFFLER TYPE FUNCTION WITH FOUR PARAMETERS
Full text linkIn this paper our main aim is establishing a fractional integration formula (of pathway type) involving the Mittag-Leffler type function with four parameters which is recently introduced by Garg, Sharma and Manohar [Thai J. Math. (2015)]. Some interesting special cases of the main result are also considered and shown to be connected with certain known ones
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
Full text linkMSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems with strong nonclassical weights on (0;+1), including a conjecture for an oscillatory weight on [¡1; 1]. Finally, we give some new results on orthogonal polynomials on radial rays in the complex plane
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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