In this study, a new crossover sine model (CSM) n was developed from a trigonometric model [M. E. Fisher, S. Zinn, and P. J. Upton, Phys. Rev. B 59, 14533 (1999)]. The trigonometric model is a parametric formulation model that is used to represent the thermodynamic variables near a critical point. Although there are other crossover models based on this trigonometric model, such as the CSM and t...

The classical Hurwitz theorem says that if n first “harmonics” (2n+1 Fourier coefficients) of a continuous function f(x) on the unit circle are zero, then f(x) changes sign at least 2n + 1 times. We show that similar facts and its converse hold for any function that are orthogonal to a Chebyshev system. These theorems can be extended for convex curves in d-dimensional Euclidean space. Namely, i...

Abstract—The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating functi...

The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline ...

In this paper, a collocation finite difference scheme based on new cubic trigonometric B-spline is developed and analyzed for the numerical solution of a one-dimensional hyperbolic equation (wave equation) with non-local conservation condition. The usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation functi...

This paper presents an overview of Nexus 3D Soccer Simulation Team. Our main concentration was on developing a new hybrid methodology for an evolutionary gait generator that uses trigonometric truncated Fourier series formulations with coefficients optimized by a Genetic Algorithm. The Fourier series is used to model joint angle trajectories of a simulated humanoid robot with 25 degrees of free...

In this paper, we present a new class of sextic trigonometric Bernstein (ST-Bernstein, for short) basis functions with two shape parameters along their geometric properties which are similar to the classical functions. A Bézier (ST-Bézier, curve and characteristics is also constructed. The continuity constraints connection adjacent ST-Bézier curves segments discussed. Shape control can provide ...

We have obtained the exact-order estimates for some approximative characteristics of Sobolev classes $$ {\mathbbm{W}}_{p,\alpha}^r and Nikоl’skii–Besov {\mathbbm{B}}_{p,\theta}^r periodic functions one several variables in norm space B∞,1. Properties linear operators realizing orders best approximation {\mathbbm{B}}_{\infty, \theta}^r this by trigonometric polynomials generated a set harmonics ...