We examine the merits of using prolate spheroidal wave functions (PSWFs) as basis functions when solving hyperbolic PDEs using pseudospectral methods. The relevant approximation theory is reviewed and some new approximation results in Sobolev spaces are established. An optimal choice of the band-limit parameter for PSWFs is derived for single-mode functions. Our conclusion is that one might gai...

In the paper, the authors first survey and review some logarithmically completely monotonic functions involving the gamma function and its various ratios, and then find sufficient conditions for a function involving the ratio of two gamma functions and originating from the coding gain to be logarithmically completely monotonic.

All-trans-retinoic acid (RA) inhibits adipogenesis in established preadipocyte cell lines. Dosing pharmacological amounts of RA reduces weight gain in mice fed a high-fat diet, i.e. counteracts diet-induced obesity (DIO). The aldehyde dehydrogenase Raldh1 (Aldh1a1) functions as one of three enzymes that converts the retinol metabolite retinal into RA, and one of many proteins that contribute to...

hybrid of rationalized haar functions are developed to approximate the solution of the differential equations. the properties of hybrid functions which are the combinations of block-pulse functions and rationalized haar functions are first presented. these properties together with the newton-cotes nodes are then utilized to reduce the differential equations to the solution of algebraic equation...

Approximate p-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization errors on the frequency parameter of the oscillatory functions show that the accuracy gain of the present formulas over those based on the

A complex unit gain graph ( T -gain graph) Φ = G , φ ) is a where the function assigns number to each orientation of an edge and its inverse assigned opposite orientation. balanced if product gains oriented cycle (if any) 1. We propose two notions distance matrices D < max min Φ, for any ordering ‘<’ vertex set. characterize graphs which are independent ordering. show holds standard vertices on...

Some Mock Theta functions have been interpreted in terms of n-color partition. In this paper we use a new technique to gain a deeper insight on these interpretations, as well as we employ this new technique to obtain in a more systematic way similar new interpretations for three other mock theta functions. keywords: mock theta functions, n-color partitions, combinatorial interpretations, modula...

In this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. We give some sufficient conditions for functions belonging to this class.