This article describes a technique of using a trigonometric function and combinatorial calculations to code or transform any finite sequence of binary numbers (0s and 1s) of any length to a unique set of three Real numbers. In reverse, these three Real numbers can be used independently to reconstruct the original Binary sequence precisely. The main principles of this technique are then applied ...

This paper proposes a trigonometric functional extension, hereafter named the Fourier model, as an alternative framework to the Volterra approach for non-linear systems modelling. This work is focused on the general advantages that trigonometric functionals show in adaptive implementations and also on the possibility they provide to reuse well-known linear processing tools in a non-linear conte...

This paper studies the generalized (2 + 1)-dimensional Zakharov-Kuznetsov Equation using the (G'/G)-expand method, we obtain many new explicit solutions of the generalized (2 + 1)-dimensional Zakharov-Kuznetsov Equation, which include hyperbolic function solutions, trigonometric function solutions and rational function solutions and so on.

In Computer Aided Geometric Design it is often needed to produce a positivity preserving curve according to the given positive data. The main focus of this work is to visualize the positive data in such a way that its display looks smooth and pleasant. A rational quadratic trigonometric spline function with three shape parameters has been developed. In the description of the rational quadratic ...

The curved-beam finite element formulation by trigonometric function for curvature is presented. Instead of displacement function, trigonometric function is introduced for curvature to avoid the shear and membrane locking phenomena. Element formulation is carried out in polar coordinates. The element with three nodal parameters is chosen on curvature. Then, curvature field in the element is int...

In this paper, by using the improved ( ′ G )-expansion method, we have successfully obtained some travelling wave solutions of the variant Boussinesq Equations. These exact solutions include the hyperbolic function solutions, trigonometric function solutions and rational function solutions. Mathematics Subject Classification: 35Q58; 37K50

In 1937, Boas gave a smart proof for an extension of the Bernstein theorem for trigonometric series. It is the purpose of the present note (i) to point out that a formula which Boas used in the proof is related with the Shannon sampling theorem; (ii) to present a generalized Parseval formula, which is suggested by the Boas’ formula; and (iii) to show that this provides a very smart derivation o...

A general approach for biorthogononal local trigonometric bases in the two-overlapping setting was given by Chui and Shi. In this paper, we give error estimates for the approximation with such basis functions. In particular, it is shown that for a partition of the real axis into small intervals one obtains better approximation order if polynomials are reproduced locally. Furthermore, smooth tri...

HIGHLIGHTS This work introduces the Gudermannian function as a sigmoid growth model. Hyperbolic and trigonometric identities provide several parameterizations of this The model can be good alternative to classical models.

Introduction. The problem of integration in finite terms asks for an algorithm for deciding whether an elementary function has an elementary indefinite integral and for finding the integral if it does. "Elementary" is used here to denote those functions built up from the rational functions using only exponentiation, logarithms, trigonometric, inverse trigonometric and algebraic operations. This...