Applied Mathematics

The elevation of the cytoplasmic calcium concentration is a central step in many intracellular signal transduction pathways. It is also observed in various systems that calcium signals can also mediate intracellular communication by eliciting and coordinating calcium signals in surrounding cells, for example, in the liver and the astrocytes network of the central nervous system. In view of above mathematical model of calcium signaling process in the presence of excess buffer has been developed for a one dimensional unsteady state case. This model incorporates important physical and physiological parameters like dissociation rate, diffusion rate, total buffer concentration and influx. The finite difference method has been employed to predict [Ca2+] and buffer concentration time course regardless of the calcium influx. The comparative study of the effect of the excess buffered diffusion and kinetic parameters of the model on the concentration time course have been performed.

A rough set, first described by Zdzis?aw I. Pawlak, is a formal approximation of a crisp set in terms of a pair of sets which give the lower and the upper approximation of the original set. Soft set theory is a generalization of fuzzy set theory, was proposed by Molodtsov to deal with uncertainties. In this paper, we present concepts of soft rough neutrosophic Sets and neutrosophic soft rough Sets, and investigate some of its properties. Furthermore, we develop a decision making approach to neutrosophic Soft Rough Sets and a numerical example is illustrated.

An analytical study is performed to investigate the effects of chemical reaction and radiation on unsteady MHD flow past an exponentially accelerated vertical plate with variable temperature and variable mass diffusion in the presence heat source or sink under the influence of applied transverse magnetic field. It is assumed that the effect of viscous dissipation is negligible in the energy equation and there is a first order chemical reaction between the diffusing species and the fluid. The flow is assumed to be in - direction which is taken along the infinite vertical plate in the upward direction and -axis is taken normal to the plate. At time >0, the both temperature and species concentration levels near the plate are raised linearly with time time t. A general exact solution of the governing partial differential equations is obtained by usual Laplace transform technique. The velocity, temperature and concentration fields are studied for different physical parameters like thermal Grashof number (Gr), mass Grashof number (Gm), Schmidt number (Sc), Prndtl number (Pr), radiation parameter (R), magnetic field parameter (M), accelerated parameter (a), heat source parameter (H), chemical reaction parameter (K) and time (t) are studied through graphs and tables.

In this paper, the magnetohydrodynamic oscillatory Stokes flow past a porous sphere has been discussed. A uniform magnetic field is applied transversely to the flow field. Flow outside the porous region is governed by unsteady Stokes equation and Darcy’s law is used in the porous region. Drag and torque are calculated using Faxen’s law. It is observed that the increase or decrease of the drag and torque depends on the effect of magnetic field with variable permeability. The effect of magnetic field on various flow quantities like drag and torque has been observed for uniform oscillatory flow, doublet in uniform flow and oscillating Stokeslet. Graphs are plotted for various measures and results are obtained using these graphs.

Effect of chemical reaction on free convection MHD flow through a porous medium bounded by vertical surface is studied here. The governing equations involved in the present analysis are solved by the two-term perturbation method. The velocity, temperature, concentration, skin friction and Nusselt number are studied for different parameters like thermal Grash of number, mass Grash of number, Schmidt number, magnetic field parameter, Permeability parameter, Prandtl number, Eckert number and chemical reaction parameter.

In this paper we will compute a new algorithm for new graph which its vertex is a graph.

This paper presents some important operational matrices of fourth kind Chebyshev wavelets. New formula of operational matrix of derivative for fourth kind Chebyshev polynomials is first obtained and then operational matrices of derivative and integration of the fourth Chebyshevwavelets basis are derived. The proposed results are of direct interest in many applications.

An analysis is presented to investigate the Dufour, soret and thermophoresis parameter effects on MHD Mixed convection, heat and mass transfer about an isothermal vertical flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation. The similarity solution is used to transform the problem under consideration into a boundary value problem of coupled ordinary differential equations, which are solved numerically by using the finite difference method. Numerical computations are carried out for the non-dimensional physical parameter. The results are analyzed for the effect of different physical parameters such as Dufour number, Soret number, thermophoretic, MHD, mixed convection, Eckert number, inertia parameter, buoyancy ratio, and Schmid number on the flow, heat, and mass transfer characteristics.

Dempster-Shafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. The significant innovation of this framework is that it allows for the allocation of a probability mass to sets or intervals. An important aspect of this theory is the combination of evidence obtained from multiple sources and the modeling of conflict between them. Plash Dutta and Tazid Ali [6,7] proposed methods to combine Fuzzy Focal elements and their corresponding Basic Probability Assignments of two variables. Using evidence theory here we make an investigation for interval focal elements by combining focal elements and their corresponding Basic Probability Assignments (BPA) under Modified Arithmetic operations rather than ordinary arithmetic operations with the help of a numerical example.

In Dr. Florentin Smarandache generalized several properties of the nedians. Here, we will continue the series of these results and will establish certain connections with the triangles which have the same coefficient of deformation.