Open Access Short Research Article

Exact Steady Solutions for the Two Dimensional Broadwell Model

Amah Séna d'Almeida, Kokou Anani Agosseme

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/jamcs/2019/v34i430220

Existence and boundedness of the solutions of the boundary value problem for the four velocity two dimensional Broadwell model for bounded boundary conditions is proved and exact analytic solutions are built. An application to the determination of the accommodation coefficients on the boundaries of a flow in a box is performed.

Open Access Original Research Article

Demonstration of the Importance of Factoring in Solving a Fundamental Equation Involving the Riemann Zeta Function

Bibek Baran Nag

Journal of Advances in Mathematics and Computer Science, Page 1-5
DOI: 10.9734/jamcs/2019/v34i230213

The author presents a simple approach which can be used to tackle various special cases of some well-known problems involving zeta functions. A self-contained argument, which requires only basic prerequisite mathematical knowledge, is used to furnish a new proof of a result involving the Riemann zeta function which can help in settling more general conjectures.

Open Access Original Research Article

On Fermat's Last Theorem

Bibek Baran Nag

Journal of Advances in Mathematics and Computer Science, Page 1-4
DOI: 10.9734/jamcs/2019/v34i230211

The author presents a simple approach which can be used to tackle some well-known Diophantine problems. A self-contained argument is used to furnish a novel proof of one such result first stated by Pierre de Fermat in the 1630s.

Open Access Original Research Article

On the Interplay of Geometrical Shapes and the Analysis of a Dispersal Model for Pattern Formations

Zakir Hossine; Md. Kamrujjaman

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2019/v34i430219

A reaction-diffusion model is put forward which is capable of generating chemical maps whose concentration contours are similar to the patterns seen on the flanks of zebras, leopards and other mammals. Initially, this type of reaction diffusion kinetics model was introduced by Turing and later Murray applied it to animal coat patterns. Among many chemical reaction mechanism, we consider Schnackenberg reaction mechanism in details and show that the geometry and scale of the domain, the relevant part of the integument, during the time of laying down plays a crucial role in the structural patterns which result. Patterns which exhibit a limited randomness are obtained for a selection of geometries. Finally the system was solved numerically using finite difference method.

Open Access Original Research Article

Further Scalable Test Functions for Multidimensional Continuous Optimization

George Anescu

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2019/v34i430221

Multidimensional scalable test functions are very important in testing the capabilities of new optimization methods, especially in evaluating their response to the increase of the search space dimension. As a continuation of a previous published paper, new sets of test functions for continuous optimization are proposed, both unconstrained (or only box constrained, 7 new test functions) and constrained (10 new test functions).