iosr-Jm   Volume-21 ~ Issue-1 ~ Jan. – Feb. 2025

Abstract : In this work, we present an original formula that proposes the unification of quantum, gravitational, and electromagnetic fields in a four-dimensional spacetime, considering the complex interactions among these fundamental forces. The formula integrates concepts from general relativity, electromagnetism, quantum mechanics, and scalar fields to provide a comprehensive description of the fundamental laws of physics. The equation is derived from a relativistic action incorporating various contributions, such as spacetime curvature, quantum fields, and matter-energy interactions. This model may open new perspectives in the quest for a unified theory of fundamental forces, being applicable to the observation and simulation of both cosmic and microscopic phenomena.......

[1] Einstein, A. (1915). "Die Feldgleichungen Der Gravitation." Sitzungsberichte Der Königlich Preußischen Akademie Der Wissenschaften.
[2] Feynman, R., Et Al. (1964). The Feynman Lectures On Physics. Addison-Wesley.
[3] Peskin, M. E., & Schroeder, D. V. (1995). An Introduction To Quantum Field Theory. Addison-Wesley.
[4] Weinberg, S. (1995). The Quantum Theory Of Fields, Vol. 1: Foundations. Cambridge University Press.
[5] Corrêa, S. (2024). A Jornada Da Consciência: Explorando A Criação E A Relatividade Do Universo

Abstract : This paper uses the Laplace transform and laplace decomposition method to solve fractional differential difference equations with interval conditions. To do this, we use the Caputo fractional derivative definition. we get laplace transform form the given fractional differential difference equation to Laplace form and taking an inverse Laplace transform, we get the solution of the fractional-differential difference equation. For the Laplace transform of a difference-type function. The equation becomes to a differential-difference equation if α=1. our proved result is valid for α=1.

Keywords: Differential-difference equation, caputo derivative, Laplace transform method,laplace decomposition method.

....

Abstract : Optimization issues are an inherent part of various disciplines like engineering, economics, and artificial intelligence to solve problems of resource allocation and training neural networks. Classical methods of optimization such as gradient descent and Newton's method give successful answers, although they do not work with challenges such as non-convexity, local optimum, and high dimension. In this paper, an attempt to present new numerical methods of optimizing classical optimization methods is made, applying the Rosenbrock function as a performance metric......

Keywords: Optimization, Rosenbrock Function, Numerical Methods, Gradient-Based Methods, Heuristic Optimization, Benchmarking.

[1] Bazaraa, M. S., Sherali, H. D., And Shetty, C. M. (2006). Nonlinear Programming: Theory And Algorithms. John Wiley & Sons..
[2] Bellemare, M. G., Dabney, W., And Munos, R. (2017). A Distributional Perspective On Reinforcement Learning. In International Conference On Machine Learning 449-458. PMLR.
[3] Bertsekas, D. P. (1996). Dynamic Programming And Optimal Control. Journal Of The Operational Research Society, 47(6), 833-833.
[4] Blum, C., & Raidl, G. R. (2016). Hybrid Metaheuristics: Powerful Tools For Optimization (Vol. 157). Cham, Switzerland: Springer International Publishing.
[5] Boussaid, I., Lepagnot, J., & Siarry, P. (2013). A Survey On Optimization Metaheuristics. Information Sciences, 237, 82-117.

Abstract : The main objective of this research article consists in giving a characteriza− tion of a non−degenerate Artinian complex Banach−Jordan pair. Goncretely me shom that under some related conditions, the pair in question is finite dimen− sional . Similar results for Banach−Jordan algebras hold to be true.

Keywords: Jordan algebra, local algebra, Artinian Banach-Jordan pair, finite dimension.

....

Abstract : This research paper investigates the convergence behavior of the Finite Element Method (FEM) applied to the Poisson equation on a unit square domain, employing crossed triangular meshes. The study utilizes the FEniCS library to discretize the domain with varying mesh sizes and analyzes the convergence rates as the mesh resolution increases. The Poisson problem is formulated using a first-order Lagrange polynomial function space with homogeneous Dirichlet boundary conditions.

Keywords: Finite element; Simulation; Convergence rate; Python FEniCs package.

[1]
The Finite Element Method: Its Basis And Fundamentals By Zienkiewicz And Taylor, 2005.
[2]
Jingtang Ma, Jinqiang Liu And Zhiqiang Zhou, Convergence Analysis Of Moving Finite Element Methods For Space Fractional Differential Equations, Journal Of Computational And Applied Mathematics, 255, Pp 661-670, 2014.
[3]
Xiaolang Wan, Haijun Yu, And Jiayu Zhai, Convergence Analysis Of A Finite Element Approximation Of Minimum Action Methods, SIAM J. NUMER. ANAL., Vol. 56, No. 3, Pp- 1597-1620, 2018.
[4]
Nithesh Naik, Prajwal Shenoy, Nithin Nayak, Swetank Awasth And Rashmi Samant, Mesh Convergence Test For Finite Element Method On High Pressure Gas Turbine Disk Rim Using Energy Norm: An Alternate Approach, International Journal Of Mechanical Engineering And Technology (IJMET), Vol. 10, No. 1,Pp. 765-775, 2019.
[5]
Cuiyu Hea, Shun Zhangb, And Xu Zhanga, Error Analysis Of Petrov-Galerkin Immersed Finite Element Methods, Elsevier: Comput. Methods Appl. Mech. Engrg., 404, 2023.

Abstract : This paper explores novel cosmological models that diverge from the traditional Einstein-de Sitter framework. We investigate the theoretical foundations and observational implications of several alternative cosmologies, including the Brans-Dicke theory, Modified Newtonian Dynamics (MOND), and the Conformal Cyclic Cosmology (CCC) model. Through a comprehensive analysis of these models, we aim to shed light on their potential to address current challenges in our understanding of the universe, such as dark matter, dark energy, and the nature of cosmic inflation........

Keywords: Cosmology, Einstein-de Sitter Model, Brans-Dicke Theory, MOND, Conformal Cyclic Cosmology.

[1]. Abbott, B. P., Abbott, R., Abbott, T. D., Acernese, F., Ackley, K., Adams, C., ... & Affeldt, C. (2017). GW170817: Observation Of Gravitational Waves From A Binary Neutron Star Inspiral. Physical Review Letters, 119(16), 161101(18).
[2]. An, D., Meissner, K. A., & Nurowski, P. (2017). Ring-Type Structures In The Planck Map Of The CMB. Monthly Notices Of The Royal Astronomical Society, 473(3), 3251-3255.
[3]. Bekenstein, J. D. (2004). Relativistic Gravitation Theory For The Modified Newtonian Dynamics Paradigm. Physical Review D, 70(8), 083509.
[4]. Bertotti, B., Iess, L., & Tortora, P. (2003). A Test Of General Relativity Using Radio Links With The Cassini Spacecraft. Nature, 425, 374-376.
[5]. Brans, C., & Dicke, R. H. (1961). Mach's Principle And A Relativistic Theory Of Gravitation. Physical Review, 124(3), 925-935.