In this paper, a numerical matrix method is used to solve the systems of high-order linear Fredholm integro-differential equations with variable coefficients under mixed conditions. The technique consists collocation points and Morgan-Voyce polynomials. residual error functions solutions are also presented. Firstly, approximate formed secondly, an problem constituted in favor function. computed...

We provide an explicit formula for the toric h-contribution of each cubical shelling component, and a new combinatorial model to prove Clara Chan’s result on the non-negativity of these contributions. Our model allows for a variant of the GesselShapiro result on the g-polynomial of the cubical lattice, this variant may be shown by simple inclusion-exclusion. We establish an isomorphism between ...

In this paper we generalize the study of Matiyasevich on integer points over conics, introducing the more general concept of radical points. With this generalization we are able to solve in positive integers some Diophantine equations, relating these solutions by means of particular linear recurrence sequences. We point out interesting relationships between these sequences and known sequences i...

In this paper, we give a sufficient condition for the linear transformation preserving the strong q-log-convexity. As applications, we get some linear transformations (for instance, Morgan-Voyce transformation, binomial transformation, Narayana transformations of two kinds) preserving the strong q-log-convexity. In addition, our results not only extend some known results, but also imply the str...

Ladder networks have been studied extensively using Fibonacci numbers, Chebyshev polynomials, Morgan-Voyce polynomials, Jacobsthal polynomials, etc. ([10], [11], [2], [14], [9]. [5], [3], and [4]). All these polynomials are, in fact, particular cases of the generalized polynomials defined by U„(x,y) = xU„_l(x,y)+yU„_2(x,y), (»>2) (la) with U0(x,y) = 0, Ul(x,y) = l, (lb) and V„(x, y) = xV^ix, y)...

In this research, we present a new computational technique for solving some physics problems involving fractional-order differential equations including the famous Bagley–Torvik method. The model is considered one of important models to simulate coupled oscillator and various other applications in science engineering. We adapt collocation operational matrix that utilizes Liouville–Caputo operat...

We begin by considering faithful matrix representations of elementary abelian groups in prime characteristic. The considered are seen to be determined up change bases a single number. Studying this number leads new family polynomials which exhibit special properties. These satisfy three term recursion and closely related zigzag zero-one sequences. Interpreting the for "prime" 1 yields classical...

where the polynomial matrices Ni(s) and D(s) form a normal external description (NED) of (C, A H ) ; see [11]. The matrices N(s) := CNx(s) and D(s) then form, not necessarily coprime, a matrix fraction description (MFD) of (C,A,B). Recall that Ni(s) and D(s) are right coprime with D(s) being column reduced. The column degrees, Cj := degciD(s), i = 1,2,... ,m, are the controllability indices of ...