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

Department of Mathematics

Unpredictable occurrence of any disaster emerges immeasurable demand in an affected society. Importance of immediate response in the aftermath of disaster is a crucial part of humanitarian logistic. Resource redistribution among the affected areas makes the optimal allocation in this chaotic situation. The research work has introduced a transportation plan considering the redistribution of resources from those areas which has already acquired relief and restored the normal condition to those areas still not being recovered from the effect of calamities. This research plan is developed to minimize the total cost of the relief operation as well as optimal allocation of the resources. The optimal allocation amidst the disruption of some resource storing points in the aftermath attack of disaster is also one of the key factors of the research. This research work has a great impact for decision-maker to derive an appropriate decision-making in such an anarchic situation of critical humanitarian supply chain. Due to the complexity of disaster, the model is considered in mixed uncertain environment. A numerical study is also performed to show the smooth functioning of the mathematical model assuming the uncertainty by trapezoidal neutrosophic number. Also, trapezoidal fuzzy number is implemented for uncertain parameters of the mathematical model and hereby compared with trapezoidal neutrosophic number. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

World University root node

School of Advanced Sciences

Vellore Campus

Soft Computing

An optimal redistribution plan considering aftermath disruption in disaster management

Let A be a complex unital Banach algebra, let be an element in it and let 0 < ϵ < 1.. In this article, we study the upper and lower hemicontinuity and joint continuity of the condition spectrum and its level set maps in appropriate settings. We emphasize that the empty interior of the -level set of a condition spectrum at a given plays a pivotal role in the continuity of the required maps at that point. Further, uniform continuity of the condition spectrum map is obtained in the domain of normal matrices. © 2019 Australian Mathematical Publishing Association Inc.

Journal of the Australian Mathematical Society

CONTINUITY of A CONDITION SPECTRUM and ITS LEVEL SETS

Let A be a complex Banach algebra with unit e. Let p be a non trivial idempotent element in A and ε> 0. For a∈ A, it is proved that the interior of the level set of (p, e- p) - ε pseudo spectrum of a is empty in the unbounded component of (p, e- p) resolvent set of a. An example is constructed to show that the condition ‘unbounded component’ can not be dropped. Further, it is proved this ‘unbounded component’ can be dropped in the case when A is B(X) where X is a complex uniformly convex Banach space. That is, if T∈ B(X) then interior of the level set of (p, I- p) - ε pseudo spectrum is empty in (p, I- p) resolvent set of T. © 2017, Forum D'Analystes, Chennai.

Fulltext

Journal of Analysis

Level sets of (p, e- p) outer generalized pseudo spectrum

The main investigation of the paper is to propose a reduction method of type-2 zigzag uncertain variables. We have also proposed an innovative, dynamic solid transportation problem (STP) considering maximization of profit and minimization of emission. The model has been presented to show an awareness among the drivers or managers of firms to emit less amount of carbon particles. The transportation parameters of the model have been taken as type-2 zigzag uncertain variables. The proposed expected value-based reduction method has been used to convert the transportation parameters into deterministic form. A real-life study has been presented here to show the use of the proposed reduction method and proposed STP. LINGO 13.0 optimization software has been used to solve the multi-objective STP using fuzzy satisficing method and intuitionistic fuzzy programming technique. The transportation parameters of the model are also presented in type-2 triangular fuzzy variables to show a comparison with the type-2 zigzag uncertain variable. A sensitivity analysis is presented with respect to different credibility levels of profit, emission, source, demand and conveyance. © 2018, The Natural Computing Applications Forum.

Neural Computing and Applications

A carbon emission optimization model with reduction method of type-2 zigzag uncertain variable

In this paper, we apply the monotone iterative method for the existence of two positive solutions of fourth-order two-point boundary value problem u′′′′ (t) = f(t, u(t)), 0 &lt; t &lt; 1, u(0) =u′ (0) = u′′ (1) = u′′′ (1) = 0, which models a cantilever beam equation, where one end is kept free. Here f ∈ C ([0, 1] × R+, R+). The sufficient condition is interesting, new and easy to verify. Our condition do not require any super-linearity or sub-linearity conditions on the function f at 0 or ∞. Our result uses the monotonically increasing property of f in a certain interval to prove the existence of a positive solution(s). This approach completely differs from the existing results in the literature. An example is presented at the end to illustrate the usefulness of our result. Although our theorem predicts the existence of two positive solutions, our example and the iterative scheme constructed in the example shows that the two iterative sequences of solutions converge to a single solution. © 2020, International Publications. All rights reserved.

Advances in Nonlinear Variational Inequalities

Monotone iterative method for solutions of a cantilever beam equation with one free end

In this paper, we discuss the existence of best proximity points of certain mappings via simulation functions in the frame of complete metric-like spaces. Some consequences and examples are given of the obtained results. © 2020 University of Kragujevac, Faculty of Science.

Kragujevac Journal of Mathematics

Best proximity point results via simulation functions in metric-like spaces

This paper is focused on the study of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium by taking into account of the Soret/Dufour effects. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-Box finite-difference scheme. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters, namely the buoyancy ratio parameter, Prandtl number, Forchheimer number, magnetohydrodynamic body force parameter, Soret and Dufour numbers. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. Increasing the Forchheimer inertial drag parameter reduces velocity but elevates temperature and concentration. Increasing the Soret number and simultaneously reducing the Dufour number greatly boosts the local heat transfer rate at the cylinder surface. A comparative study of the previously published and present results in a limiting sense is made and an excellent agreement is found between the results. © 2020 B. Vasu et al., published by Sciendo 2020.

International Journal of Applied Mechanics and Engineering

MHD Free Convection-Radiation Interaction in a Porous Medium-Part II: Soret/Dufour Effects

Frank Harary and Allen J. Schwenk have given a formula for counting the number of non-isomorphic caterpillars on n vertices with n > 3. Inspired by the formula of Frank Harary and Allen J. Schwenk, in this paper, we give a formula for counting the number of non-isomorphic caterpillars with the same degree sequence. © 2020 Charles Babbage Research Centre. All rights reserved.

Journal of Combinatorial Mathematics and Combinatorial Computing

Enumeration of caterpillars

An analysis has been carried out the effect of binary chemical reaction on the MHD Casson fluid flow over an exponentially stretching surface in the presence of Cattaneo-Christov heat flux. Additionally, the aspects of binary chemical reaction effects with modified Arrhenius activation energy are analyzed. The stretching velocity, reaction rate, wall temperature and wall concentration are expected to differ according to specific exponential form. Appropriate self-transformed variables are used to deal with non-linear differential systems which are solved by the Runge-Kutta scheme. The impacts of active parameters are manifested graphically in velocity, temperature and concentration fields for two different fluid cases namely Newtonian and Non-Newtonian. This investigation divulges that the Newtonian fluid has a higher temperature than non-Newtonian fluid. Strengthen the magnetic field causes the Newtonian/non-Newtonian fluid flow tends to declines. © IMechE 2020.

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Effectiveness of binary chemical reaction on magneto-fluid flow with Cattaneo–Christov heat flux model

Human trafficking is a modernist form of heavy labor and is a well-known fact throughout the world. In addition to drug trafficking and the arms industry, sex trafficking is now the second-largest illegal activity in the world and is a growing crime. Sex trafficking is a crime when women or children participate by force in commercial sexual acts. While the twilight world of sexual relations around the world corresponds to an intriguing theme in our way of life, many people are unaware that sexual relations are happening on our terraces. The most common forms of sex trafficking are including forced labor, sexual exploitation, and child trafficking. There are many forms of human trafficking that are not as well-known but that, nevertheless, also require legal and policy responses. In this research, the authors attempted to analyze the crime of women in three phases. The first step is the analysis of the types of crimes, especially for women in every state of India. In the next step, the analysis of the purpose of kidnapping women and children in India and identified the most affected age group. Finally, based on previous results, the authors described the health problems of people affected by sex trafficking. The authors used three machine learning algorithms, such as the hierarchical agglomerative clustering algorithm, the multivariate linear regression and the OneR algorithm for analysis. The above methods are solved through the use of the R software and identify valuable results, such as the dangerous states of India in the crimes of women, identify the age group most affected for kidnapping and abduction and discussing symptoms important for victims of sex trafficking. © 2020, Research Trend. All rights reserved.