Journal of Applied & Computational Mathematics

Around 1637 Fermat wrote few lines in the margin of Arithmetica, an Ancient Greek text on mathematics written by Diophantus of Alexandria, an Alexandrian mathematician in 3rd century AD. Fermat wrote that “it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a marvelous proof of this, which this margin is too narrow to contain”. After 358 years, in 1995. Published a successful proof that Xⁿ+Yⁿ ≠ Zⁿ, for ‘n’ >2, as Pierre de Fermat was talking about some marvelous demonstration of this theorem, since than no clue was found about the marvelous demonstration. In this paper some historical evidences and facts are highlighted and some anticipated demonstration related to Fermat’s Last Theorem is devised, may be it will contribute and facilitate the mathematicians to search out some facts associated to Fermat’s Last Theorem and the demonstration.

In this study, effects of variables properties on magnetrodynamics (MHD) flow through a vertical channel in a porous medium are investigated. The governing equations are transformed into a set of coupled nonlinear ordinary differential equations. The transformed equations are solved numerically using Runge-kuta Method of order four with the aid of Maple 18 software. The influence of the flow parameters on fluid temperature, porosity, concentration and velocity are presented graphically. From the course of investigation, it was revealed that fluid temperature increases within the channel with increasing variable viscosity and heat generation parameter.

Statistical Inference on Random Fields in the IEEE Proceedings while looking for a topic for my Ph.D. dissertation. Methods for estimating parameters and testing hypotheses in two-dimensional non-causal models were the subject of this article. This paper led me to classic papers as well as a paper on parameter estimation in Gaussian Markov random field models. I was naturally drawn to the possibilities of using a mathematical statistical framework for computer vision problems because I had been exposed to fundamental concepts in parameter estimation, random processes, and decision theory as a student of electrical and computer engineering. My dissertation dealt with stochastic models for understanding and processing images. Since then, I have worked on computer vision problem-solving strategies based on mathematical statistics. Mathematical statistics tools are very helpful in solving computer vision problems because the majority of them involve inferring some properties (radiometric, geometric, etc.) from images and videos. For mathematical statisticians, computer vision problems can be extremely challenging when it comes to inferring 3D geometry from images and videos. The ability to use appropriate distributions to account for degradations in the data is another reason why statistical methods may be useful for computer vision issues; A Bayesian framework can also take into account any previous data. Manifolds, non-parametric inference tools, and other tools, it's possible to have even more fun.

Numerous nations have prioritized electrifying their transportation sector to decarbonize it in support of the transition to net zero because decarbonisation is becoming increasingly significant. As a result, research on the use of electric vehicles has grown dramatically in recent years. The process of optimizing the transition to electric vehicles relies heavily on mathematical modeling. The adoption of electric vehicles is mathematically modeled in this systematic literature review that is described in this article. In order to answer six research questions regarding the process of modeling transitions to electric vehicles, 53 articles containing mathematical models of electric vehicle adoption are systematically reviewed in this study. The main obstacles to the adoption of electric vehicles, as well as the mathematical modeling techniques observed in the existing literature, are discussed, and suggestions for future research directions are made.