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

Mathematics mainly concern with sets and functions. Cantor set is identified by George Cantor. After the notion of vagueness raises set concepts extended to fuzzy sets by Zadeh and an alternate idea of vagueness is implemented by Pawlak in 1982 based on boundary regions. Solving any problem algebraically gives a perfect solution. In that sense, many algebraic concepts are implemented on the fuzzy sets, rough sets etc. Focusing that in mind, in this review artice, we give some study of algebraic approach on rough sets.&nbsp;

School of Advanced Sciences

Vellore Campus

Advances in Mathematics: Scientific Journal

A REVIEW OF ALGEBRAIC APPROACH ON ROUGH SETS

World University root node

Understanding Complex Systems

Fractal functions, dimensions and signal analysis

Purpose: The aim of the present paper is to investigate the homogeneous and heterogeneous reactions on Prandtl fluid flow at a stretching sheet with an induced magnetic field and slip boundary conditions. Design/methodology/approach: The governing equations include the continuity, induced magnetic field, momentum, energy and homogeneous–heterogeneous equations. Initially, with suitable similarity variables, the governing partial differential equations and converted into a system of ordinary differential equations. Then, the nonlinear ordinary differential equations are solved by a shooting technique with the help of the BVC5C Matlab package. Findings: The results of the present investigation are presented through graphs for different values of the various parameters. The authors observed that the large values of the stretching ratio and the induced magnetic parameters are moderate magnetic field, velocity and temperature primarily. Also, the authors found the more velocity and temperatures by boosting the slip parameters. Originality/value: In addition, the values of the skin friction and the rate of heat transfer for various values of physical parameters are tabulated and deliberated in detail. © 2020, Emerald Publishing Limited.

Multidiscipline Modeling in Materials and Structures

Influence of induced magnetic field and slip conditions on convective Prandtl fluid flow over a stretching surface with homogeneous and heterogeneous reactions

In the present work, we emphasize the impacts of an inclined magnetic field, viscous dissipation and radiation on the unsteady flow of a Williamson nanofluid over a vertical stretching porous surface with the presence of non-uniform heat source/sink and chemical reaction. In this study, we considered different kinds of nanoparticles such as silver, copper, aluminium oxide (Al 2O 3) , titanium oxide (TiO 2) , and magnesium oxide (MgO). The basic equations of this investigation are transmuted into a system of nonlinear and coupled ODEs using suitable similarity variables and elucidated numerically by R.-K. Fehlberg-based shooting technique. Influences of the pertinent parameters on the velocity, the temperature and the concentration distributions are deliberated with the assistance of graphs and tables. This study depicts that Al 2O 3 nanofluid has greater velocity since it has less dense nanoparticles compared to other nanoparticles. However, Cu-nanofluid has greater heat transfer due to greater thermal conductivity. Further, we identified that the thermal boundary layer thickness can be increased with the help of the viscous dissipation parameter. The inclination angle of the magnetic field strengthens the magnetic field on the fluid flow © 2021, The Author(s), under exclusive licence to EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.

European Physical Journal: Special Topics

Unsteady MHD flow of a Williamson nanofluid on a permeable stretching surface with radiation and chemical reaction effects

This paper investigates the three-dimensional magnetohydrodynamic (MHD) flow of an upper convected Maxwell (UCM) nanofluid with the thermal radiation, cross-diffusion and heat source effects along a stretching sheet. The effects of chemical reaction, thermophoresis and Brownian motion are also studied. We have applied suitable similarity variables and transformed the governing boundary layer equations into a system of non-linear ordinary differential equations. The present problem is solved numerically by R–K-based shooting technique. The variations of the velocity, temperature and concentration profiles are shown graphically and discussed in detail. The numerical results of skin friction coefficient, Nusselt and Sherwood numbers are presented in tabular form for different physical parameters. It is noticed that the Dufour and thermal radiation parameters decrease the temperature field and raise the concentration field. The rising values of Deborah number and magnetic field reduce the friction factors, Nusselt and Sherwood numbers. Heat source and chemical reaction parameters decline the Nusselt number and boost the Sherwood number. Also, noticed that the Dufour and Soret numbers enhance the Nusselt number but they decrease the Sherwood number. © 2021, The Author(s), under exclusive licence to EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.

Cross-diffusion and heat source effects on a three-dimensional MHD flow of Maxwell nanofluid over a stretching surface with chemical reaction

Purpose: This paper aims to study the attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips. Numerical investigations are performed for the phase and damped velocity profiles of the wave. For numerical computation purposes, water-saturated limestone and kerosene oil saturated sandstone for the first and second porous strips, respectively. Some other peculiarities have been observed and discussed. Design/methodology/approach: Dispersion and attenuation characteristic of the shear wave propagations have been studied in an inhomogeneous poro-anelastic strip of finite thickness, which is clamped between an inhomogeneous poroelastic strip of finite thickness and an elastic half-space. Both the strips are initially stressed and the half-space is self-weighted. Analytical methods are used to calculate the interior deformations of the model with the involvement of special functions. The determination of the frequency equation, which includes the Bessel’s and Whittaker functions, has been obtained using the prescribed boundary conditions. Findings: Impacts of attenuation coefficient, dissipation factor, inhomogeneities, initial stresses, Biot’s gravity, porosity and thickness ratio parameters on the velocity profile of the wave have been demonstrated through the graphical visuals. These parameters are playing an important role and working as a catalyst in affecting the propagation behaviour of the wave. Originality/value: Inclusion of the concept of doubly layered initially stressed inhomogeneous porous structure of elastic and anelastic medium bedded over a self-weighted half-space medium brings a novelty to the existing literature related to the study of shear wave. It may be helpful to geologists, seismologists and structural engineers in the development of theoretical and practical studies. © 2021, Emerald Publishing Limited.

Engineering Computations (Swansea, Wales)

Attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips

We concern this manuscript with Geraghty type contraction mappings via simulation functions and pull down some sufficient conditions for the existence and uniqueness of point of coincidence for several classes of mappings involving Geraghty functions in the setting of metric spaces. These findings touch up many of the existing results in the literature. Additionally, we elicit one of our main results by a non-trivial example and pose an interesting open problem for the enthusiastic readers. © Soc. Paran. de Mat.

Fulltext

Boletim da Sociedade Paranaense de Matematica

Simulation functions and geraghty type results

Nickel-catalyzed [4 + 2] annulation of benzylamines and nitriles via C-H/N-H bond activation, providing straightforward atom-economic access to a wide variety of multisubstituted quinazolines, is reported. Mechanistic investigation revealed that the in situ formed amidines from the coupling of benzylamines and nitriles direct the nickel catalyst to activate the ortho-C-H bond of the phenyl ring of the benzylamine.

Journal of Organic Chemistry

Nickel-Catalyzed [4 + 2] Annulation of Nitriles and Benzylamines by C-H/N-H Activation

Transport properties of non-Newtonian nanofluids and applications

Incorporating qualities and environmental concerns have received significant attention in the literature on production and inventory management for deteriorating items; however, scarce papers have emphasized these two concurrently. Therefore, it is required to incorporate these two aspects for deteriorating items to fill this gap in the literature and provide a better insight into practice. This paper elaborates a sustainable production inventory model for poor quality deteriorating items which (a) items deteriorate at a constant rate and the deterioration progress can be controlled by investing in preservation technology; (b) carbon is emitted due to production operations, and it can be controlled by investing in carbon reduction technology; (c) a fraction of manufacture items are imperfect, and the quality can be enhanced by investing in quality improvement. The paper aims to discuss the impact of preservation and carbon reduction technologies on the total profit to help decision-makers make more efficient replenishment and pricing decisions. An algorithm is proposed to determine optimal values for five decision variables. A numerical experiment is illustrated to validate the mathematical formulation, and the impact of parameters on total profit and managerial insights are discussed using sensitivity analysis. © 2021 Elsevier Ltd