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1

  • Convex-Cyclic Abelian semigroups of matrices on Rn



Anjeet Kumar and Dr. Shree Nath Sharma

Abstract:
\r\n\r\n\r\nConvex-cyclicity in higher dimensions, convex cyclicity is an interesting issue that overlaps with a number of different areas of mathematics, such as geometry, topology, and dynamical systems. The features and behavior of convex sets multidimensional space, as well as the cyclic aspects of these sets, are the set of particular study. Within the scope of this paper, we will investigate the fundamental ideas that under pin convexity, extend those ideas to higher dimensions, and go the particular concept of convex-cyclicity, analyzing its consequences, applications and mathematical structure that are associated with it.\r\n


1-16
2

  • ON THE BANACH-STEINHAUS THEOREM



Dr. Sheo Shankar Kumar

Abstract:
In this paper we have discussed Banach-Steinhaus theorem. Here we have provided proof of the main theorem by a new method. Before proving the Banach-Steinhaus theorem, we have stated three Lemmas (Lemma 1 – Lema 3) along with their proof which are much useful in proving the theorem.


17-20
3

  • Mathematical Modelling for the Transmission Dynamics of the Human Immunodeficiency Virus (HIV)



Dr. Jay Nandan Pd. Singh and Pramod Ranjan

Abstract:
Dr. Jay Nandan Pd. Singh Pramod Ranjan The present paper provides that a major problem with AIDS is the variable length of the incubation period from the time the patient is diagnosed as seropositive until he exhibits the symtoms of AIDS. This has major concequences for the spread of virus. Here we have considered two mathematical models. The first model deals with the time evolution of the disease between those infected and those with AIDS. The second one is epidemic model, where we have discussed the development of an AIDS epidemic in a homosexual population.


21-30
4

  • Spherically Symmetric Charged Fluids in General Relativity



Mukesh Kumar and Dhruv Kumar Singh

Abstract:
Here in this paper we have solved Einstein-Maxwell field equations for charged fluid sphere using different assumptions. We have also discussed central and boundary conditions. The pressure, matter density, electric field and charge density for the distribution have been also obtained and discussed.


30-45
5

  • A STUDY ON OPTIMALITY AND DUALITY FOR MULTI- OBJECTIVE FRACTIONAL PROGRAMMING



Sushma Kumari

Abstract:
This paper presents the extension of the concept of Hanson, Pini and Singh (2001) in the context of multi-objective fractional programming (MFP) to establish sufficient optimality and duality theorems and the results are compared with Liu (1999). Here we have also discussed optimality conditions along with weak, strong and converse duality.


46-55
6

  • Spherically Symmetric Cosmological Models with Shear Viscosity



Rajesh Kumar and Purushottam

Abstract:
In the present paper, considering a time dependent geometry which is spherically symmetric about a single point, we have solved Einstein’s field equations with an acceleration free imperfect fluid source with shear viscosity using different conditions. We have also obtained and discussed various physical parameters for the solutions obtained.


56-68
7

  • A STUDY ON MULTI-OBJECTIVE PROBLEM WITH RECENT ECONOMIC SIGNIFICANCE



Dr. Anupama Sinha and Dr. Vikas Kumar Raju

Abstract:
The present paper provides description of multi-objective programming problem in general with suitable simple example. Here along with mathematical formulation, we have given various applications of the investigation with recent economic significance.


69-74
8

  • Some Mathematical Models for Controlling Water Pollution



Dr. Suman Kumar Bharti

Abstract:
The present research paper provides some water pollution control models along with water quality management. For this purpose, we have used linear and non-linear programming technique and also technique of goal programming or integer programming etc. as well. The optimization problem arises since we want to minimize the total cost of treatment for obtaining the desired (max.) improvements in quality of water.


75-81
9

  • ANALYSIS OF ISOTOPIC AND ANISOTROPIC CYLINDER AND SPHERES



M. T. Kolhe G.R.Yerawar

Abstract:
In the realm of materials science and engineering, the concepts of isotropy and anisotropy play a pivotal role in understanding the mechanical behavior of various structures. These properties are particularly relevant when considering cylindrical and spherical geometries, which are ubiquitous in numerous applications, from engineering structures to biological systems. Isotropic materials exhibit properties that are independent of direction. This means that their mechanical, thermal, and electrical properties remain consistent regardless of the direction of measurement. In the context of cylinders and spheres, isotropic materials possess uniform properties throughout their volume. Consequently, their response to external forces or temperature changes is predictable and can be modeled using relatively simple equations. Anisotropic materials, on the other hand, exhibit properties that vary with direction. This directional dependence can arise from various factors, including crystal structure, fiber orientation, and manufacturing processes. In the case of cylinders and spheres, anisotropic materials may have different properties along radial, tangential, and axial directions. This directional variation can significantly influence the material's response to stress, strain, and other external stimuli.


88-93
10

  • Solving Parabolic Partial Differential Equations Using the Crank-Nicolson Method



Laxmi DR .S.H.Thakar

Abstract:
In various scientific and engineering disciplines, numerical solutions for partial differential equations (PDEs) have been indispensable due to the nonavailability of solutions in closed analytical forms. Some of these include parabolic PDEs describing heat conduction, diffusion processes, and other types of time-dependent phenomena. The Crank-Nicolson method, being second-order accurate and an implicit scheme, has been one of the most efficient techniques for solving parabolic PDEs. This paper deals with detailed analysis on the Crank-Nicolson method, its application to the parabolic PDEs, and its advantages and limitations. Apart from the contemporary developments, a discussion on the integration of Crank-Nicolson with modern computational techniques and further future directions for large-scale simulations have also been included. It has provided a comprehensive comparison of the Crank-Nicolson method with other numerical methods to understand its strength and weakness.


94-103
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