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

The present study deals with the transient flexural gravity wave motion associated with floating elastic plate in the presence of permeable bottom. Integral form of the floating plate deflection is obtained analytically using Laplace–Fourier transform method and the asymptotic solution is derived for large time using stationary phase method. Also, using fast Fourier transform method the time domain simulation of floating plate deflection is obtained. The effect of current, compressive force and porosity parameter on phase and group velocities and floating plate deflection are analyzed. It is observed that in the absence of current, due to the presence of porosity parameter there exist two points where there is a situation of no wave propagation. It is also observed that the current and compressive force have significant effect on transient flexural gravity wave motion whereas the porosity parameter has small impact on the gravity wave motion associated with floating elastic plate. The properties of the roots of the dispersion relation associated with the flexural gravity wave motion in the presence of permeable bed are discussed analytically and numerically. © 2020, Springer Nature B.V.

School of Advanced Sciences

Vellore Campus

Meccanica

Time dependent wave motion in a permeable bed

Rosa, in his classical paper (Rosa, 1967) introduced a hierarchical series of labelings called (Formula presented.) and (Formula presented.) labeling as a tool to settle Ringel’s Conjecture which states that if (Formula presented.) is any tree with (Formula presented.) edges then the complete graph (Formula presented.) can be decomposed into (Formula presented.) copies of (Formula presented.). Inspired by the result of Rosa, many researchers significantly contributed to the theory of graph decomposition using graph labeling. In this direction, in 2004, Blinco, El-Zanati and Vanden Eynden introduced (Formula presented.) -labeling as a stronger version of (Formula presented.) -labeling. A function (Formula presented.) defined on the vertex set of a graph (Formula presented.) with (Formula presented.) edges is called a (Formula presented.) -labeling if (i) (Formula presented.) is a (Formula presented.) -labeling of (Formula presented.), (ii) (Formula presented.) is tripartite with vertex tripartition (Formula presented.) with (Formula presented.) and (Formula presented.) such that (Formula presented.) is the unique edge joining an element of (Formula presented.) to (Formula presented.), (iii) for every edge (Formula presented.) with (Formula presented.), (Formula presented.), (iv) (Formula presented.). Further, Blinco et al. proved a significant result that if a graph (Formula presented.) with (Formula presented.) edges admits a (Formula presented.) -labeling, then the complete graph (Formula presented.) can be cyclically decomposed into (Formula presented.) copies of the graph (Formula presented.), where (Formula presented.) is any positive integer. Motivated by the result of Blinco et al., we show that a new family of almost bipartite graphs each admits (Formula presented.) -labeling. The new family of almost bipartite graphs is defined based on the supersubdivision graph of certain connected graph. Supersubdivision graph of a graph was introduced by Sethuraman and Selvaraju in Sethuraman and Selvaraju (2001). A graph is said to be a supersubdivision graph of a graph (Formula presented.) with (Formula presented.) edges, denoted (Formula presented.) if (Formula presented.) is obtained from (Formula presented.) by replacing every edge (Formula presented.) of (Formula presented.) by a complete bipartite graph (Formula presented.), (Formula presented.), (where (Formula presented.) may vary for each edge (Formula presented.)) in such a way that the ends of (Formula presented.) are identified with the 2 vertices of the vertex part having two vertices of the complete bipartite graph of (Formula presented.) after removing the edge (Formula presented.) of (Formula presented.). In the graph (Formula presented.), the vertices which originally belong to the graph (Formula presented.) are called the base vertices of (Formula presented.) and all the other vertices of (Formula presented.) are called the non-base vertices of (Formula presented.). More precisely, we prove that if (Formula presented.) is a connected graph containing a cycle (Formula presented.), where (Formula presented.) and having a vertex of degree two with one of its adjacent vertices of degree one and its other adjacent vertex is of degree at least two, then certain supersubdivision graph of the graph (Formula presented.), (Formula presented.) plus an edge (Formula presented.) admits (Formula presented.) -labeling, where (Formula presented.) is added between a suitably chosen pair of non-base vertices of the graph (Formula presented.). Also, we discuss a related open problem. © 2018 Kalasalingam University. Published with license by Taylor & Francis Group, LLC.

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AKCE International Journal of Graphs and Combinatorics

-labeling of supersubdivided connected graph plus an edge

This paper is mainly concerned with the synchronization problem of reaction-diffusion neural networks (RDNNs) with delays and its direct application in image secure communications. An adaptive control is designed without a sign function in which the controller gain matrix is a function of time. The synchronization criteria are established for an error model derived from master-slave models through solving the set of linear matrix inequalities derived by constructing the suitable novel Lyapunov-Krasovskii functional candidate, Green's formula, and Wirtinger's inequality. If the proposed sufficient conditions are satisfied, then the global asymptotic synchronization of the error model is guaranteed. The numerical illustrations are provided to demonstrate the validity of the derived synchronization criteria. In addition, the role of system parameters is picturized through the chaotic nature of RDNNs and those unprecedented solutions is utilized to promote better security of image transactions. As is evident, the enhancement of image encryption algorithm is designed with two levels, namely, image watermarking and diffusion process. The contributions of this paper are discussed as concluding remarks. © 2013 IEEE.

IEEE Transactions on Cybernetics

Adaptive Synchronization of Reaction-Diffusion Neural Networks and Its Application to Secure Communication

Doubly truncated data are sometimes encountered in several applications, mainly in survival and astronomical data analysis. This occurs when the data falls between two points. In this study, we focus on the Shannon entropy measure of doubly truncated random variables. We propose ordering and various aging properties based on this measure. Characterizations of some useful life distributions are obtained. It is showed that under certain condition, the proposed measure determines the distribution function uniquely. Some results on discrete distributions are presented. Finally, applications are given. © 2020 The Authors. Published by Atlantis Press SARL. This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Journal of Statistical Theory and Applications

Properties of shannon entropy for double truncated random variables and its applications

This manuscript highlights the controllability of Hilfer fractional neutral differential systems with infinite delay. A vivid study on the primary outcomes is carried out by applying fractional calculus, and for the main results, we use fixed point technique to the measures of noncompactness. The results, thus acquired, are extend to the concept of nonlocal conditions. Lastly, a model is presented for the illustration of theory. © 2020

Chaos, Solitons and Fractals

Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness

This article explores the theoretical investigation of peristaltic motion of a non-Newtonian fluid accompanied in a horizontal channel with elastic walls. Most of the physiological fluids (blood) behaves like a non-Newtonian fluid. To characterize the fluid flow behavior, Casson fluid model is considered which a yield stress model and it holds good to explain the behavior of blood flow through small diameter conduits at low shear rates. The deformation in the walls of the channel is studied under two aspects, one is peristalsis and another is elasticity. Exact solutions are obtained for velocity and stream function. The size of the trapped food bolus increases with increasing values of yield stress parameter. The theoretical obtained results may be useful in understanding of pathological conditions arising due to change in elasticity and different peristaltic wave forms. © 2020 International Information and Engineering Technology Association.

Mathematical Modelling of Engineering Problems

Axisymmetric peristaltic flow of a non-Newtonian fluid in a channel with elastic walls

Fuzzy lattice theory have been widely used in image processing as it allows map functions residing in an original space to functions in a transformed space, resulting in powerful knowledge extraction and image pattern recognition. Despite recognition efficiency and best means of knowledge extraction, the computational complexity and the noise rate involved have been an open problem to be addressed. In this paper, to reduce the computational complexity by optimizing the number of granules between pixels and improving the PSNR through linear fuzzy transform, a method called Euclidean Fuzzy Lattice Orthogonal Image Transform (EFL-OIT) has been presented. © Springer Nature Singapore Pte Ltd 2020.

Advances in Intelligent Systems and Computing Artificial Intelligence and Evolutionary Computations in Engineering Systems

Fuzzy Lattice-Based Orthogonal Image Transformation Technique for Natural Image Analysis

In this paper, an intuitionistic fuzzy C-irreducible function on intuitionistic fuzzy C-Hausdorff spaces is defined and several properties of it are discussed. Moreover, the intuitionistic fuzzy absolute C-centred structures are coined and proved that they are homeomorphic under the natural mapping, πR. © 2020, Research Publication. All rights reserved.

Advances in Mathematics: Scientific Journal

On intuitionistic fuzzy absolute c-centred structures ωc (r)

A common coupled fixed point theorem supported with an illustrative example, and a related problem of existence of solution of system of Fredhlom type integral equations, are presented for two mappings, which satisfy mixed weakly monotone property in a partially ordered b-metric space. © 2020 Kyungnam University Press.

Nonlinear Functional Analysis and Applications

Common coupled fixed point in a partially ordered b-metric space

This article is investigates the effect of aligned magnetic field flow and heat transfer of carbon nanotubes over a moving extensible stretching surface through a porous medium. Definitions of thermal radiation and heat generation/absorption are utilized in the thermal expression. Carbon nanotubes (single-walled and multiwalled) and base fluids (seawater, blood, and ethylene glycol) are used to explore the impacts of heat transfer characteristics. A similarity transformation is used to transform the governing boundary layer coupled partial differential equations into a system of nonlinear ordinary differential equations, which are explored numerically using the Runge–Kutta fourth-order method along with shooting procedure. The streamlines are closer to the surface wall when there are lower values of magnetic parameter and porosity parameter. Strengthening the thermal radiation parameter value enhances the rate of heat transfer. A comparative study between the formerly published results and the present results for a special case is found to be in tremendous agreement. © 2020 by Begell House, Inc.