# Recent Trends And Advances In Mathematics And Its Applications'15

"SPMVV 2015 Conference Papers "

Effects of Additives in Finite Journal Bearing Using Finite Difference Method[ ]

In this paper general bearing considered and the effect of additives in lubrication of journal bearing. The generalized Reynolds equation for two layer fluid is derived in and is applied finite journal bearing. The finite modified Reynolds type equation is obtained for solved numerically by using FDM technique with a grid space of ?=90and =0.05. The effect of two layer increases the pressure and increases load.

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Generalized *-derivations in Prime*-rings[ ]

In this paper it is proved that a prime*-ring R admits a generalized reverse*-derivation F associated with non-zero*-derivation d, then either [d(x),z] = 0 or F is reverse*-centralizer. Next it is aimed to prove that a Prime*-Ring R admits a generalized*-left derivation F with associated *-left derivation d then either R is commutative or F is Right *-multiplier.

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SOLUTION OF ONE-DIMENSIONAL WAVE EQUATION THROUGH THE NUMERICAL METHODS[ ]

In the present work, we find the solution of one-dimensional wave equation with certain initial and boundary conditions using the numerical methods. The solution is obtained as a polynomial in terms of a dependent variable and time variable.

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An Additive Structure of Viterbi Semirings[ ]

In this paper, we study on additive and multiplicative properties of viterbi semirings. The modern interest in semirings arises primarily from fields of Applied Mathematics such as Optimization theory, the theory of discrete-event dynamical systems, automata theory and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics and the questions being asked is, for the most part, motivated by applications. This paper deals with some definitions, which are needed for the study of main results of this paper. We also discuss the additive properties of viterbi semirings. Here, we established that let (S, +, •) be a viterbi semiring, then S satisfies the condition a2 = a + a2, for all `a’ in S, if and only if (S, •) is a band.

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EFFECT OF CHEMICAL REACTION AND THERMO – DIFFUSION ON CONVECTIVE HEAT AND MASS TRANSFER FLOW OF A JEFFREY FLUID IN A CONCENTRIC CYLINDRICAL ANNULUS WITH NON – LINEAR DENSITY TEMPERATURE RELATION[ ]

The effect of non linear density temperature variation on mixed convective heat and mass transfer flow of a Jeffrey’s fluid through a porous medium in a circular annulus region between the concentric porous cylinder r = a and r = b in the presence of heat sources have been investigated. The equations governing the flow heat and mass transfer have been solved by employing Gauss-Seidel iteration procedure. The effect of various governing parameters on the flow characteristics have been discussed graphically. The rate of heat and mass transfer are evaluated numerically for different variations.

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Bondage Numbers of Interval Graphs[ ]

Interval graphs have drawn the attention of many researchers for over 30 years. They are extensively studied and revealed their practical relevance for modelling problems arising in the real world. In this paper we study various bondage numbers of an interval graph such as cobondage number, efficient bondage number, nonbondage number and find some bounds for these parameters.

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Total Zero-Divisor Graphs of Idealizations with Respect to Prime Modules[ ]

Let R be a commutative ring with identity and let M be a prime R-module. let R(+)M be the idealization of ring R by the R-module M. we study the diameter and girth of the Total zero divisor graph of the ring R(+)M. In this paper we discuss the Total zero divisor graphs of idealization with respect to the prime modules. In this, we consider R be a commutative ring and let M be a P-prime R- module and P = (0:M) then we prove that (i) if P?0 then (a,m) ? Z(R(+)M) if and only if a ? P?Z(R) (ii) if P = 0 then (a,m) ? Z(R(+)M) if and only if a = 0 and m ? M*. Using this result we prove that let Z(?(R) ? f, Z(R) is an ideal of R then Z(?(R(+)M)) is complete if and only if Z(R) ?(0:M). and also we prove that (i) if P = 0 then Z(?(R(+)M)) is complete, (ii) if P?0 and Z(R) is not an ideal of R then diam(Z(?(R(+)M))) = 2. Also we show that if ?P?=0 then diam(Z(?(R(+)M))) = 1,if ?P??0 then diam(Z(?(R(+)M))) = 2.

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Influence of non-uniform heat source/sink on MHD nanofluid flow over a moving vertical plate in porous medium[ ]

We investigated the influence of magneticfield, radiation and non-uniform heat source/sink on nanofluid flow over a moving vertical plate in porous medium.We considered two types of nanofluids namely Cu-Ethylene glycol, Ag-Ethylene glycol. The governing partial differential equations of the flow are transformed to ordinary differential equations using similarity transformations and then solved numerically by using shooting technique. The effects of various non-dimensional governing parameters on velocity, temperature and concentration profiles are discussed and presented through graphs. Also, the skin friction, local Nusselt and Sherwood numbers are discussed and given for tabular form for two nanofluids separately.

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Stagnation-point flow and heat transfer of a nanofluid towards stretching/shrinking cylinders[ ]

In this study we analyzed the stagnation point flow and heat transfer behavior of Ag-water nanofluid towards horizontal and exponentially permeable stretching/shrinking cylinders in presence of suction/injection. The governing boundary layer equations are transformed to nonlinear ordinary differential equations by using similarity transformation which are then solved numerically using bvp4c technique with Matlab package. The influence of non-dimensional governing parameters on the flow field and heat transfer characteristics are discussed and presented through graphs and tables.

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MHD nanofluid flow over an exponentially stretching surface with suction/injection[ ]

Present study deals with the heat and mass transfer in MHD nanofluid flow over an exponentially stretching surface in presence of internal heat generation/absorption, chemical reaction, radiation and suction/injection effects. The governing partial differential equations of the flow are converted into nonlinear coupled ordinary differential equations by using similarity transformation. Shooting technique is employed to yield the numerical solutions for the model. The effect of non-dimensional parameters on velocity, temperature and concentration profiles are discussed and presented through graphs.

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VISCOUS DISSIPATION EFFECTS ON MHD FLOW PAST A PARABOLIC STARTED VERTI-CAL PLATE WITH VARIABLE TEMPERATURE AND MASS DIFFUSSION[ ]

Viscous dissipation effects on the unsteady mhd free convective flow past a parabolic starting motion of the infinite vertical plate with variable temperature and variable mass diffusion is investigated. The plate temperature and the concentration level near the plate are raised linearly with time. The dimensionless governing unsteady, non-linear, coupled partial equations are solved by using the unconditionally stable explicit finite difference method of DuFort – Frankel’s type. The effect of velocity profiles are studied for different physical parameters like Eckert number, Prandtl number, thermal Grashof number, mass Grashof number, Schmidt number, magnetic parameter and time. It is observed that the velocity increases as the value of the thermal Grashof number or mass Grashof number increase. The trend is just reversed with respect to the Schmidt number.

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HEAT AND MASS TRANSFER ON MHD FLOW OF A VISCOUS FLUID THROUGH POROUS MEDIUM WITH THE EFFECT OF RADIATION AND CHEMICAL REACTION[ ]

The effect of chemical reaction and radiation on heat and mass transfer in the MHD flow of a viscous fluid through porous medium in the presence of transverse magnetic field is investigated. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by applying Runge Kutta fourth order method along with shooting technique. The velocity, temperature and concentration distributions are discussed numerically through graphs for different parameters. It has been observed that with increase of chemical reaction and radiation parameters the concentration and temperature increases respectively. The results for local skin friction, Nusselt number and Sherwood number are tabulated and discussed.

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Stagnation-point flow of a micropolar fluid over a nonlinearly stretching surface with suction[ ]

In this study we analyzed the stagnation-point flow of a micropolar fluid towards a nonlinearly stretching surface with suction/injection effects. The governing equations of the flow and heat transfer are transformed in to system of nonlinear ordinary differential equations by using similarity transformation and then solved numerically using bvp4c technique with Matlab Package. The influence of non-dimensional governing parameters like viscous dissipation parameter, suction/injection parameter, buoyancy parameter ,and material parameter on velocity and temperature profiles along with friction factor and heat transfer rate was discussed and presented through graphs and tables.

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HOMOMORPHISM AND ANTI-HOMOMORPHISM OF REVERSE DERIVATIONS ON PRIME RINGS[ ]

In this paper we show that if a reverse derivation acts as a homomorphism or an anti-homomorphism on a non-zero right ideal of a prime ring , then .

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Role of Computer Technology in Developing Positive Attitude towards Mathematics[ ]

Mathematics is considered to be very important in each and every country in the world. It is a subject which has extensive application in our day to day life situations. It has been explained as the tool to define, measure and special relations for the elements to improve quality of existed and advancements of science and technology. Attitude plays a pivotal role in achievement and performance in Mathematics. This paper resembles the impact of attitude towards mathematics that which may provide an answer to the questionnaire of application, usage, how prolong, complexity and so on as one will work. To avoid the compactness and confusion in Mathematics, computers are the excellent sources of new learning. The present paper enlightens the development of positive attitude towards mathematics in school children by using new trends i.e., computer technology and its application. Computers can be mainly used in educational curriculum which notifies many purposes to analyze students’ capabilities, solve complexity of problems and Simulates feeling of success.

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Radiation And Chemical Reaction Effects Of Mass Transfer And Hall Current On Unsteady MHD Flow Of A Viscoelastic Fluid In A Porous Medium with Heat Generation[ ]

This study investigated the radiation and chemical reaction effects of mass transfer and Hall current on unsteady MHD flow of a viscoelastic fluid in a porous medium with heat generation. The resultant equations have been solved analytically. The velocity, temperature and concentration distributions are derived, and their profiles for various physical parameters are shown through graphs. The coefficient of Skin friction, Nusselt number and Sherwood number at the plate are derived and their numerical values for various physical parameters are presented through graphs. The influence of various parameters such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, viscoelasticity parameter, the frequency of oscillation on the flow field and heat generation are discussed qualitatively.

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Commutators in the Middle Nucleus[ ]

In this paper, we assume that R is an antiflexible ring with commutators in the middle nucleus. First we prove that, let B =? (N, N) + (N, N) R, B is an ideal of R such that BA = 0 where A is an associator ideal of R. If R is prime then R is associative or (N, N) = 0. Using these results, we prove that, (i) a semiprime antiflexible ring is commutative, (ii) a prime antiflexible ring is either associative or commutative and finally (iii) a semiprime antiflexible ring is isomorphic to a direct sum of a semi prime associative ring and a semiprime commutative ring.

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Generalized derivations of Rings in the center[ ]

Ashraf, Rehman, Bell, Martindale and Daif have obtained commutativity of prime and semiprime rings with derivations satisfying cer-tain polynomial constants. Ashraf and Nadeem established that a prime ring R with nonzero ideal A must be commutative if it admits a derivation d satisfying either of the properties d(xy) + xy?U ord(xy) – xy?U for all x, y ?R. Hvala initiated the algebraic study of generalized derivation and extended some results concerning derivation to generalized derivation. In 2007 Ashraf, Asma Ali and Shakir Ali studied commutativity of a prime associative ring in which the generalized derivation F satisfies certain properties. In this paper we prove the commutativity of a prime nonassociative ring R satisfying any one of the following properties :

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Effects of Soret, Dufour, Hall currents and thermal radiation on a steady mixed convective heat and mass transfer over a stretching sheet in a rotating fluid[ ]

The non – linear boundary layer flow of a viscous incompressible electrically conducting fluid over a linearly stretching sheet in a rotating fluid in the presence of Hall currents, thermal radiation, heat source/ sink with Soret and Dufour effects. The partial differential equations governing the flow are numerically solved using fourth order Runge – Kutta method together with shooting technique. The Coriolis force reduces both the primary and secondary velocities while it enhances the temperature distribution. The magnetic field reduces (increases) the primary velocity (secondary velocity) and enhances the temperature where as the Hall parameter produces an opposite effect. The heat source, thermal radiation and Dufour effect favor heat transfer. In the range of Df = 1 - 3, the skin friction coefficient increases with increasing Soret number while an opposite trend when Df = 4 is noticed. The Dufour number decreases the Sherwood number in the range 0.1 – 0.85 of Soret number while a reverse trend is observed for Sr > 0.85.

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Efficient Dominating sets of lexicographic product graph of Euler totient cayley graphs with Arithmetic graphs[ ]

Graph Theory has been realized as one of the most useful branches of Mathematics of recent origin with wide applications to combinatorial problems and to classical algebraic problems. Graph theory has applications in diverse areas such as social sciences, linguistics, physical sciences, communication engineering etc.

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Matching Dominating Sets of Strong Product Graph of Euler Totient Cayley Graphs with Arithmetic Graphs[ ]

Theory of domination in graphs introduced by Ore and Berge is an emerging area of research in graph theory today. It has been studied extensively and finds applications to various branches of Science & Technology. Products are often viewed as a convenient language with which one can describe structures, but they are increasingly being applied in more substantial ways. Every branch of mathematics employs some notion of product that enables the combination or decomposition of its elemental structures.

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SEMI PRIME DERIVATION ALTERNATOR RINGS[ ]

In [4] Rich showed that a prime ring with idempotent e ?1 and if every idempotent lies in their nuclei, then R is alternative. In this section we prove that a semiprime derivation alternator ring with idempotent e?1 and characteristic ? 2, then idempotent is in flexible nucleus. At the end of this section we give some examples.

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Dominating Sets Of Divisor Cayley Graphs[ ]

Let n ?? 1 be an integer and S be the set of divisors of n .Then the set S*= {s, n- s / s?? S, n ? s} is a symmetric subset of the group (Zn, ), the additive abelian group of integers modulo n. The Cayley graph of (Zn, ), associated with the above symmetric subset S* is called the Divisor Cayley graph and it is denoted by G(Zn , D) .That is, G(Zn , D) is the graph whose vertex set is V={0,1,2,…,n-1} and the edge set is E = {(x , y) / x-y or y-x is in S*}. Let G (V,E) be a graph. A subset D of V is said to be a dominating set of G if every vertex in V \ D is adjacent to a vertex in D. A dominating set with minimum cardinality is called a minimum dominating set and its cardinality is called the domination number of G and is denoted by ? (G) .

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Total Dominating Sets Of Divisor Cayley Graphs[ ]

Let n ?? 1 be an integer and S be the set of divisors of n .Then the set S*= {s, n- s / s ? S, n ? s} is a symmetric subset of the group (Zn, ), the additive abelian group of integers modulo n. The Cayley graph of (Zn, ), associated with the above symmetric subset S* is called the Divisor Cayley graph and it is denoted by G(Zn , D) .That is, G(Zn , D) is the graph whose vertex set is V={0,1,2,…,n-1} and the edge set is E = {(x , y) / x-y or y-x is in S*}. Let G be a graph without isolated vertices. Then a total dominating set T is a subset of V(G) such that every vertex in V is adjacent to some vertex in T. A total dominating set with minimum cardinality is called a minimum total dominating set and the cardinality of a minimum total dominating set is called the total domination number of G and is denoted by ?t (G).

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A two-phase model of blood flow in a stenosed artery under the influence of external magnetic field[ ]

A two-phase macroscopic model of blood in a stenosed catheterized artery under the influence of external transverse magnetic field is studied. The governing partial differential equations of the physical problem are solved analytically. The important blood flow characteristics in arteries namely resistive impedance and wall shear stress are discussed for various governing parameters like Hematocrit C, Hartmann number M and catheter size K involved in the model. It is observed that the resistive impedance and shear stress increases with increase in the stenosis height and decreases drastically with increase in the magnetic field parameter. The results are found in good agreement with the physiological conditions.

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Soret and Dufour Effects on MHD Free Convective Flow over a Permeable Stretching Surface with Chemical Reaction and Heat Source[ ]

In this chapter we consider a convective flow in a porous medium of an incompressible viscous fluid over a permeable stretching surface with chemical reaction and heat source. Using a similarity transformation the governing equations of the problem are reduced to first order linear differential equations. The governing equations are solved numerically by using shooting technique. The nonlinear differential equations for various values of the physical parameters are shown graphically.

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Radial Vibrations Due to a Spherical Cavity in an Unbounded Micro-Isotropic, Micro-Elastic Solid in the Presence of Time Dependent Force and Couple[ ]

In the study of radial vibrations, the frequency equations are derived due to a spherical cavity contained in an unbounded micro-isotropic, micro-elastic medium subject to time dependent force and couple. It is observed that two additional frequencies are found which are not encountered in classical theory of elasticity and micro- strains are dependent on a time dependent stress moment.

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Effect of Thermal Radiation and Hall Effect on Mixed Convective Heat and Mass Transfer Flow of a Viscous Electrically Conducting Fluid in Vertical Wavy Channel [ ]

In this paper, we investigate the convective heat and mass transfer flow of a viscous electrically conducting fluid in a vertical wavy channel under the influence of an inclined magnetic field with walls maintained at constant temperature and concentration. The governing equations of the flow heat and mass transfer are solved using perturbation technique with the slope ‘?’ of the wavy wall. The graphs are drawn for the velocity, temperature and concentration. The rate of heat and mass transfer are calculated and analyzed for different variations of the governing parameters.

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Effects of Velocity Slip and Viscosity Variation in Slider Bearings with Two Layer Lubricant[ ]

A theoretical study of slider bearing considering viscosity variation across the film and slip of the bearing surface with thermal effect is presented. A generalized Reynolds equation for the lubrication of two layers is derived. It is applied to study these effects in slider bearing by taking the fluid film into three zones. Expressions for pressure, load capacity and force of friction are studied by evaluating them numerically for various parameters.

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STRUCTURES SOME SPECIAL CLASSES OF SEMIRINGS[ ]

In this paper we studied that semirings with non-empty zeroed and also semirings satisfying the condition ab = a+b + ab for all a, b in S. Every divided semiring is semi-invertable. The theory of rings and the theory of semigroups have considerable impact on the developments of the theory of semirings.

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Some Characterizations Of Ternary Semigroups[ ]

F.M. Sison gave the idea of regular ternary semigroups. Recently, M. L. Santiago and S. Bala developed the theory of ternary semigroups. In this paper we proved some properties of ternary semigroups and mainly we proved that “A lateral zero ternary semigroup is regular if and only if is an idempotent ternary semigroup” and “A quasi commutative ternary semigroup is a commutative ternary semigroup if all elements of are idempotent”

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CONVEXITY OF MINIMAL DOMINATING AND TOTAL DOMINATING FUNCTIONS OF CORONA PRODUCT GRAPH OF A PATH WITH A STAR[ ]

Domination in graphs’ has been studied extensively and at present it is an emerging area of research in graph theory. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et al. [1,2]. Product of graphs occurs naturally in discrete mathematics as tools in combinatorial constructions. They give rise to an important classes of graphs and deep structural problems. In this paper we study the dominating and total dominating functions of corona product graph of a cycle with a complete graph.

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Minus Dominating and Total Minus Dominating Functions of Corona Product Graph of a Path with a Star[ ]

Graph theory is one of the most flourishing branches of modern mathematics and computer applications. Domination in graphs has been studied extensively in recent years and it is an important branch of graph theory. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et al. [ 6,7]. Recently dominating functions in domination theory have received much attention. In this paper we present some results on minimal minus dominating and total minus dominating functions of corona product graph of path with a star.

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Effects of Chemical Reaction on Mixed Convective Rivlin–Ericksen MHD Flow with Variable Temperature, Concentration and Suction[ ]

This paper is focuses on the effect of chemical reaction on a two dimensional, laminar, mixed convective heat and mass transfer flow of a viscous, incompressible, electrically conducting and radiating Rivlin-Ericksen fluid along a semi-infinite vertical permeable moving plate in the presence of a transverse applied magnetic field. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time dependent suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two- term harmonic and non- harmonic functions. To observe physical insight and interesting aspects of the problem, the velocity, temperature, and concentration field are numerically studied and displayed graphically for pertinent parameters.

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Implementation of an efficient e-voting system based on Involutory elements of an algebraic structures equipped with biometrics[ ]

Democratic Countries highly depends on e-voting system for electing their interesting person among all the election context group. system are reduce the cost, manpower and risk for conducting the election e-voting process along with the fast counting process options. Even thou this system mainly have the following failures: no authentication, correctness of e-voting systems are needed 100% on trusted part, the authenticated person can able to caste more than one vote if the trusted party allow him and especially, button press e-voting system have no authentication ,so there is more chance to cast votes without authorization if the trusted party allow him. Based on the above fact , this paper mainly implement the model to eliminate the above failures of the e-voting systems especially in Indian EVMs by using involuntary loop algebraic structures along with biometrics.

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FINITE ELEMEMT ANALYSIS OF NON-DARCY MIXED CONVECTIVE HEAT AND MASS TRANSFER IN A CIRCULAR ANNULUS WITH RADIATION ABSORPTION[ ]

In this chapter we discuss the free and forced convection flow through a porous medium in a co-axial cylindrical duct where the boundaries are maintained at constant temperature and concentration. The Brinkman Forchhimer extended Darcy equations which take into account the boundary and inertia effects are used in the governing linear momentum equations. The effect of density variation is confined to the buoyancy term under Boussinesq approximation.

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Legendre Wavelet Based Approximation Method To Steady State Reaction-Diffusion Model Arising In Mathematical Chemistry[ ]

The mathematical model of steady state mono-layer potentiometric biosensor is studied and the model is based on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents a numerical method based on Legendre wavelets operational matrix method. These results are compared with available limiting case results and that are found to be in good agreement. Moreover, the use of Legendre wavelet operational matrix is found to be simple, efficient, accurate and computationally attractive.

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SOME DOMINATING SETS OF LEXICOGRAPHIC PRODUCT GRAPHS OF EULER TOTIENT CAYLEY GRAPHS WITH ARITHMETIC GRAPHS[ ]

The theory of domination in graphs is an emerging area of research in graph theory today. It has been studied extensively and finds applications to various branches of Science & Technology.Products are often viewed as a convenient language with which one can describe structures, but they are increasingly being applied in more substantial ways. In this paper, we consider lexicographic product graph of Euler totient Cayley graphs with Arithmetic graphs and present some results on domination parameters of these graphs.

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Radiation and Chemical Reaction Effects on MHD Free Convection Flow of a Uniformly Vertical Porous Plate with Heat Source[ ]

In this paper deals with the combined effect of thermal radiation and heat source on the MHD free convection heat and mass transfer flow of a viscous incompressible fluid past a uniformly vertical porous plate. The velocity, temperature and concentration field are obtained and discussed graphically for various values of the physical parameters present. In addition, expressions for the skin friction is also derived and finally discussed with the help of table and graphs.

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Effect Of Magnetic Field On the Dispersion Of a Solute in Fluid Flow Through a Conduit With Interphase Mass Transfer[ ]

The combined effect of magnetic field and irreversible boundary reaction on dispersion in Newtonian fluid through a conduit (pipe/channel) is studied by using generalized dispersion model. The study explains the development of dispersive transport following the injection of a tracer in terms of three effective transport coefficients namely exchange, convective and dispersion coefficients. The absorption coefficient is seen to be independent of magnetic field. The convection coefficient is influenced by the magnetic field.

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