This chapter delivers a new nonlinear model, Ultra high frequency Polynomial and Trigonometric Higher Order Neural Networks (UPT-HONN), for control signal generator. UPTHONN includes UPS-HONN (Ultra high frequency Polynomial and Sine function Higher Order Neural Networks) and UPC-HONN (Ultra high frequency Polynomial and Cosine function Higher Order Neural Networks). UPS-HONN and UPC-HONN model...

Abstract There has been an intense study on the eigenvalue and eigenfunction of nonrelativistic quantum system. The Schrodinger equation is important in system that used to analyze information system, so it attached interest researchers conduct exploration it. In most studies, expand solution physical properties thermodynamical property one key analyzing characteristic materials. It needs more ...

The sums of three trigonometric series with logarithmic coefficients are derived by extending an approach first utilized Lerch. By applying Frullani's theorem to two these series, non-trivial integrals involving hyperbolic functions evaluated in terms the digamma function.

The aim of this paper is to develop a local positivity preserving scheme when the data amassed from different sources is positioned at sparse points. The proposed algorithm first triangulates the irregular data using Delauny triangulation method, therewith interpolates each boundary and radial curve of the triangle by C¹ rational trigonometric cubic function. Half of the parameters in the descr...

A generalized ( G′ G ) -expansion method is devised to construct the exact traveling wave solutions of mKdV equation. With the aid of symbolic computation, many hyperbolic function solutions, trigonometric function solutions and rational function solutions are obtained. It is shown that the proposed method is more effective and powerful than the ( G′ G ) -expansion method in constructing the tr...

Contemporary research has proved that Mittag-Leffler function is the solution of fractional differential and integral equations. Fractional Calculus is rapidly gaining recognition as an important branch of Mathematical Sciences. In this paper, we study a newly defined Mittag-Leffler type E-function that unifies many special functions including some newly defined generalized trigonometric functi...

The Theory of Approximation. By Dunham Jackson. New York (American Mathematical Society Colloquium Publications, Volume 11), published by this Society, 1930. v+178 pp. In 1885 Weierstrass announced his now famous theorem: Any continuous function j•(#)> defined over a finite interval (a, b), can be approximated in (a, b) uniformly and indefinitely by a sequence of polynomials Pn(x), whose degree...

Predominantly in the faltering atmosphere, the precise value of some factors is difficult to measure. Though, it can be easily approximated by intuitionistic fuzzy linguistic term in the real-life world problem. To deal with such situations, in this paper two information measures based on trigonometric function for intuitionistic fuzzy sets, which are a generalized version of the fuzzy informat...

A rational function can always be integrated, that is, the integral of such a is an elementary function. The integration procedure complex and consists four steps: elimination common zero-points numerator denominator, reduction to true function, decomposition into partial fractions obtained expressions using direct integration, substitution method or method. Integrating functions important beca...

The method of undetermined coefficients is commonly applied to solve linear, constant coefficient, non-homogeneous ordinary differential equations when the forcing function from a selected class functions. Often hyperbolic sine and cosine functions are not explicitly included in this list Through set guided examples, work argues that ought be select Careful explanation provided for necessary tr...