Department of Mathematics

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Mathematics

Human immunodeficiency virus (HIV) is a lenti-virus (a member of the retrovirus family) that causes acquired immunodeficiency syndrome (AIDS), a critical condition in humans in which progressive failure of the immune system allows life-threatening opportunistic infections. Over the past few years HIV has been spreading rapidly in the population. Almost, everyday there are thousands of new human cases of HIV infection being recorded in the world and these occur in almost every country of the world. However, the spread of HIV is relatively faster in the developing countries as compared to developed countries because developing countries have limited resources. Worldwide, 70% of HIV infections in the adults have been transmitted through heterosexual contact and vertical transmission accounts for more than 90% of global infection in infants and children. In this paper, we propose a nonlinear mathematical model to study the spread of HIV by considering transmission of disease by heterosexual contact and vertical transmission. A stage structured model is proposed and analyzed by considering the total population variable and dividing the whole population under consideration into three stages: children, adults and old. Also, in this paper it is assumed that the rates of recruitment are different in different groups of population. Equilibria of the model and their stability are also discussed. Using the stability theory of differential equations and computer simulation, it is shown that due to the increase in the awareness of the disease in the adult class the total infective population decreases in the region under consideration.

World University root node

School of Advanced Sciences

Chennai Campus

International Journal of Biomathematics

MODELING THE SPREAD OF HIV IN A STAGE STRUCTURED POPULATION: EFFECT OF AWARENESS

Abstract: This paper concerns the problem of creeping flow of an incompressible micropolar fluid past a fluid sphere with non-homogeneous boundary condition for micro rotation vector i.e. the micro rotation on the boundary of the fluid sphere is assumed to be proportional to the rotation rate of the velocity field on the boundary. The stream functions are determined by matching the solution of micropolar field equation for flow outside the fluid sphere with that of the Stokes equation for the flow inside the fluid sphere. The drag force experienced by a fluid sphere is evaluated and its variation is studied with respect to the material parameters. Some well-known results are then deduced.

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International Journal of Engineering & Technology

Creeping flow of Micropolar fluid past a fluid sphere with non-zero spin boundary condition

In this paper, we propose a two strain epidemic model with single host population. It is assumed that strain one can mutate into strain two. Also latent-stage progression age and mutation are incorporated into the model. Stability of equilibria (including the disease free equilibrium, dominant equilibria and the coexistence equilibrium) is investigated and it is found that they are locally stable under suitable and biological feasible constraints. Results indicate that the competition exclusion and coexistence of the two strains are possible depending on the mutation. Numerical simulations are also performed to illustrate these results.

COEXISTENCE OF THE STRAINS INDUCED BY MUTATION

Graph embedding has been known as a powerful tool for implementation of parallel algorithms and simulation of interconnection networks. In this paper, we introduce a technique to obtain a lower bound for the dilation of an embedding. Moreover, we give algorithms for embedding variants of hypercubes with dilation 2 proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding folded hypercubes and augmented cubes into hypercubes.

Department of Design and Automation

School of Mechanical Engineering

Vellore Campus

Journal of Interconnection Networks

EMBEDDING VARIANTS OF HYPERCUBES WITH DILATION 2

This paper investigates robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. The delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov-Krasovskii functional (LKF), some inequality techniques and stochastic stability theory, new delay-dependent stability criteria have been obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results. © 2012 Elsevier Ltd. All rights reserved.

Chaos, Solitons and Fractals

Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays

The aim of this paper is to study the problem of asymptotic stability analysis for T-S fuzzy neural networks with discrete interval and distributed time-varying delays by employing a further improved free-weighting matrix approach. Based on the new Lyapunov-Krasovskii functional with triple-integral term, using some integral inequality and convex combination technique, a new delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs) that can be checked easily by the LMI Control Toolbox in MATLAB. Finally, numerical examples are given to illustrate the strength of the proposed method and an improvement over some existing results. © 2012 Springer-Verlag London Limited.

Neural Computing and Applications

Asymptotic stability criteria for T-S fuzzy neural networks with discrete interval and distributed time-varying delays

VIT Unitversity

Communications in Computer and Information Science Trends in Intelligent Robotics, Automation, and Manufacturing

Implementation of Multi Objective Fuzzy Integer Programming Technique by Using Suppy Chain Management

Discussiones Mathematicae Graph Theory

On total vertex irregularity strength of graphs

A lot of research has been devoted to finding efficient embedding of trees into hypercubes. On the other hand, in this paper, we consider the problem of embedding hypercubes into k-rooted complete binary trees, k-rooted sibling trees, binomial trees and certain classes of caterpillars to minimize the wirelength. © 2011 Elsevier B.V. All rights reserved.

Discrete Applied Mathematics

Wirelength of hypercubes into certain trees

A Petri net can be represented as a particular kind of bipartite graph consisting of two kinds of nodes called places and transitions. Directed arcs are used to connect places to transitions (output of places) and to connect transitions to places (input of places). The study of structural properties and behavioral properties for the bounded conflict free Petri net has been made utilizing siphons and traps [2]. © 2012 Springer-Verlag.