This paper is concerned with establishing novel expressions that express the derivative of any order orthogonal polynomials, namely, Chebyshev polynomials sixth kind in terms themselves. We will prove these involve certain terminating hypergeometric functions type 4F3(1) can be reduced some specific cases. The derived along linearization formula serve obtaining a numerical solution non-linear o...

In this paper, we generalize the application of Levi-Civita (L-C) and Kustaanheimo–Stiefel (K-S) regularization methods to quantum mechanical systems in two three dimensions. Schrödinger equations dimensions, describing a particle moving under combined influence [Formula: see text] potentials are mapped that harmonic oscillator with inverted sextic potential, interactions, four respectively. Us...

Based on the shifted Schensted correspondence and the shifted Knuth equivalence, a shifted analog of the Poirier-Reutenauer algebra as a higher lift of Schur’s P-functions and a right coideal subalgebra of the Poirier-Reutenauer algebra is constructed. Its close relations with the peak subalgebra and the Stembridge algebra of peak functions are also uncovered.

None of the existing methods for computing the oscillatory integral ∫ b a f(x)e iωg(x) dx achieve all of the following properties: high asymptotic order, stability, avoiding deformation into the complex plane and insensitivity to oscillations in f . We present a new method that satisfies these properties, based on applying the gmres algorithm to a shifted linear differential operator.

Valence shifting is the task of rewriting a text towards more/less positively or negatively slanted versions. This paper presents a rule-based approach to producing Turkish sentences with varying sentiment. The approach utilizes semantic relations in the Turkish and English WordNets to determine word polarities and involves the use of lexical substitution and adverbial rules to alter the sentim...

An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of precondi...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

The emission of soft radiation provides a fundamental probe the consistency underlying Quantum Field Theory. Correspondingly, measurement photon bremsstrahlung, such as one proposed with planned future upgrade ALICE experiment at LHC, is great interest. In this letter we explore possibility to implement analytic techniques that have been recently developed for gluon resummation Next-to-Leading-...