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Coefficient Asymptotics of Algebraic Multivariable Generating Functions
Analytic combinatorics in several variables (ACSV) seeks to extract the asymptotic behavior of coefficients from a generating function in several...
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Partial-fraction decomposition of a rational function and its application
In this paper, by using the residue method of complex analysis, we obtain an explicit partial fraction decomposition for the general rational...
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Continued fraction representation of the generating function of Bernoulli polynomials
Continued fraction and quasi-reciprocal continued fraction expansions of the generating function of Bernoulli numbers have been obtained. The...
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Zipper rational fractal interpolation functions
A classical piecewise interpolant can be redefined by utilizing horizontal contractive maps that project the entire domain onto subintervals,...
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The Visible-Volume Function of a Set of Cameras is Continuous, Piecewise Rational, Locally Lipschitz, and Semi-Algebraic in All Dimensions
The visible-volume function assigns to a configuration of cameras and a flexible environment in a convex room the volume that can be supervised by...
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Formulas for characteristic function and moment generating functions of beta type distribution
We study on the beta type distribution associated with the Bernstein type basis functions and the beta function, which was defined by authors (Yalcin...
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Algorithms for Constructing Minimal Generating Set of Solutions for Systems of Linear Equations
The authors consider optimization transformations of the algorithm for constructing minimal generating sets of solutions of systems of linear...
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Analysis of Generating Functions for Special Words and Numbers and Algorithms for Computation
Our aim is to construct and compute efficient generating functions enumerating the k -ary Lyndon words having prime number length which arise in many...
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Positivity Preserving Rational Quartic Spline Zipper Fractal Interpolation Functions
In this paper, we introduce a class of novel \(C^1\)...
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Computation Signature Reliability of Computer Numerical Control System Using Universal Generating Function
The aim of this research is to deal with a complex manufacturing system using the Computer Numerical Control as the bottom case manufacturing system,...
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Large-Degree Asymptotics of Rational Painlevé-IV Solutions by the Isomonodromy Method
The Painlevé-IV equation has two families of rational solutions generated, respectively, by the generalized Hermite polynomials and the generalized...
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Hochschild cohomology of symmetric groups and generating functions, II
We relate the generating functions of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups with those of blocks of...
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On generating Sobolev orthogonal polynomials
Sobolev orthogonal polynomials are polynomials orthogonal with respect to a Sobolev inner product, an inner product in which derivatives of the...
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Reflexive polygons and rational elliptic surfaces
In this note we study in detail the geometry of eight rational elliptic surfaces naturally associated to the sixteen reflexive polygons. The elliptic...
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Generalized Popoviciu Expansions for Bernstein Polynomials of a Rational Module
We study Bernstein polynomials for simple nonsmooth rational module functions. We show that these polynomials can be represented as special sums of...
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Generating functions for polynomials derived from central moments involving bernstein basis functions and their applications
The main objective of this article is to construct generating functions for central moments involving Bernstein basis functions. We give some...
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Convergence for noncommutative rational functions evaluated in random matrices
One of the main applications of free probability is to show that for appropriately chosen independent copies of d random matrix models, any...
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Rational points over complex function fields: remarks on isotriviality and dominatedness
The complex function field version of Lang’s conjecture describes the qualitative distribution of sections of a non-isotrivial fibration over a curve...