Discrete Hahn polynomials (DHPs) and their moments are considered to be one of the efficient orthogonal they applied in various scientific areas such as image processing feature extraction. Commonly, DHPs used object representation; however, suffer from problem numerical instability when moment order becomes large. In this paper, an operative method compute basis is proposed high orders. This p...

In this ‎article‎‎, ‎an ‎ap‎plied matrix method, which is based on Bernouli Polynomials, has been presented to find approximate solutions of ‎high order ‎Volterra ‎integro-differential‎ equations. Through utilizing this approach, the proposed equations reduce to a system of algebric equations with unknown Bernouli coefficients. A number of numerical ‎illustrations‎ have been ‎solved‎ to ‎assert...

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

In this study test-day records of milk (kg), fat (g), and protein (g) yields, somatic cell score (SCS, cells/ML) collected by Animal Breeding Center of Iran during 2007 and 2009 were used to estimate genetic parameters using random regression model. Models with different order of Legendre polynomials were compared using Bayesian information criterion (BIC).For milk, fat yield and SCS genetic an...

In this work, we consider variable order difusion and wave equations. The derivative is describedin the Caputo sence of variable order. We use the Genocchi polynomials as basic functions andobtain operational matrices via these polynomials. These matrices and collocation method help usto convert variable order diusion and wave equations to an algebraic system. Some examples aregiven to show the...

Motivated by higher vanishing multiplicity generalizations of Alon's Combinatorial Nullstellensatz and its applications, we study the following problem: for fixed k ? 1 $k\geqslant 1$ n $n$ large with respect to $k$ , what is minimum possible degree a polynomial P ? R [ x ? ] $P\in \mathbb {R}[x_1,\dots ,x_n]$ ( 0 ) ? $P(0,\dots ,0)\ne 0$ such that $P$ has zeroes at least all points in { } ? $\...