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

Peristaltic transport of Newtonian nanofluid in an inclined annulus terms of radii regarding peristalsis and elasticity. It is noticed that with an increase in amplitude ratio, flux is getting enhanced in the absence of nanoparticles when compared with viscous fluid with nanoparticles. Our results reduce to the corresponding ones of Rubinow and Keller as a special case for the viscous flow in an elastic tube. The effect of various emerging parameters bounded by two concentric cylinders is studied under the assumption of long wavelength and dominance of viscous effects over inertial effects. The outer cylinder is elastic in nature and has a sinusoidal wave traveling down in its wall, whereas the inner cylinder is rigid. Analytical solutions have been established for velocity, flux, pressure rise, temperature distribution, and nanoparticle concentration. The flux, pressure rise, and frictional forces have been obtained in on the flow characteristic are presented and discussed. Obtained results may be useful in understanding the behavior of peristaltic transport of blood flow in small blood vessels and blood flow through elastic arteries. © 2020 Wiley Periodicals LLC

World University root node

School of Advanced Sciences

Vellore Campus

Heat Transfer

Influence of elasticity in an inclined annulus of nanofluid with peristaltic transport

An unprecedented upsurge of COVID-19-positive cases and deaths is currently being witnessed across India. According to WHO, India reported an average of 3.9 lakhs of new cases during the first week of May 2021 which equals 47% of new cases reported globally and 276 daily cases per million population. In this letter, the concept of SIR and fractal interpolation models is applied to predict the number of positive cases in India by approximating the epidemic curve, where the epidemic curve denotes the two-dimensional graphical representation of COVID-19-positive cases in which the abscissa denotes the time, while the ordinate provides the number of positive cases. In order to estimate the epidemic curve, the fractal interpolation method is implemented on the prescribed data set. In particular, the vertical scaling factors of the fractal function are selected from the SIR model. The proposed fractal and SIR model can also be explored for the assessment and modeling of other epidemics to predict the transmission rate. This letter investigates the duration of the second and third waves in India, since the positive cases and death cases of COVID-19 in India have been highly increasing for the past few weeks, and India is in a midst of a catastrophizing second wave. The nation is recording more than 120 million cases of COVID-19, but pandemics are still concentrated in most states. In order to predict the forthcoming trend of the outbreaks, this study implements the SIR and fractal models on daily positive cases of COVID-19 in India and its provinces, namely Delhi, Karnataka, Tamil Nadu, Kerala and Maharashtra. © 2021, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.

Fulltext

European Physical Journal Plus

The second and third waves in India: when will the pandemic be culminated?

The purpose of this paper is to establish the uniqueness and existence of the common fixed point under generalized contractive conditions in b-metric spaces with supportive examples. We also approximate the common fixed point by Jungck-Picard and Picard iteration procedures along with the P property of the mappings. Further, (T,f)-stability of Jungck-Picard iterative and T-stability of Picard iterative schemes are proved. © 2022 World Scientific Publishing Company.

Asian-European Journal of Mathematics

On existence and approximation of common fixed points in b -metric spaces

Best proximity results for cyclic and noncyclic (Formula presented.) -contractive operators in (strictly convex) Banach spaces are obtained via the measure of noncompactness. The work extends some of recent investigations in this direction. The obtained results are applied to investigation of optimum solutions for a system of second order differential equations with two initial conditions followed by an example. © 2021 Taylor & Francis Group, LLC.

Numerical Functional Analysis and Optimization

Best Proximity Point Results via Measure of Noncompactness and Application

In this paper, we present existence, uniqueness and Ulam-Hyers stability results for the n−tupled fixed points of a pair of contractive type singlevalued and respectively multivalued operators on complete metric spaces. The approach is based on Perov type fixed point theorem for contractions in spaces endowed with vector-valued metrics. © Palestine Polytechnic University-PPU 2021.

Palestine Journal of Mathematics

Application of n−tupled fixed points of contractive type operators for ulam-hyers stability

The object of the present paper is to study contact CR-submanifolds of (LCS)n-manifolds. We obtain the integrability conditions of the distributions of contact CR-submanifolds of (LCS)n-manifolds. Finally, we give an interesting example of a contact CR-submanifold of (LCS)7-manifold. © 2021 by TJM.

Thai Journal of Mathematics

On contact CR-submanifolds of (LCS)n-manifolds

In this paper, we prove some fixed points, coupled coincidence point and coupled common fixed point results for mappings satisfying an almost generalized contraction conditions in partially ordered b-metric spaces. These results generalize, extend and unify many comparable results in the existing literature. Few examples are given to support our results. © World Scientific Publishing Company

Coupled fixed points theorems for generalized weak contractions in ordered b-metric spaces

We establish coincidence point theorem for g-non-decreasing mappings under generalized (ψ, θ, φ)-contraction on partially ordered metric spaces. With the help of the obtain result, we indicate the formation of a coupled coincidence point theorem of generalized compatible pair of mappings F,G: X2 → X. We apply our result to obtain the solution of integral equation and also give an example to show the degree of validity of our hypothesis. Our results modify, improve, sharpen, enrich and generalize various known results. © 2021 by TJM.

Coincidence point results for generalized (ψ, θ, Φ) - contraction on partially ordered metric spaces

An analytical model has been considered to study the scattering phenomenon of the quasi-plane wave in functionally graded piezoelectric material (FGPM) layer sandwiched between two similar piezoelectric (PE) media. In more contrast, the effect of material gradient factor on amplitude ratios of various reflected and transmitted waves has been investigated. The composite structure consists of an FGPM layer bonded between two similar transversely isotropic PE half-spaces. It has been shown that incident quasi-longitudinal wave (qP-mode) at lower interface generates reflected and transmitted waves namely qP and quasi-shear vertical waves (qSV-mode). These transmitted waves further give rise to reflected and transmitted waves at the upper interface. At the interfaces of the FGPM layer, the stresses, displacements and electric potential functions are continuous. Due to the scattering of waves, 12 independent amplitude ratios of displacement components are obtained. Amplitude ratios of various reflected and transmitted waves (for the electrically short case) have been obtained by solving a set of linear algebraic equations (using Crammer’s rule). The impact of gradient factor has been examined on amplitude ratios against the angle of incidence and presented graphically. The plot of the slowness section is also demonstrated through graph. In addition, deduced results are compared with the earlier studies and found to be in agreement with the findings. © 2019 Taylor & Francis Group, LLC.

Mechanics Based Design of Structures and Machines

Analysis of wave scattering in 3-layer piezo composite structure [Pb[ZrxTi1-x]O3-ALN-Pb[ZrxTi1-x]O3]

Herein we report an exclusively ligand-centered redox controlled approach for the dehydrogenation of a variety of N-heterocycles using a Zn(II)-stabilized azo-anion radical complex as the catalyst. A simple, easy-to-prepare and bench-stable Zn(II)-complex (1b) featuring the tridentate arylazo pincer, 2-((4-chlorophenyl)diazenyl)-1,10-phenanthroline, in the presence of zinc-dust, undergoes reduction to form the azo-anion radical species [1b]- which efficiently dehydrogenates various saturated N-heterocycles such as 1,2,3,4-tetrahydro-2-methylquinoline, 1,2,3,4-tetrahydro-isoquinoline, indoline, 2-phenyl-2,3-dihydro-1H-benzoimidazole, 2,3-dihydro-2-phenylquinazolin-4(1H)-one and 1,2,3,4-tetrahydro-2-phenylquinazolines, among others, under air. The catalyst has further been found to be compatible with the cascade synthesis of these N-heterocycles via dehydrogenative coupling of alcohols with other suitable coupling partners under air. Mechanistic investigation reveals that the dehydrogenation reactions proceed via a one-electron hydrogen atom transfer (HAT) pathway where the zinc-stabilized azo-anion radical ligand abstracts the hydrogen atom from the organic substrate(s) and the whole catalytic cycle proceeds via the exclusive involvement of the ligand-centered redox events where the zinc acts only as the template.