Issue 1 Volume 6 (2018)

ISSUE 1− A ISSUE 1− B ISSUE 1− C ISSUE 1− D ISSUE 1− E ISSUE 1− Special Issue
Authors : K. Renuka Devi, Fuad. S. Al Sarari and S. Latha
Title : On Certain Janowski Symmetrical Functions with Negative Coefficients
Volume, Issue, Year : 6(1−E)(2018)
Pages : 847−852

Abstract: In this paper we study a class $\mathcal{{S}}^{(j,k)}(A,B)$ of analytic functions with negative coefficients defined by using notions of Janowski symmetrical functions. We derive necessary and sufficient conditions, extreme point results and integral means inequalities for functions belonging to this class.

Keywords: Janowski functions, Subordination, Extreme points, $(j,k)$-symmetric points.

Authors : Mukund V. Bapat
Title : Cordial Labeling of Double Antenna One Point Union Graphs
Volume, Issue, Year : 6(1−E)(2018)
Pages : 853−858

Abstract: We discuss graphs of type $G^{(k)}$ i.e. one point union of k-copies of G for cordial labeling. We take G as double tail graph of $C_{3}$. i.e. $G= tail(C_{3},2-P_{m})$. In $tail(C_{3},2-P_{m})$ graph double paths are attached at same point of $C_{3}$. We restrict our attention to $m = 2, 3, 4 $. Further we consider all possible structures of $G^{(k)}$ by changing the common point on G and obtain non-isomorphic structures. We show all these structures as cordial graphs. This is called as invariance of different structures under cordial labeling.

Keywords: Cordial, labeling, tail graph, invariance, path, one point union.

Authors : S. Thiruveni and A. Solairaju
Title : Neutrosophic Q-Fuzzy Subgroups
Volume, Issue, Year : 6(1−E)(2018)
Pages : 853−858

Abstract: In this paper, the notation of concept of neutrosopy in Q-fuzzy set is introduced. Further some properties and results on neutrosophic Q-fuzzy subgroups are discussed.

Keywords: Neutrosophic Q-fuzzy set, neutrosophic Q-fuzzy subgroup (NQLFG), neutrosophic Q-fuzzy normal subgroup.

Authors : R.Srivastava and Yamini Singh
Title : An Analysis of Interpolatory polynomials on finite interval
Volume, Issue, Year : 6(1−E)(2018)
Pages : 867−875

Abstract: The main object of this paper is to construct a interpolatory polynomial with hermite conditions at end points of interval [-1,1] based on the zeros of the polynomials $P_n^{(k)}(x)$ and $P_{n-1}^{(k+1)}(x)$ where $P_{n}^{(k)}(x)$ is the ultraspherical polynomial of degree n .In this paper, we prove existence ,explicit representation and order of convergence of the interpolatory polynomials.

Keywords: P\' al-type interpolation; Ultraspherical polynomial; Explicit form; Order of convergence

Authors : Vikash Goswami and R. K. Shrivastava
Title : Cloud Load Prediction for Multiuser Mixed Distribution Task Length and Task Arrival Scenario
Volume, Issue, Year : 6(1−E)(2018)
Pages : 877−887

Abstract: In the mathematics queuing theory is one of the fields which can be used for finding solutions of a wide range of practical problems. One of the recently growing application of this field is in computer network traffic management. In this paper we applied the queuing theory for the prediction of job request queue in a cloud network where the job requests are arriving through a single queue and are combination of jobs generated by a number of users with each having the different job request patterns (distribution function). The growing adaption of cloud systems, resulting in excessive loading of cloud servers. Since the cloud is designed to provide different resources as service over the internet. The cloud user requests required resources from the cloud and the cloud serves these requests by forming virtual machines and allotting it some the resources from cloud resource pool. The resources allotted to VMs depends upon the requirements of the task and guaranteed QoS of the cloud. Once the task is completed these VM’s can either be dissolved to utilize its resources for another VM or can be suspended for later utilization and saving power. The creation of a VM may take several seconds while activation of a suspended VM is also required some time, which may ultimately cause sluggish response and latency in cloud response. Such situations can be avoided by predicting the upcoming task requirements. The knowledge of upcoming tasks can be used to decide whether VM’s needs to keep alive, suspended or dissolved to efficiently utilize the resources, saving power and serve the requests with minimum latency. The prediction of task requirements is a difficult job especially when the task requests are generated by different users and each user may follow different distribution function. This paper presents the HMM-based prediction model for such conditions and evaluates its performance.

Keywords: P\Queue Prediction, Cloud Computing, HMM, Task Scheduling.

Authors : Lewis N. Nyaga
Title : Transitivity of the Direct Product of the Alternating Group Acting on the Cartesian Product of Three Sets
Volume, Issue, Year : 6(1−E)(2018)
Pages : 889−893

Abstract: The transitivity of the action of the direct product of the alternating Group on Cartesian product of three sets is investigated. In this paper, we show that the group action is transitive.

Keywords: P\Direct Product, Alternating Group, Cartesian product, Transitive group action.

Authors : Shibaji Halder
Title : A Sequence of Complete Cosmic Scenario from Inflation to Late Time Acceleration with Adiabatic Particle Creation
Volume, Issue, Year : 6(1−E)(2018)
Pages : 895−902

Abstract: In the background of a flat FRW model, we assume the non-equilibrium thermodynamical process to be isentropic so that the entropy per particle does not change and consequently the dissipative pressure can be expressed linearly in terms of the particle creation rate. This paper deal with the Friedman equations and by a sequence of proper choices of the particle creation rate as a function of the Hubble parameter, it is possible to show a continuous cosmic evolution from inflation to late time acceleration.

Keywords: Particle creation, dissipative pressure, entropy production, isentropic process, unified cosmic evolution.

Authors : S. Loghambal, A. J. Agvinos Catherine and S. Velu Subash
Title : Analysis of Langmuir-Hinshelwood Kinetics Model for Photocatalytic Degradation of Aqueous Direct Blue 71 Through Analytical Expression
Volume, Issue, Year : 6(1−E)(2018)
Pages : 903−913

Abstract: An analysis of the Langmuir-Hinshelwood expression is presented for the photocatalytic degradation of Aqueous Direct Blue 71. This analysis contains a nonlinear term that explains the kinetics of the heterogeneous catalytic processes. In this paper, we obtain approximate analytical solutions for the nonlinear equation by employing the Perturbation-Iteration Algorithms (PIA). The main objective is to propose an analytical method of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Furthermore, in this work decolorization efficiency (DE\%) and the numerical solution to the problem is also reported using MATLAB program. The analytical results are compared with the numerical and limiting case result. The obtained results are valid for the whole solution domain. A good agreement between the theoretical predictions and numerical results is observed. Langmuir-Hinshelwood model is analyzed with the help of analytical result for the different values of $H_{2}O_{2}$ and $SiO_{2}$-NP to describe photocatalytic degradation of the dye.

Keywords: Langmuir-Hinshelwood kinetics, First order catalytic kinetics, Perturbation-Iteration Algorithms, Photocatalysis, Degradation.

Authors : B. Sridevi and D. V. Ramy Reddy
Title : On Commutativity of Assosymmetric Rings With Some Identities
Volume, Issue, Year : 6(1−E)(2018)
Pages : 915−923

Abstract: In this paper we present some results on assosymmetric rings satisfying some identities. A non-associative ring is defined as a nilpotent if there exists $k \geq0$ such that any product having k elements is zero. A ring is solvable if the chain of sub rings $S \supseteq S^{2} \supseteq (S^{2})^{2} \supseteq \dots$ reaches zero in a finite number of steps. While solvable associative rings are obviously nilpotent, solvable alternative rings need not be nilpotent [1].

Keywords: Assosymmetric rings, Non-associative ring, Solvable associative rings, commutative ring.

Authors : Zahra Sarmast, Mohammad Reza Safi and Elham Farzaneh
Title : Post Optimality Analysis in Fuzzy Multi Objective Linear Programming
Volume, Issue, Year : 6(1−E)(2018)
Pages : 925−937

Abstract: Models of linear programming problems with fuzzy constraints are well known in the current literature. In this paper, the post optimality analysis (POA) of a given fuzzy efficient solution in a general fuzzy multi-objective linear programming (FMOLP) problem is considered. The POA determines the largest sensitivity region of changes in the input data the fuzzy efficient solution of FMOLP problem remains unchanged. For this reason, three cases are considered separately: changing in one objective function coefficient (the change in one of objective functions' coefficient), objective function removal and objective function addition. Each case is illustrated by a numerical example.

Keywords: Fuzzy multi objective linear programming, Fuzzy efficiency, Pareto optimality, Post optimality analysis.

Authors : S. C. Shiralashetti, L. M. Angadi and S. Kumbinarasaiah
Title : Laguerre Wavelet-Galerkin Method for the Numerical Solution of One Dimensional Partial Differential Equations
Volume, Issue, Year : 6(1−E)(2018)
Pages : 939−949

Abstract: In this paper, we proposed Laguerre wavelet-Galerkin method for the numerical solution of one dimensional partial differential equations. Here, we used Laguerre wavelets as a weight functions that are assumed basis elements which allow us to obtain the numerical solutions of the differential equations. The obtained numerical results are compared with the classical finite difference method and exact solution. Numerical test problems are considered to demonstrate the applicability and validity of the purposed technique.

Keywords: Galerkin method, Laguerre wavelet basis, differential equations, Finite difference method.

Authors : G. Thamizhendhi
Title : Types of Irregular Product Vague Line Graphs
Volume, Issue, Year : 6(1−E)(2018)
Pages : 951−960

Abstract: In this paper, neighborly irregular, highly irregular and totally irregular product vague line graphs are defined. Also, some properties of neighborly irregular and totally irregular product vague line graphs are given. Further, the applications of product vague line graph to model road network have been discussed with an example.

Keywords: Vague line graphs, Product vague line graph, Neighborly irregular, Totally irregular.

Authors : Nadeem Ansari, R. S. Chandel and Rizwana Jamal
Title : b-coloring of Central Graph of Triangular Snake
Volume, Issue, Year : 6(1−E)(2018)
Pages : 961−964

Abstract: A given k-coloring c of a graph $G=(V,E)$ is a b-coloring if for every color class $c_i$, $1 \leq i \leq k$, there is a vertex colored i whose neighborhood intersect every other color class $c_j$, $1 \leq i \leq k$, of c. The b-chromatic number of G is the greatest integer k such that G admits a b-coloring with k colors. In this paper, the authors find the b-chromatic number of central graph of the triangular snake.

Keywords: Graph coloring, b-coloring, central graph, triangular snake.

Authors : Nidhi Pandya and Mohammad Suleman Quraishi
Title : Effect of Chemical Reaction and Rotation on MHD Unsteady Flow Past an Inclined Oscillating Infinite Porous Plate Embedded in Porous Medium for Heat Generation/ Absorption with Mass Transfer and Variable Temperature
Volume, Issue, Year : 6(1−E)(2018)
Pages : 965−975

Abstract: In this paper we have studied Chemical reaction, rotation and oscillation effect on MHD unsteady flow over an inclined infinite porous plate embedded in porous media. The dimensionless governing equation of flow field is solved analytically by Laplace Transform technique for different values of governing flow parameters. The primary velocity profile along the plate and secondary velocity profile perpendicular direction to plate, concentration profile and temperature profile are shown through graphs for different values of flow parameters.

Keywords: MHD, porous medium, heat and mass transfer.

Authors : V. R. Kulli
Title : Edge Version of Multiplicative Atom Bend Connectivity Index of Certain Nanotubes and Nanotorus
Volume, Issue, Year : 6(1−E)(2018)
Pages : 977−982

Abstract: We define the edge version of multiplicative atom bond connectivity index of a molecular graph. In this paper, we compute this index for different chemically interesting nanotubes and nanotorus.

Keywords: Multiplicative atom bond connectivity index, nanotubes, nanotorus.

Authors : B. Sridevi and D. V. Ramy Reddy
Title : Commutative Results for Rings
Volume, Issue, Year : 6(1−E)(2018)
Pages : 983−987

Abstract: In this paper, we provided two commutativity theorems are : If R is a semi prime ring and there exist a fixed positive integer $m>1$ such that either (i) $[[a, b]^{m}-[a^{m}, b^{m}], a]=0$ or $[(a \circ b)^{m}-(a^{m} \circ b^{m}), a] = 0$, then R is commutative ring. (ii) For all a, b in R there exists a positive integer $m = m(a, b) >1$ such that $(a b)^{m}= b a$, then R is commutative ring.

Keywords: Commutativity ring, associative ring, Center.

Authors : D. D. Pawar and Y. S. Solanke
Title : Two-Fluid Dark Energy Cosmological Models In Saez-Ballester Theory of Gravitation
Volume, Issue, Year : 6(1−E)(2018)
Pages : 989−995

Abstract: The present paper deals with cylindrically symmetric metric in the form of Marder (1958) with Saez-Ballester theory of gravitation in the presence of perfect fluid and dark energy. In order to obtain the deterministic solution of the field equations we have assumed that the expansion scalar in the model is proportional to the Eigen value of the shear tensor. We have also assumed that the two sources, here the perfect fluid and dark energy interact minimally with separate conservative parts of their energy momentum tensors together with the constant EoS parameter of the perfect fluid. The role of the dark energy in the present model with variable equation of state parameter is studied more in detail. Some physical properties of model are also discussed.

Keywords: Cylindrically symmetric metric, perfect fluid and dark energy as the source, Saez-Ballester theory of gravitation.

Authors : C. Loganathan and M. Lalitha
Title : Solving Multi-Objective Mathematical Programming Problems in Fuzzy Approach
Volume, Issue, Year : 6(1−E)(2018)
Pages : 997−1004

Abstract: In this paper we compare the solution of multi objective nonlinear programming problem with this solution obtained in Zimmermann's method. Zimmermann used membership function to solve the multi objective nonlinear programming problems. We have used $\alpha $-cut to solve the multi objective nonlinear programming problems.

Keywords: Fuzzy nonlinear programming, Triangular fuzzy number, optimal solution, multi objective, $\alpha $-cut, Fuzzy number, Fuzzy set theory.

Authors : Sivagnanam Mutharasu and Duraisamy Kumar
Title : $E_k$-Super Vertex Magic Labeling of Graphs
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1005−1012

Abstract: Let $G$ be a graph with $p$ vertices and $q$ edges. An $E_k$-super vertex magic labeling ($E_k$-SVML) is a bijection $f: V(G) \cup E(G)\rightarrow \{ 1,2 , \ldots, p + q \}$ with the property that $f(E(G)) = \{ 1,2,\ldots, q \}$ and for each $v \in V(G)$, $f(v) + w_k(v) = M$ for some positive integer $M$. For an integer $k \geq 1$ and for $v \in V(G)$, let $w_k(v) = \sum\limits_{e \in E_k(v)}f(e)$, where $E_k (v)$ is the set of all edges which are at distance at most $k$ from $v$. The graph $G$ is said to be \textit{$E_k$-regular} with regularity $r$ if and only if $\left| E_k(e) \right| = r$ for some integer $r \geq 1$ and for all $e \in E(G)$. A graph that admits an $E_k$-SVML is called $E_k$-super vertex magic ($E_k$-SVM). This paper contain several properties of $E_k$-SVML in graphs. A necessary and sufficient condition for the existence of $E_k$-SVML in graphs has been obtained. Also, the magic constant for $E_k$-regular graphs has been obtained. Further, we establish $E_2$-SVML of some classes of graphs such as cycles, complement of cycles, prism graphs and a family of circulant graphs.

Keywords: $E_k$-super vertex magic labeling, $E_k$-regular graphs, circulant graphs.

Authors : G. Ayyappan and J. Udayageetha
Title : Analysis of Preemptive Priority Retrial Queueing System with Starting Failure, Modified Bernoulli Vacation with Vacation Interruption, Repair, Immediate Feedback and Impatient Customers
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1013−1023

Abstract: This paper considers $M^{[X_{1} ]} ,M^{[X_{2} ]} /G_{1} ,G_{2} /1$ general retrial queueing system with priority services. The server serves two types of customers and follows the pre-emptive priority rule subject to starting failure, repair, immediate feedback, orbital search and modified Bernoulli vacation with vacation interruption. High priority customes are considered as a feedback customer. After vacation completion, service completion and repair completion if there is no high priority customers present in the system the server may go for orbital search or remains idle. The high priority customer may renege the queue and the low priority customers may balk the orbit. Retrial time, service times, repair time and vacation time are assumed to be arbitrarily distributed. Various performance measures are derived and numerical results are presented. Using the supplementary variable technique, the steady-state distributions of the server state and the number of customers in the orbit are obtained. Further, some particular cases of interest are discussed. Finally, numerical illustrations are provided.

Keywords: Priority queueing systems, Starting failure, Modified Bernoulli vacation, Vacation interruption, Immediate feedback, Reneging, Balking.

Authors : J. Suresh Kumar
Title : Degrees and Degree Sequences of PAN Critical Graphs
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1025−1028

Abstract: A pseudo-complete coloring of a graph G is an assignment of col¬ors to the vertices of G such that for any two distinct colors, there exist adjacent vertices having those colors. The maximum number of colors used in a pseudo-complete coloring of G is called the pseudo-achromatic num¬ber of G and is denoted by $\psi_s (G)$. A graph G is called edge critical if $\psi_s (G-e)< \psi_s (G)$ for any edge e of G. A graph G is called vertex critical if $\psi_s (G-v)< \psi_s (G)$ for every vertex v of G. These graphs are generally called as pseudo-achromatic number critical graphs (shortly as PAN Critical graphs). In this paper, we investigate the properties of these critical graphs.

Keywords: Pseudo-complete coloring, Pseudo-achromatic number, k-edge critical graph, k-vertex critical graph.

Authors : N. Elumalai, B. Arthi and K. Ramaselvi
Title : K-Idempotent Centro Symmetric Matrices
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1029−1033

Abstract: The basic concepts and theorems of k-Idempotent Centro symmetric matrices are introduced with examples.

Keywords: Idempotent Matrix, Centro symmetric Matrix, k -Idempotent Centro symmetric Matrix.

Authors : M. Kaliraja and S. Rumenaka
Title : M-N Anti Fuzzy Normal Soft Groups
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1035−1042

Abstract: In this paper, we have discussed the concept of M-N anti fuzzy normal soft group, we then define the M-N anti level subsets of a normal fuzzy soft subgroup and its some elementary properties are also discussed.

Keywords: Fuzzy group, M-N anti fuzzy group, M-N anti fuzzy soft subgroup, M-N anti level subset, M-N anti fuzzy soft normalize.

Authors : S. Sampathu, S. Anita Shanthi and A. Praveen Prakash
Title : A Study on Q-Intuitionistic L-Fuzzy Submerging of a Semiring Under Homomorphism and Anti-Homomorphism
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1043−1050

Abstract: In this paper, we made an attempt to study the algebraic nature of Q-intuitionistic L-fuzzy subsemiring of a semiring under homomorphism and anti-homomorphism.

Keywords: Fuzzy subset, (Q, L)-fuzzy subset, (Q,L)-fuzzy subsemiring, Q-intuitionistic L-fuzzy subset, Q-intuitionistic L-fuzzy subsemiring, Q-intuitionistic L-fuzzy relation, Q-level subset Q-intuitionistic L-fuzzy subsets, Product of Q-intuitionistic L-fuzzy subsets.

Authors : T. Nicholas and T. Sheeba Helen
Title : Global Cototal Domination in Graphs
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1051−1055

Abstract: A set of vertices D in a graph G is a dominating set, if each vertex of G is dominated by some vertices of D. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set of G. A dominating set D of a graph G is a global dominating set if D is also a dominating set of $\bar{G}$. The global domination number $\gamma_g(G)$ is the minimum cardinality of a global dominating set of G. A dominating set D of a graph G is a cototal dominating set if the induced sub graph, $\langle V-D\rangle$ has no isolated vertices. The cototal domination number $\gamma_{cot}(G)$ is the minimum cardinality of a cototal dominating set of G. In this paper we introduce a new concept, the global cototal domination number $\gamma_{gcot}(G)$. A dominating set D of a graph G is a global cototal dominating set if D is both a global dominating set and a cototal dominating set. The global cototal domination number $\gamma_{gcot}(G)$ is the minimum cardinality of a global cototal domination set of G. We initiate the study of global cototal domination number and present bounds and some exact values of $\gamma_{gcot}(G)$ for some classes of graphs.

Keywords: Domination number, Global domination number, Total domination number, Cototal domination number, Global cototal domination number.

Authors : B. Stephen John and S. N. Leena Nelson
Title : Fixed Point Theorems in Quasi Semi linear 2-Normed Space
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1057−1061

Abstract: C. Park [9] introduced the term of a quasi 2-normed space. Also he proved some properties of quasi 2-norm and M. Kir and M. Acikgoz [7] elaborated the procedure for completing the quasi 2-normed space. In this paper, we introduced quasi semi linear 2-normed spaces and $\varphi'$-contraction mapping in these spaces are defined. It is investigated that under suitable conditions, $\varphi'$-contraction mapping have fixed points in quasi semi linear 2-normed spaces.

Keywords: Linear 2-normed space, quasi semi linear 2-normed space, $\varphi'$-contraction mapping, fixed points.

Authors : T. Srinivasarao
Title : K-Horizontal Symmetric Measurable Functions
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1063−1066

Abstract: A non negative measurable function \textit{f} on a measurable space has a \textit{K}-Horizontal Symmetric Measurable Function $f^{KS} $ non negative and measurable function such that $\int _{E}fd\mu =\int _{E}f^{KS} d\mu $ where \textit{E} is a measurable set.

Keywords: Measurable function, Non negative measurable function, \textit{K}-Horizontal Symmetric Measurable Function.

Authors : Mukund V. Bapat
Title : Snakes Related Families of Closed Neighbourhood Prime Graphs
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1067−1070

Abstract: In this paper we prove that double snake of $C_3$, double snake of $C_4$, snake of $K_{4}$ and snake of wheel $W_{4}$ are Closed Neighbourhood Prime Graphs.

Keywords: Closed neighborhood, prime, double snake, flag, labeling, snakes, double snake.

Authors : S. Benazier Fathima and S. Syed Ali Fathima
Title : On Soft $\# \pi g$-continuous Function in Soft Topological Spaces
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1071−1076

Abstract: This paper focuses on soft $\# \pi g$-continuous function in soft topological spaces and compare its relationship with other soft continuous function.

Keywords: Soft $\# \pi g$-closed set, soft $\# \pi g$-continuous function,soft $\# \pi g$-irresolute,soft generalized closed, soft topological spaces.

Authors : B. Shashidar Reddy
Title : Diffusion-Thermo Effects on Heat and Mass Transfer of Non-Newtonian Power Law Fluid past a Porous Flat Plate with Chemical Reaction
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1077−1083

Abstract: The diffusion-thermo effects on heat and mass transfer of a laminar boundary layer flow of a non-Newtonian power law fluid past a porous flat plate in the presence of magnetic field with chemical reaction effects have been considered. A suitable set of dimensionless variables is used and similar equations governing the flow are obtained. The resulting the non-linear ordinary differential equations are first linearised using Quasi-linearization technique and then an adequate implicit finite difference scheme is employed to obtain a numerical solution for the ordinary differential equations. The Representative results for the velocity, temperature and concentration profiles illustrating the influence of various governing parameters are presented and discussed. Temperature rises with increase in Dufour number and the effect of Chemical reaction parameter is to decrease the concentration of the fluid.

Keywords: Non-Newtonian fluid, power law index, Dufour number, Chemical reaction parameter, Finite Difference method.

Authors : Arslan Hojat Ansari, R. Krishnakumar, K. Dinesh and D. Dhamodharan
Title : Fixed Point of Cyclic Contraction Mappings in Banach Spaces Via $C$-Class Function
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1085−1092

Abstract: In this paper, we discuss some fixed point theorems for cyclic mapping with contractive and non-expansive condition and $\varphi-\psi-$ contractive mappings in Banach space and analogous to the results presented in the literature.

Keywords: Fixed Point, Contractive Mapping, Cyclic Contraction, Banach spaces, C-class function.

Authors : K. Divya Joseph and P. A. Dinesh
Title : Study of Forchheimer, Ohmic, Joule Effects and Variable Viscosity on Magnetohydrodynamic Viscous Flow Aacross the Slendering Stretching Surface
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1093−1105

Abstract: The boundary layer viscous flow across the slendering sheet has caught considerable attention due to its wide applications in microfluidics, duct design, nano-fluids and nano-devices and plastics molding, and many other fields. Noticing this we have examined the two –dimensional magnetohydrodynamic boundary layer viscous flow across the slendering sheet under the influence of Forchheimer, Ohmic, Joule’s effect and as well as the variable viscosity effect on the fluid flow. Similarity transformations are used to simplify the partial differential equations to ordinary differential equations which are further solved analytically using the generalized homotopy method. The computational results without these effects agree excellently with the previous results by [11].

Keywords: Boundary layer flow, Slendering stretching sheet, Heat transfer.

Authors : S. Savitha, A. Merceline Anita and S. Vijaya
Title : Reliability of Insulin administered to Diabetic Patients
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1107−1111

Abstract: This paper works a new approach to estimate the Reliability of Insulin administered to diabetic patients. The aim of this work is to maintain Normoglycemia of diabetic patients by determining the Reliability of the insulin injected daily to them. We proposed a Mathematical model for the Type 1 Diabetic Mellitus Patient. The model takes into account Glucose concentration and Insulin concentration. The solutions arrived by solving the differential equations arising in our model, represent the variation of glucose and insulin concentration in diabetic patients and hence from these solutions the Reliability of Insulin, Mean Time to Failure and Hazard Rate are found.

Keywords: Diabetic Mellitus, Normoglycemia, Juvenile diabetes, Hyperglycemia, Insulin.

Authors : A. Merceline Anita, J. Sangeetha and S. Kalaiarasi
Title : Reliability and Availability of Systems in Real Life
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1113−1119

Abstract: In this Paper, we focus our attention to deal with Systems involving Mixed Series and Parallel Configurations and the System Reliability of some Repairable Models involving Series and Parallel subunits existing in real life are studied with the aid of Markov method. We discuss two models in our study namely PP-model and PSP-model. Also we calculate the Availability of the System. We apply this technique to Railway Tracks involving Series and Parallel connections. We determine their Availability and the knowledge of which helps in the proper maintenance of the Tracks in the Railway Department.

Keywords: Reliability, Availability, Series Configuration, Parallel Configuration, Mixed Configurations and Markov Method.

Authors : Mukund V. Bapat
Title : Some More One Point Union Cordial Graphs Related to $C_{4}$ and Paths
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1121−1132

Abstract: In this paper we define tail graph and obtain one point union graphs $G^{(k)}$ on it and show them to be cordial. We take all structures on $G = tail(C_{4},P_{m})$, $m = 2,3,4,5$. We have split $P_{m}$ to obtain two tails (attached to same fixed point) keeping sum of edges fixed to $m-1$. We show that all these structures are cordial.

Keywords: Label, cordial, tail graph, antenna, one point union.

Authors : Ravikiran A. Mundewadi and Bhaskar A. Mundewadi
Title : Haar Wavelet Collocation Method for the Numerical Solution of Integral and Integro-Differential Equations
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1133−1149

Abstract: Haar wavelet collocation method is developed for the numerical solution of nonlinear Fredholm, Volterra, mixed Volterra-Fredholm integral and integro-differential equations. The method is tested on some of illustrative examples and made a comparison with the exact solution and existing methods. It shows that the proposed method yields better results than the others. Hence, the proposed scheme is a new alternative approach and efficient numerical method for the solution of nonlinear integral and integro-differential equations.

Keywords: Haar wavelet, Collocation method, Integral equations, Integro-differential equations.

Authors : V. Sangeetha
Title : Acyclic Distance Closed Domination Critical Graphs
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1151−1157

Abstract: In a graph $G = (V, E)$, a set $S\subset V(G)$ is said to be an acyclic distance closed dominating set if (i) $\langle S\rangle$ is distance closed and (ii) $\langle S\rangle$ is acyclic. The cardinality of the minimum acyclic distance closed dominating set is called an acyclic distance closed domination number and it is denoted by $\gamma_{adcl}(G)$. In this paper, we discuss the critical concept in acyclic distance closed domination which deals with those graphs that are critical in the sense that their acyclic distance closed domination number drops when any missing edge is added. Also, we analyze some structural properties of those acyclic distance closed domination critical graphs.

Keywords: Acyclic distance closed dominating set, acyclic distance closed domination critical graphs.

Authors : B. Vijayabasker Reddy and V. Srinivas
Title : Fixed Point Theorem For Pair of Weakly Compatible Mappings Using $CLR_T$ Property
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1159−1163

Abstract: The purpose of this paper is to prove a common fixed point theorem in a fuzzy metric space using the concept of weakly compatible mappings and $CLR_{T}$ property.

Keywords: Fixed point, weakly compatible mappings, $CLR_{T}$ property.

Authors : Y. Preethi Ceon
Title : Analyzing of Ebola Disease Using Rough Set Theory
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1165−1174

Abstract: The concept of rough set theory in data mining is discussed. Using data mining we diagonize Ebola disease. The pre n post processing stage has been discussed. The lower \& upper approximation of set are interior and closure operation is generated for Ebola. Analysis of the artibutes is given in a table.

Keywords: Data mining, closure, interior.

Authors : G. Balasubramanian and P. Vani
Title : Group Action on Fuzzy R-Subgroup of a Near-Ring
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1175−1180

Abstract: Meldrum [7] studied new rings and their algebraic links with groups. Osman Kazanci [8] discussed intuitionistic Q-fuzzy R-subgroup in a near-ring, and found few contributions on their union and intersection. Cho and Jun [2] discussed intuitionistic fuzzy right (left) R-subgroup in a near-ring, and analyzed the usual algebraic properties like as the union, intersection, complement and decomposition of intuitionistic fuzzy right (left) R-subgroup in a near-ring. In this paper, group action on a right (respectively left) R subgroup and same type of fuzzy right (respectively left) R-subgroup of a near-ring R are studied. Few characterizations are obtained.

Keywords: Set action on a fuzzy set; group action on fuzzy R-subgroup on a near-ring.

Authors : A. Solairaju and M. Shajahan
Title : Neutrosohic Fuzzy Magdm Environment Based on Normal Distribution
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1181−1187

Abstract: The attribute weights calculated from completely unknown information using the normal distribution. The neutrosophic fuzzy ordered weighted averaging operator is utilized to aggregate all individual neutrosophic fuzzy decision matrices provided by the decision-makers into the collective neutrosophic fuzzy decision matrix, and then we use the obtained attribute weights from Poisson distribution and the neutrosophic fuzzy hybrid averaging operator to fuse the neutrosophic fuzzy information in the collective neutrosophic fuzzy decision matrix to get the overall neutrosophic fuzzy values of alternatives, and then rank the alternatives, and select the most desirable alternative.

Keywords: Ordered weighted averaging, Hybrid averaging operator, normal based weights.

Authors : Satyaprakash Sahu and A. J. Khan
Title : Use of Repetition on n Person Dice Game (Ludo Gambling) Under Game Theory
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1189−1192

Abstract: Here we study about how to increase winning probability of n person dice game (Ludo) by using repetition. This paper shows that by using of repetition we can see a player can increase his winning probability.

Keywords: Game, Game theory, Player, n person game.

Authors : Suhas S. Patil and U. P. Dolhare
Title : Applications of Random Fixed Point Theorem to Integral Equation
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1193−1198

Abstract: In this paper random fixed point theorem has been applied seeking to prove the existence and uniqueness of volterra type integral equation and we show how the proper conditions guarantee the uniqueness of the solution of volterra type integral equation in complete metric space.

Keywords: Random fixed point, Contraction Mapping, Volterra Integral Equations.

Authors : K. Rajeshwar Reddy and M. Chenna Krishna Reddy
Title : Transient MHD Free Convective Fluid Flow Past a Moving Accelerated Vertical Porous Plate in the Presence of Viscous Dissipation
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1199−1213

Abstract: A numerical study is presented on the effect Transient MHD free convective fluid flow past a moving accelerated vertical porous plate in the presence of viscous dissipation has been studied. The dimensionless governing coupled non-linear boundary layer partial differential equations are solved by an efficient finite element method. The variations of the fluid velocity, temperature and concentration fields with the help of different flow parameters are presented graphically. And also,the effects these flow parameters on Skin-friction, Rate of heat and mass transfer are discussed through tabular forms. This model finds applications in geophysics, astrophysics and also in the design of high temperature industrial processing systems.

Keywords: Transient, MHD, Free convection, Viscous dissipation and FEM.

Authors : Rohan Sharma
Title : Analysis of the Pattern Leading to Final Descent in a Hailstone Sequence
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1215−1218

Abstract: This paper analyses and presents the pattern in hailstone sequence for any positive integer that makes it possible to predict a particular number in the sequence, from where after multiple descents and ascents the sequence will start to finally descent to the endless cycle 4, 2, 1.

Keywords: Hailstone Sequence, Collatz Conjecture.

Authors : Krishna B. Chavaraddi and Md. Hanif PAGE
Title : Solution of Blasius Equation by Adomian Decomposition Method and Differential Transform Method
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1219−1226

Abstract: The efficient semi-numerical schemes combining the features of Adomian polynomials (ADM) and Differential Transform method have been presented to solve the well-known non-linear Blasius equation. A numerical method for solving two forms of Blasius equation is proposed. The Blasius equation is a third order nonlinear ordinary differential equation, which arises in the problem of the two-dimensional laminar viscous flow over a half-infinite domain. The approaches are based on differential transform method and Adomian Decomposition method. In these schemes, the solution takes the form of a convergent series with easily computable components. The obtained series solution is combined to handle the boundary condition at infinity for only one of these forms. The numerical results demonstrate the validity and applicability of the methods and a comparison is made with both the methods.

Keywords: Differential transform method, Adomain Decomposition method, Blasius equation.

Authors : R. U. Ndubuisi, U. I. Asibong-Ibe and I. U. UdoAkpan
Title : A Class of *-Simple Type A I-Semigroups
Volume, Issue, Year : 6(1−E)(2018)
Pages : 1227−1234

Abstract: *-simple type A I-semigroups as the generalized Bruck-Reilly *-extensions is studied and properties obtained. It is proved that a semigroup $S$ is a *-simple type A I-semigroup if and only if it can be expressed as $S=GBR^*(T,\theta)$ where $T$ is a finite chain of cancellative monoids. Thus the structure of *-simple type A I-semigroups is described and the results obtained is amplified in the light of studies on simple I-regular semigroups by Warne and that of *-simple type A $\omega$-semigroups by Asibong-Ibe.

Keywords: Type A I-semigroups, cancellative monoids, generalized Bruck-Reilly *-extensions.