water quality prediction is a valuable tool for pollutant control in aquatic environments. a river system is selected and one-dimensional flow is assumed for the simulation of pollutant transport in this paper. advective and diffusive terms of transport equation are considered separately. different functions of advective transport are proposed and applied for a specified velocity on the discret...

in this paper, based on sinh-cosh method and sinh-gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.these solutions include jacobi elliptic function solution, soliton solution,trigonometric function solution.

In this paper, based on sinh-cosh method and sinh-Gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.These solutions include Jacobi elliptic function solution, soliton solution,trigonometric function solution.

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeomet-ric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E 7 (ellip-tic, hyperbolic) and of type E 6...

In this article, we give several integrability formulas of special and composite functions including trigonometric function, inverse trigonometric function, hyperbolic function and logarithmic function. The notation and terminology used here are introduced in the following papers:

We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degreè in dimension d, we need about d ` =`! function values if d is large. Only a small number of arithmetical operations is needed to construct the cubature formulas using Smolyak's technique. We also compare diierent methods to obtain formulas with high trigonometric degree. Abs...

(1) If p ≥ 0 and r ≥ 0, then p+ r ≥ 2 ·√p · r. (2) sin is increasing on ]0, 2 [. (3) sin is decreasing on ]2 ,π[. (4) cos is decreasing on ]0, 2 [. (5) cos is decreasing on ]2 ,π[. (6) sin is decreasing on ]π, 2 ·π[. (7) sin is increasing on ] 3 2 ·π,2 ·π[. (8) cos is increasing on ]π, 2 ·π[. (9) cos is increasing on ] 3 2 ·π,2 ·π[. (10) sin(t1) = sin(2 ·π ·n+ t1). (11) cos(t1) = cos(2 ·π ·n+ t1).

This study after reviewing  construction methods of generators in Archimedean copulas (AC),  proposes several useful lemmas related with generators of AC. Then a new trigonometric Archimedean family will be shown which is based on cotangent function. The generated new family is able to model the low dependence structures.

An infeasible interior-point algorithm for solving the$P_*$-matrix linear complementarity problem based on a kernelfunction with trigonometric barrier term is analyzed. Each (main)iteration of the algorithm consists of a feasibility step andseveral centrality steps, whose feasibility step is induced by atrigonometric kernel function. The complexity result coincides withthe best result for infea...