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

Unique and outstanding physiochemical properties of zeolite materials make them extremely useful in a variety of applications which offer a great potential for the development of material science. Recent studies of heavy element doping and insertion into these zeolites have opened up novel applications to tungsten-based biofuels, luminescence spectra and so on. Although a recent study by Prabhu et al. [Mater. Res. Exp. 7, 055006 (2020)] presents several distance-based and bond additive topological indices of Linde type A zeolites, we show here that their results are erroneous. We also present novel techniques for zeolite materials impregnated or doped with very heavy elements such as W, Au, Pt, Bi to obtain topological indices that include relativistic parameters derived from relativistic quantum computations. We have derived exact mathematical expressions for the various topological indices with relativistic parameters and yet in a simple three dimensional symmetrical formula based on the structural descriptions of Linde type A zeolites with very heavy atoms. We obtain closed formula for nine types Mostar indices to quantify peripherality measures of zeolite structures. © 2020 Informa UK Limited, trading as Taylor & Francis Group.

World University root node

School of Advanced Sciences

Vellore Campus

Molecular Physics

Relativistic distance-based topological descriptors of Linde type A zeolites and their doped structures with very heavy elements

The words fractional calculus were born from a communication between L’Hospital and Leibniz in 1695. By denoting the nth derivative of f with respect to x as dnfdxn, Leibniz had written a letter to L’Hospital. In his letter, Leibniz assumed that n takes the value from the positive integers, i.e., n∈ N. L’Hospital replied by raising the question of what meaning could be recognized to dnfdxn if n is 1/2, a fraction. This question became a historical statement to pronounce the new name in the theory of mathematic and was also universally accepted as the first existence of the so-called fractional derivative. The name fractional calculus has stayed being used ever since, despite the fact that it is notable at this point that there is no motivation to confine n to the rational numbers. Without a doubt, any real number will do similarly too, even complex numbers might be permitted, yet this is well beyond the aim of this book. Like fractals, the notion of fractional calculus has also been applied to numerous fields of science. Fractional calculus has never experienced the popularity currently enjoyed by fractals since it does not lend itself to produce complex graphical structures. In [13], significant effort has been devoted to relating fractional calculus to fractal geometry. In addition, the relationship between fractional calculus, such as Riemann–Liouville fractional calculus, and the von Koch curve has been revealed. Further, this study found that the value of the fractal dimension of von Koch curve is a linear function of its order of the Riemann–Liouville fractional calculus. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Understanding Complex Systems

Fractional Calculus on Fractal Functions

Fractal functions, dimensions and signal analysis

Montes Taurus Journal of Pure and Applied Mathematics

Fekete-Szeg{\"o} Problems for the k th Root Transform of Subclasses of Starlike and Convex Functions with Respect to Symmetric Points

Montes Taurus J. Pure Appl. Math

Fekete-Szego Inequalities for Certain Subclasses of Analytic Functions Related with Leaf-Like Domain

Sahand Communications in Mathematical Analysis

A Generalized Class of Univalent Harmonic Functions Associated with a Multiplier Transformation

The main intention of this article is to explore the significance of electronmagnetohydrodynamic (EMHD) dusty nanofluid on the stagnation point flow in the presence of radiation and Ohmic heating. Water is considered as base fluid with single-wall carbon nanotubes along with suspended dust particles. The numerical solutions for both dusty phase and fluid phase differential systems are obtained by using Runge Kutta 4th order with shooting method. Influence of embedded parameters such as Biot number, electric field, viscous dissipation, magnetic field, thermal radiation, Joule heating and stagnation point flow are presented graphically. Dust particles play a significant role in food pharmaceutical industries particularly for efficient cultivation of microorganisms and also these type of studies may be applicable in atmospheric fields, wastewater treatment, metal objects covered with plastic materials and solids drying. The higher values of electric field parameter (E) increases the fluid phase velocity and dusty phase velocity. An increase in the thermal radiation parameter releases thermal energy into the flow, so this energy helps to increase the fluid phase temperature and dusty phase temperature. The fluid phase temperature and dusty phase temperature declines with increasing the electric field parameter for dusty fluid and dusty nanofluid cases. © IMechE 2021.

Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering

Comparative study on electromagnetohydrodynamic single-wall carbon nanotube–water dusty nanofluid in the presence of radiation and Ohmic heating

This article mainly emphases on the study of magneto Cu-Al2O3/water hybrid nanofluid flow in a non-Darcy porous square cavity. The square geometry is a lid-driven enclosure with an inside heated square obstacle. Cattaneo-Christov heat flux pattern is used for the formulation of the heat equation. This type of problems may be applicable in the high temperatures in the different scientific processes, extrusion of polymers, aerodynamics extrusion and cooling hot glass. Dimensionless forms of governing flow expressions are computed numerically with Finite Volume Method via SIMPLER algorithm simultaneously. The characteristics of numerous dimensionless parameters such as; Richardson number 0.1⩽Ri⩽100, Hartmann number 0⩽Ha⩽100, height of hot square obstacle 0.1⩽H⩽0.5, width of hot square obstacle 0.1⩽W⩽0.5, Reynolds number 0.1⩽Re⩽25 and Darcy number 10-2⩽Da⩽10-6 are analyzed. The achieved results are projected graphically via streamlines, isotherms, local and average Nusselt numbers. The fluid flow and rate of heat transfer in the direction of the moving heated obstacle isfound to play an important role. The higher values of Ha decreases the local Nusselt number. Hybrid nanofluid provides a higher heat transfer rate than the nanofluids. Increasing the width of the obstacle cause to decline in the thickness of the right wall, this enhances the heat transfer in the clockwise direction. © 2020 Faculty of Engineering, Alexandria University

Fulltext

Alexandria Engineering Journal

Impact of heated obstacle position on magneto-hybrid nanofluid flow in a lid-driven porous cavity with Cattaneo-Christov heat flux pattern

In this work the perception of vector space is initiated over Pre A*-algebras. This article discusses the basic properties of Pre A*-vector spaces, the notion of norm and their worth while representations. © 2020 the author(s).

Mathematics

Chennai Campus

Journal of Mathematical and Computational Science

Analysis on properties of vector spaces over pre A*-algebras

Remote sensor systems experience basic investigation of network security because of inexplicable operational imperatives. The challenge flinches with the fragment of worms in the remote system. A solitary contaminated hub is adequate to spread the worms over the entire system. The tainted hub hastily contaminates the contiguous hubs in a relentless way. In this paper, a scientific model depending on pandemic hypothesis is proposed which is an enhancement of the SIRS, SEIS, SEIRS models. SEIQRV (susceptible-exposed-infectious-quaraintain-recovered-vaccinated) model enriched with the additive white noise conquers the hindrances of existing models. Using Routh-Hurwitz criteria, reproduction number, existence of steady states, and stability about endemic steady state are analyzed. The proposed system’s stability is substantiated varying for different values of communication radii and node densities. The additional constituent to the proposed model is the stochastic fluctuation implemented and the examination of the stochastic variations. This model incorporates a limited correspondence span and the related hub thickness. The assessment of the proposed model with other existing models are presented and analyzed based on different executions. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.