We consider the solitary wave solutions of a Korteweg-de Vries equation, where the coefficients in the equation vary with time over a certain region. When these coefficients vary rapidly compared with the solitary wave, then it is well-known that the solitary wave may fission into two or more solitary waves. On the other hand, when these coefficients vary slowly, the solitary wave deforms adiab...

In this paper a method of design minimal phase digital filters with arbitrary amplitude characteristics is presented. The filters designed using proposed method can be directly implemented in the hardware. Filter coefficients obtained using proposed method are immune on rounding error. Because these coefficients are created in required bit word length (based on numerical format which is used in...

Over the past ten years, many examples of natural polynomial families from combinatorics and number theory have emerged whose zeros for high degrees appear to converge to intriguing curves in the complex plane. One interesting collection of examples appears on the website [16] of Richard Stanley which includes chromatic polynomials of complete partite graphs, q-analogue of Catalan numbers, Bern...

In this paper we study the properties of coefficients appearing in the series expansions for zeros of generalized Rogers-Ramanujan series. Our primary purpose is to address several conjectures made by M. E. H Ismail and C. Zhang. We prove that the coefficients in the series expansion of each zero approach rational multiples of π and π as q → 1−. We also show that certain polynomials arising in ...

Abstract We study how some coefficients of two-variable coboundary polynomials can be derived from Betti numbers Stanley–Reisner rings. also explain the connection with these rings forces and Möbius to satisfy certain universal equations.

The second cohomology group of a left skew brace with coefficients in trivial non-trivial actions is defined, its connection extensions by braces established and Wells' like exact sequence relating the inducible automorphisms an extension constructed.

The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials. Expansions in terms of orthogonal polynomials are very common in many applications. While the connection problem may be solved by directly computing the change–of–basis matrix, ...

We obtain a combinatorial formula related to the shear transformation for semi-invariants of binary forms, which implies classical characterization in terms differential operator. Then, we present proof an identity Hilbert, leads relation Cayley on semi-invariants. This plays crucial role original Sylvester’s theorem connection with Gaussian coefficients. Moreover, show that additivity lemma Pa...

The main purpose of this article is to solve the connection problems between (p, q)−Fibonacci polynomials and the two polynomials, namely Chebyshev polynomials of third and fourth kinds which are considered as two nonsymmetric polynomials of the Jacobi polynomials. Moreover, the inversion connection formulae for the latter formulae are given. We show that all the connection coefficients are exp...

An L-function, as the term is generally understood, is a Dirichlet series in one complex variable s with analyic continuation to all complex s, a functional equation and an Euler product. The coefficients are thus multiplicative. Weyl group multiple Dirichlet series are a new class of Dirichlet series that differ from L-functions in two ways. First, they are Dirichlet series in several complex ...