iosr-Jm   Volume-16 ~ Issue-1 ~ Jan – Feb 2020

Abstract: In this paper we define inductive limits of locally convex spaces and relation between inductive limits and Barrelled Spaces.

Key words: Topological vector spaces, locally convex spaces, inductive limits, Barrelled spaces.

[1]. A. Grothendick : Topological vector spaces. springer verlag, Berlin, 1964
[2]. A. Mallics : Topological Algebras : Selected Topics (North Holland Mathematics) Studies. 124 (1986)
[3]. J.I. Nagata : Modern general topology. North-Holland Mathematics Library 33 (1985)
[4]. Kothe. G : Topological vector spaces, Vol. I and II. Springer verlag, berlin, 1969 and 1989.
[5]. Treves. F. :Topological vector spaces. Distributions and Kernels Academy press. 1987

Abstract: In this paper, derivative free optimization methods specifically Genetic Algorithm is discussed. The solution of bound-constrained optimization problems by using Genetic algorithm, the concept of the project is divided into five parts: The first part is the introduction part; under this statement of the problem and objective of the study are included. The second part is the preliminary which includes some lemma and theorems which are used in the body of the seminar paper. The part includes detail explanation of derivative free optimization methods specifically, Genetic Algorithm and Simulated Annealing and also supporting examples of them. The last part presents the summary of the study what was discussed in the main part of the paper. A Non linear Mathematical model is proposed and studied the combined effect of vertical Transmission (MTCT) and variable inflow of infective.......

Keywords: HIV/AIDS, Unaware and Aware Infective Immigrant, Vertical Transmission (MTCT), Screening, Local Stability, Reproduction Number

[1]. Argaez M. 2001. Optimization Theory Application, On the global convergence of a modified augmented Lagrangian line search interior-point Newton method for nonlinear programming, 144:1-25
[2]. Elizabeth D. Dolan and Jorge J.More. 2007. Benchmarking optimization software with performance profiles. Mathematical programing, 49(4):673-692.
[3]. Goldberg D.E. and Holland J.H. 1988.Genetic algorithms and machine learning. Machine Learning3: 95-99.
[4]. Hollad.J.H. 1975.Adaption in Natural and Artificial Systems.University of Michigan.Press. Ann Arbor. Michigan.
[5]. Ingber L. and Rosen B. 1992.Genetic Algorithms and very fast reannealing. A Comparison Mathl, Comput, Modelleing. 16(11), 87-100..

Abstract: This paper aims to study the Spread of disease in prey-predator system with treatment given to infected prey and predator population only .For these problem a system of five ordinary differential Equations has been proposed . Positivity, Boundedness of model equation has been analyzed. Existence of the solution has been checked using Derrick and Groosman theorem. Stability of all possible Equilibrium points of the model has been done. Local and global stability of disease free and endemic equilibrium points are performed. Numerical simulations are presented to clarify analytical results

Key Words: Mathematical eco-epidemiology, predator-prey system, Local Stability, Routh –Hurwitz Criterion, Reproduction Number, Simulation Study.

[1]. Alfred Hugo, Estomih S. Massawe, and Oluwole Daniel Makinde. An Eco-Epidemiological Mathematical Model with Treatment and Disease Infection in both Prey and Predator Population. Journal of Ecology and natural environment Vol. 4 (10), pp. 266-273, July 2012.
[2]. Sachin Kumar and Harsha Kharbanda. Stability Analysis Of Prey-Predator Model With Infection, Migration and Vaccination In Prey, arXiv:1709.10319vl [math.DS], 29 Sep 2017.
[3]. Paritosh Bhattacharya, Susmita Paul and K .S. Choudhury (2015). Mathematical Modeling of Ecological Networks, Structure and Interaction Of Prey and Predator, Palestine Journal of Mathematics Vol. 4(2), 335–347.
[4]. C. M. Silva (2017). Existence of periodic solutions for periodic eco-epidemic models with disease in the prey, J. Math. Anal. Appl. 453(1), 383–397.
[5]. J. Chattopadhyay and O. Arino. A predator-prey model with disease in the prey, Nonlinear Analysis, 36 (1999), 747–766.

Abstract: The main motive behind to the preparation of this project is to understand the graph search algorithm in a simple way. This work introduces and discusses concepts to implement graph algorithms in a reusable fashion The module begin with the introduction of graph search ,preliminary and followed by chapter three which is graph search algorithm and finally chapter four that studies about application of graph search.

Keywords: Search algorithm, connected graphs, trees and forest

[1]. Rowan Garnier, John Taylor: Discreet mathematics
[2]. Narsingh Deo: Graph theory with application to engineering and computer science.
[3]. Keneth H.Rose: Discreet mathematics and its application.
[4]. A.Tamilarasi: Ddiscrete mathematics and its applications
[5]. Wikipedia: http://en.wikipedia.org/wiki/Shortest_path_problem

Abstract: In this work......

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Abstract: Among all ellipses inscribed in a triangle, T, the midpoint, or Steiner, ellipse is interesting and wellknown [2]. It is the unique ellipse tangent to T at the midpoints of all three sides of T and is also the unique ellipse of maximal area inscribed in T. What about ellipses inscribed in quadrilaterals, Q ? Not surprisingly, perhaps, there is not always a midpoint ellipse-i.e., an ellipse inscribed in Q which is tangent at the midpoints of all four sides of Q; In fact, in [1] it was shown that if there is a midpoint ellipse, then Q must be a parallelogram. That is, if Q is not a parallelogram, then there is no ellipse inscribed in Q which is tangent at the midpoint of all four sides of Q; But can one do better than four sides of Q ? In other words, if Q is not a parallelogram, is there an ellipse inscribed in Q which is tangent at the midpoint of three sides of Q ? In Theorem 1 we prove that the answer is no. In fact, unless Q is a trapezoid(a quadrilateral with......

[1]. John Clifford and Michael Lachance, Quartic Coincidences and the Singular Value Decomposition, Mathematics Magazine, December, 2013, 340-349.
[2]. Heinrich Dörrie: 100 Great Problems of Elementary Mathematics, Dover, New York, 1965.
[3]. Alan Horwitz, Ellipses Inscribed in Parallelograms, Australian Journal of Mathematical Analysis and Applications, Volume 9, Issue 1(2012), 1-12.
[4]. Alan Horwitz, "Dynamics of ellipses inscribed in quadrilaterals", IOSR Journal of Mathematics, Volume 15, Issue 5, Series-4 (Sep- Oct 2019)
[5]. Alan Horwitz, "A generalization of parallelograms involving inscribed ellipses, conjugate diameters, and tangency chords", Forum Geometricorum, to appear.
[6]. Alan Horwitz, "Ellipses of maximal area and of minimal eccentricity inscribed in a convex quadrilateral", Australian Journal of Mathematical Analysis and Applications, 2(2005), 1-12.