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

A set 5 of vertices in a graph G is called a dominating set of G if every vertex in V(G)\S is adjacent to some vertex in 5. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. A zero forcing set of G is a subset of vertices B such that if the vertices in B are colored blue and the remaining vertices are colored white initially, repeated application of the color change rule can color all vertices of G blue. The power domination number and the zero forcing number of G are the minimum cardinality of a power dominating set and the minimum cardinality of a zero forcing set respectively of G. In this paper, we obtain the power domination number, total power domination number, zero forcing number and total forcing number for m-rooted sibling trees,/-sibling trees and l-binary trees. We also solve power domination number for circular ladder, Mobius ladder, and extended cycle-of-ladder. © 2020 Charles Babbage Research Centre. All rights reserved.

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School of Advanced Sciences

Chennai Campus

Journal of Combinatorial Mathematics and Combinatorial Computing

Power domination in tree derived architectures

Crime and corruptions are two major problems in developing nations. They spread like infectious disease in the population. Here, a nonlinear mathematical model is formulated and analyzed to study the interaction between criminal population and non-criminal population by considering non-monotone incidence rate. Non-monotone incidence rate shows a behavioral change in non-criminal populations. First, we consider constant recruitment and death type demography and then we take logistic growth type demography. For both the models the basic reproduction number R is computed. All possible equilibria of the models are obtained and stabilities of these equilibria are discussed in details. Further these models are extended to optimal control problem to study the impact of time-dependent law enforcement rate on the size of criminal population. Numerical simulations are presented to illustrate our analytical findings. © 2020, Springer-Verlag GmbH Austria, part of Springer Nature.

Social Network Analysis and Mining

Modeling and analysis of crime prediction and prevention

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused the global pandemic, coronavirus disease-2019 (COVID-19) which has resulted in 60.4 million infections and 1.42 million deaths worldwide. Mathematical models as an integral part of artificial intelligence are designed for contact tracing, genetic network analysis for uncovering the biological evolution of the virus, understanding the underlying mechanisms of the observed disease dynamics, evaluating mitigation strategies, and predicting the COVID-19 pandemic dynamics. This paper describes mathematical techniques to exploit and understand the progression of the pandemic through a topological characterization of underlying graphs. We have obtained several topological indices for various graphs of biological interest such as pandemic trees, Cayley trees, Christmas trees, and the corona product of Christmas trees and paths. We have also obtained an analytical expression for the thermodynamic entropies of pandemic trees as a function of R0, the reproduction number, and the level of spread, using the nested wreath product groups. Our plots of entropy and logarithms of topological indices of pandemic trees accentuate the underlying severity of COVID-19 over the 1918 Spanish flu pandemic. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

Fulltext

Symmetry

Topological and thermodynamic entropy measures for covid-19 pandemic through graph theory

In this paper zero suffix method with element-wise operations of fuzzy numbers is proposed to solve fully fuzzy transportation problem. The proposed method assures the optimality, feasibility and positivity conditions of the fuzzy solution. The proposed method is easy to understand since it follows zero suffix algorithm and easy to compute since it considers the fuzzy numbers as ordered pairs as it uses the element-wise operations. © 2020 Forum-Editrice Universitaria Udinese SRL. All rights reserved.

Italian Journal of Pure and Applied Mathematics

Fuzzy zero suffix algorithm to solve fully fuzzy transportation problems by using element-wise operations

This article studies the existence of solutions of the non-linear fuzzy fractional panto-graph equations. Strongly anomalous media problems are modeled by using panto-graph equations. Fixed point technique used to derive the results. An example is given to demonstrate the consequences. © 2020. All Rights Reserved.

International Journal of Mathematics and Computer Science

Existence of Solutions of Fuzzy Fractional panto-graph Equations

The present work addresses to analyse the heat transfer enhancement of unsteady laminar incompressible MHD flow of couple stress nanofluid through a rectangular squeezing channel with thermal radiation. The governing transport equations are reduced into an ordinary differential equation using relevant similar transformations and then solved numerically with the shooting method Runge–Kutta fourth-order scheme. The results are sketched as two-dimensional graphs and explained in detail for flow and heat transfer with non-dimensional physical parameters. Further calculated the skin friction and heat transfer rates at the upper plate. The axial velocity of engine oil/ethylene glycol has been increased by β and Da−1 towards the centre of the channel decreased for squeezing, and it is opposite for the separation case. The numerical results have good agreement with published work for temperature profile. © 2020, Akadémiai Kiadó, Budapest, Hungary.

Journal of Thermal Analysis and Calorimetry

A comparative study of heat transfer analysis on ethylene glycol or engine oil as base fluid with gold nanoparticle in presence of thermal radiation

The present problem is on the mass transport process through an annular tube, where a chemical species is discharged into a flowing stream driven by a harmonic pressure gradient. The species may undergo linear reversible and irreversible reactions at the outer boundary of the annulus. Also, two non-linear chemical decay are assumed within the bulk flow and at the outer wall. However, the degree of the non-linearity of these reactions are different. The problem is analyzed based on the three-time scale, and thus the homogenization method is utilized to average the two-dimensional mass transport problem. We establish analytical expressions for different transport coefficients in terms of rigorous mathematical calculations. The results exhibit some paradoxical behavior with the radius ratio. The transport coefficients linearly increase with the associated reactions rate but decrease with the wall absorption rate. © 2019 Elsevier Ltd

International Communications in Heat and Mass Transfer

Effect of multiple reactions on the transport coefficients in pulsatile flow through an annulus

This paper examines the effect of heterogeneous chemical reaction on the transport of a solute in a Casson fluid flow through an annular pipe under a periodic pressure gradient. Aris–Barton's method of moments is employed to understand the transport process. A finite difference implicit scheme is utilized to solve the momentum equation as well as the integral moment equation arising from the unsteady convective diffusion equation. Using the Hermite polynomial representation, the mean concentration distribution in the axial direction is acquired from the first four central moments. The transport phenomenon is discussed by three transport coefficients, namely exchange, advection, and dispersion coefficients owing to wall reactions, yield stress, radius ratio, etc. The present study can, therefore, be helpful to understand the transport process in blood flow through arteries. © 2019 Informa UK Limited, trading as Taylor & Francis Group.

International Journal of Computer Mathematics

On transport of reactive solute in a pulsatile Casson fluid flow through an annulus

In this paper, we introduce a new form of fuzzy number named as Icosikaitetragonal fuzzy number with its membership function. It includes some basic arithmetic operations like addition, subtraction, multiplication and scalar multiplication by means of a-cut with numerical illustrations. © 2020 Charles Babbage Research Centre. All rights reserved.

A new operation on icosikaitetragonal fuzzy number

An unsteady two-dimensional transport equation is considered to investigate the distribution of suspended sediment in an open channel turbulent flow, where the mechanism of hindered settling is also taken into account. Due to the consideration of concentration-dependent settling velocity on sediment transportation, the transport equation is a partial differential equation with a highly nonlinear term, which has been solved numerically by using the alternating direction implicit (ADI) finite-difference method. It is found that the sediment concentration increases along the vertical direction due to the inclusion of hindered settling effect. © Springer Nature Singapore Pte Ltd 2020.