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

The steady axisymmetric uniform flow of an incompressible micropolar fluid past a porous sphere embedded in another porous medium has been studied analytically. The stream function solution for both the inner and outer flow field is acquired by using the Brinkman equation. Explicit expressions are determined for both the flow fields by taking the appropriate boundary conditions across the surface of the porous sphere. Furthermore, the non-dimensional drag experienced by a porous sphere embedded in another porous medium of micropolar fluid is calculated. Effects of drag force and shearing stress on permeability parameter, the viscosity ratio for the porous sphere is presented graphically and numerically. Some special cases of flow past a porous sphere have been validated with earlier well-known cases. © 2020 by Begell House, Inc.

School of Advanced Sciences

Chennai Campus

World University root node

Special Topics and Reviews in Porous Media

Flow of micropolar fluid past a porous sphere embedded in another porous medium

Let G = (V, E) be a graph. A function f: V ? {0, 1} of the graph G is called a Biconditional cordial labeling of G if an induced edge function f*: E ? {0, 1} defined by f*(uv)={ 1,iff(u)=f(v)0,iff(u)?f(v) satisfies the following two conditions. i)|vf(0)-vf(1)|=1ii)|ef*(0)-ef*(1)|=1 In this manuscript, we prove the existence of the Biconditional cordial labeling for complete bipartite graph, book graph with triangular pages, sunflower graph and web graph. © 2020 Author(s).}, author_keywords={Biconditional Cordial Labeling; Cordial Labeling; Graphs}, references={Bloom, G.S., Hsu, D.F., On Graceful Digraphs and a Problem in Network Addressing (1982) Congr, Number, 35, pp. 91-103; Cahit, I., On Cordial and 3-Equitable Labeling of Graph (1990) Utilitas Math, 370, pp. 189-198; Gallian, J.A., A Dynamic Survey of Graph Labeling (2019) Electronic Journal of Combinatories, 17 (DS6); Harary, F., (1972) Graph Theory, , Addison Wesley; Lakshmi Prasana, N., Saravanthi, K., Sudhakar, N., Applications of Graph Labeling in Major Areas of computing science (2014) International Journal of Research in Computer and Communication Technology, 3 (8). , Vol., No.; Murali, B.J., Thirusangu, K., Meenakshi, M., Biconditional Cordial Labeling of Cycles (2015) International Journal of Applied Engineering Research, 10 (80), pp. 188-191. , R., Vol., No.; Murali, B.J., Thirusangu, K., Balamurugan, B.J., Biconditional Cordial Labeling of Ladder Graph and K2+ nK1Graph (2016) International Journal of Control Theory and Applications, 9 (51), pp. 37-45. , Vol., No.; Murali, B.J., Thirusangu, K., Balamurugan, B.J., (2017) Combination Cordial Labeling of Flower Graphs and Corona Graph, 117 (11), pp. 45-51. , Vol., No.; Nedumaran, P., Thirusangu, K., Mary, C., 1-Near Mean Cordial and Biconditional Cordial Labeling of Certain Classes of Graphs (2017) International Journal of Pure and Applied Mathematics, 117 (12), pp. 297-307. , Vol., No.; Rosa, A., (1966), pp. 349-359. , On Certin Valuations of the Vertices of a Graph, In Theory of Graphs (Internat. Sympos. Rome.), Gordan and Breach, Newyork, Dunod, Paris, 1967; West, D.B., (2009) Introduction to Graph Theory, , PHI Learning Private Limited, 2nd Edition}, correspondence_address1={Kalaimathi, M.; School of Advanced Sciences, Vandalur-Kelambakkam road, India; email: kalaimathi.m2018@vitstudent.ac.in}, editor={Baskaran B., Rajesh C., Ravikumar J.}, publisher={American Institute of Physics Inc.}, issn={0094243X}, isbn={9780735440128}, language={English}, abbrev_source_title={AIP Conf. Proc.}, document_type={Conference Paper}, source={Scopus},

AIP Conference Proceedings

Biconditional cordial labeling of cycle related graphs

Tobacco smoking is a social problem. It is a well-established fact that the smoking of tobacco products can cause severe health problems. It is also observed that the smokers are having higher risk of getting tuberculosis infection than the non-smokers. In this article a non-linear mathematical model is proposed and analyzed to demonstrate the impact of tobacco smoking on transmission dynamics of the tuberculosis. The basic reproduction number of the model is computed and the stabilities of different equilibria of the model are studied in-detail. The model system exhibits backward bifurcation for some specific set of parameters which suggests that mere reducing the basic reproduction number corresponding to TB below one is not enough to establish the stability of TB-free equilibrium point. So efforts are needed to reduce this basic reproduction number much below one to have TB-free equilibrium to be stable. It is also observed that the smoking habits can influence the stability of co-existence equilibrium and it can lead to persistence of TB in the population even though the basic reproduction number corresponding to TB is much less than one. Furthermore, this model is extended to the optimal control problem and the optimal control model is analyzed using the Pontryagin’s Maximum Principle and is solved numerically using MATLAB. Finally, numerical simulations are performed to analyze the effect of optimal control on the infected population. We observe that the optimal control model gives better result as compared to the model without optimal control as it reduces the number of infectives significantly within desired interval of time. © 2020, Springer Nature Singapore Pte Ltd.

Springer Proceedings in Mathematics and Statistics

Impact of Tobacco Smoking on the Prevalence of Tuberculosis Infection: A Mathematical Study

Graph embedding is an important technique used in studying the problem of efficiently implementing parallel algorithms on parallel computers. Wirelength is an embedding parameter widely studied in data structures and data representations, electrical networks, VLSI network and chemical graphs. This parameter had been studied for embedding complete bipartite graphs into complete necklace, star necklace and windmill graphs. © 2020 The Authors. Published by Elsevier B.V.

Fulltext

Procedia Computer Science

Embedding complete bipartite graphs into necklace graphs

Department of Sensor and Biomedical Technology

School of Electronics Engineering

Vellore Campus

VIT Unitversity

Centre for Biomaterials, Cellular and Molecular Theranostics

Estimating the Human Cost of Transportation Accidents

Preface

The mathematical model of hydrodynamic dispersion through a porous medium is developed in the presence of transversely applied magnetic fields and axial harmonic pressure gradient. The solute introduce into the flow is experienced a first-order chemical reaction with flowing liquid. The dispersion coefficient is numerically determined using Aris’s moment equation of solute concentration. The numerical technique employed here is a finite difference implicit scheme. Dispersion coefficient behavior with Darcy number, Hartmann number and bulk flow reaction parameter is investigated. This study highlighted that the dependency of Hartmann number and Darcy number on dispersion shows different natures in different ranges of these parameters. © 2020, The Korean Society of Rheology and Springer.

Korea Australia Rheology Journal

Mathematical model on magneto-hydrodynamic dispersion in a porous medium under the influence of bulk chemical reaction

For positive integers d and n, the vector space Hd(x1, x2, … , xn) of homogeneous polynomials of degree d is a representation of the symmetric group Sn acting by permutation of variables. Regarding this as a representation for the dihedral subgroup Dn, we prove a formula for the dimension of all the isotypical subrepresentations. Our formula is simpler than the existing one found by Zamani and Babaei (Bull. Iranian Math. Soc.40(4) (2014) 863–874). By varying the degrees d we compute the generating functions for these dimensions. Further, our formula leads us naturally to a specific supercharacter theory of Dn. It turns out to be a ∗ -product of a specific supercharacter theory studied in depth by Fowler et al. (The Ramanujan Journal (2014)), with the unique supercharacter theory of a group of order 2. © 2020, Indian Academy of Sciences.

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Dimension formula for the space of relative symmetric polynomials of Dn with respect to any irreducible representation

In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role. c 2021 the Author(s).

Mathematical Biosciences and Engineering

A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: Deterministic vs. stochastic

In this paper, a non-linear mathematical model for tumor-immune system is formulated and analyzed by considering saturated incidence for the interaction between tumor cells and cytotoxic-T lymphocytes (CTLs). It is assumed that both the tumor cells as well as T-helper cells follow logistic growth. In Addition, a time lag exists in the activation of CTLs because of T-helper cells. Existence and stability of different equilibria of the model are discussed in detail. The model is analyzed using the theory of delay differential equations. It was observed that delay played an important role in defining the dynamics of the system. The system exhibited Hopf-bifurcation when the value of time delay crossed a certain threshold. Existence of Hopf-bifurcation and condition for stability switch are discussed in detail. Numerical simulation is performed to support the analytical findings. © 2020 NSP Natural Sciences Publishing Cor. All Rights Reserved.

Applied Mathematics and Information Sciences

Modeling of Tumor-Immune Competitive System with Saturated Incidence

In this article, an age structured SVEIR epidemic model for TB is formulated and analyzed by considering three types of ages e.g., latent age, infection age and vaccination age. The presented model also incorporates the environmental transmission of TB. The dynamics of the disease is governed by a system of differential-integral equations. We assume that the vaccines for TB are partially effective. Some vaccinated individuals get permanent immunity to this disease, but some vaccinated individuals lose its protective power over a time and become susceptible again. The dynamical property of the model is established by using LaSalle’s invariance principle and constructing suitable Lyapunov functions. It has been shown that the dynamics of the model is governed by basic reproductive number. The disease-free equilibrium is globally stable if the basic reproductive number. The endemic equilibrium is locally and globally stable if. As the basic reproduction number plays an important role in determining the stability of the system, reducing this number below one through vaccination can lead to decrease in the transmission of this disease. Additionally, contaminated environment also contributes to the increase in , so we also need to keep the environment clean to decrease the basic reproduction number below one. These types of control measures are easy to implement in our society and certainly this will improve the well-being of the society. © 2020, Springer Nature Singapore Pte Ltd.