The paper is devoted to the study of Brenstien Polynomials and development of some new operational matrices of fractional order integrations and derivatives. The operational matrices are used to convert fractional order differential equations to systems of algebraic equations. A simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

the paper is devoted to the study of brenstien polynomials and development of some new operational matrices of fractional order integrations and derivatives. the operational matrices are used to convert fractional order differential equations to systems of algebraic equations. a simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

We combine recently-developed finite element algorithms based on Bernstein polynomials [1, 14] with the explicit basis construction of the finite element exterior calculus [5] to give a family of algorithms for the Rham complex on simplices that achieves stiffness matrix construction and matrix-free action in optimal complexity. These algorithms are based on realizing the exterior calculus base...

In this paper, we consider the higher-order Changhee numbers and polynomials which are derived from the fermionic p-adic integral on Zp and give some relations between higher-order Changhee polynomials and special polynomials. 366 Dae San Kim, Taekyun Kim, Jong Jin Seo and Sang-Hun Lee

We further investigate the high order positivity-preserving discontinuous Galerkin (DG) methods for linear hyperbolic and radiative transfer equations developed in [14]. The DG methods in [14] can maintain positivity and high order accuracy, but they rely both on the scaling limiter in [15] and a rotational limiter, the latter may alter cell averages of the unmodulated DG scheme, thereby affect...

In the recent progress [BE1], [Me] and [Z2], the wellknown JC (Jacobian conjecture) ([BCW], [E]) has been reduced to a VC (vanishing conjecture) on the Laplace operators and HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent). In this paper, we first show the vanishing conjecture above, hence also the JC, is equivalent to a vanishing conjecture for all 2nd or...

We present a method to decompose a set of multivariate real polynomials into linear combinations of univariate polynomials in linear forms of the input variables. The method proceeds by collecting the first-order information of the polynomials in a set of operating points, which is captured by the Jacobian matrix evaluated at the operating points. The polyadic canonical decomposition of the thr...

Motivated by Kurt’s work [Filomat 30 (4) 921-927, 2016], we …rst consider a class of a new generating function for (p; q)-analog of Apostol type polynomials of order including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order . By making use of their generating function, we derive some useful identities. We also introduce (p; q)-analog of Stirling numbers of second kind...