Several authors have examined connections among 132-avoiding permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we find analogues for some of these results for permutations π avoiding 132 and 1223 (there is no occurrence πi < πj < πj+1 such that 1 ≤ i ≤ j − 2) and provide a combinatorial interpretation for such permutations in terms of lattice paths. ...

Abstract— A new wavelet based approximation method for solving the second order differential equations arising science and engineering is presented in this paper. Such differential equation is often applied to model phenomena in various fields of science and engineering. In this study, shifted second kind Chebyshev wavelet (CW) operational matrices of derivatives is introduced and applied for s...

The purpose of this survey is to present some approximation and shape preserving properties of the so-called nonlinear (more exactly sublinear) and positive, max-product operators, constructed by starting from any discrete linear approximation operators, obtained in a series of recent papers jointly written with B. Bede and L. Coroianu. We will present the main results for the max-product opera...

In a recent article, the first and second kinds of multivariate Chebyshev polynomials fractional degree, relevant integral repesentations, have been studied. this we introduce pseudo-Lucas functions show possible applications these new functions. For kind, compute Newton sum rules any orthogonal polynomial set starting from entries Jacobi matrix. representation formulas for powers r×r matrix, a...

This paper discusses several current attempts to use acoustic and electromagnetic wave propagation for modeling physical phenomena and the role that wavelet analysis is playing in these eeorts. The rst problem involves recent application of wavelets to computational uid dynamics. The second problem involves geophysical modeling of the ocean oor, using acoustic waves, and wavelets have recently ...

In this paper we propose a new solution technique for numerical solution of fractional Benney equation, a fourth degree nonlinear fractional partial differential equation with broad range of applications. The method could be described as a hybrid technique which uses advantages of both wavelets and operational matrices. Having applied the present method, fractional Benney equation is converted ...