Volume 5 (2017) Article in Press

Authors : B. K. Pedge and D. S. Palimkar
Title : Three Point Boundary Value Problem for Random Differential Inclusions
Volume, Issue, Year : 5(4−F)(2017)
Pages : 809−813

Abstract: In this paper, we prove the existence of solution on a compact interval to a-three-point boundary value problem for a class of second order random differential inclusions. We shall employees random fixed point theorem for condensing maps due to Martelli.

Keywords: Three point boundary value problems, random differential inclusion, random fixed point.

Authors : S. S. Hambarde and D. S. Palimkar
Title : Existence of Solution for Functional Random Differential Equation
Volume, Issue, Year : 5(4−F)(2017)
Pages : 815−820

Abstract: In this paper, we discuss the existence of solution for functional random differential equation under caratheodory, compactness and monotonic conditions. Here, we shall employees random fixed point theorem of Dhage.

Keywords: Random functional differential equation, random fixed point theorem, caratheodory condition.

Authors : R.Uma, P.Murugadas and S.Sriram
Title : The Determinant and Adjoint of Fuzzy Neutrosophic Soft Matrices
Volume, Issue, Year : 5(4−F)(2017)
Pages : 821−833

Abstract: In this paper, we have introduced the determinant and adjoint of a square Fuzzy Neutrosophic Soft Matrices (FNSMs). Also we define the circular FNSM and study some relations on square FNSM such as reflexivity, transitivity and circularity.

Keywords: Fuzzy Neutrosophic Soft Set, Fuzzy Neutrosophic Soft Matrix, Determinant of a square FNSM, Adjoint of a square FNSM.

Authors : Abdul-Qawe Kaed and Salem Abdullah Basardah
Title : New Properties of Almost Finitely Cogenerated Module and New Result
Volume, Issue, Year : 5(4−F)(2017)
Pages : 835−838

Abstract: In \cite{ER13} The concept of almost finitely cogenerated is introduced and studied with some properties of it. recall that: Let $R$ be a ring with identity. An $R$-module $M$ is called almost finitely cogenerated if $M$ is not finitely cogenerated but every factor of $M$ is finitely cogenerated. In this paper we will introduce and study New properties of the almost finitely cogenerated $R$-module and prove a new result of it.

Keywords: A finitely cogenerated module, Almost finitely cogenerated module, A Hopfian module, A Co-Hopfian module.

Authors : Manju Somanath, J. Kannan and K. Raja
Title : On Polynomial Solutions of Quadratic Diophantine Equation
Volume, Issue, Year : 5(4−F)(2017)
Pages : 839−844

Abstract: Let $P:= P(t)$ be a polynomial in $Z\left[X\right]$. In this paper, we consider the polynomial solutions of Diophantine Equation $D:x^2-6y^2-10x+24y=0$. We also obtain some formulae and recurrence relations on the Polynomial solution $(x_n, y_n)$ of $D$.

Keywords: Diophantine equation, Polynomial solution, Pellís equation, Continued fraction expansion.

Authors : A.K.Bincy and B.Jeba Presitha
Title : Graph Coloring and its Real Time Applications an Overview
Volume, Issue, Year : 5(4−F)(2017)
Pages : 845−849

Abstract: Graph coloring is one of the most important concepts in graph theory and it has huge number of applications in daily life. Various coloring methods are available and can be used on requirement basis. The proper coloring of a graph G is the coloring of the vertices and edges with minimal number of colors such that no two vertices should have the same color. The minimum number of color is called the chromatic number $\chi(G)$ and the graph \textit{G} is called properly colored graph. This paper presents the applications of graph coloring and its importance in various fields.

Keywords: Chromatic number $\chi(G)$, Edge coloring, Vertex coloring.

Authors : G. Uthra, K. Thangavelu and P. Kannagi
Title : Intuitionistic Fuzzy Replacement Problem with Change in Money Value
Volume, Issue, Year : 5(4−F)(2017)
Pages : 851−856

Abstract: Due to lack of accuracy or fluctuation in collected data, often it is too difficult to evaluate the precise value, especially in the continuous degradation element or system. To overcome this challenge, fuzzy set theory is employed to assess the performance. In this paper, the imprecise costs of the replacement problem, whose money value changes with time are taken as Triangular Intuitionistic Fuzzy Numbers (TIFN). A method is proposed to find the optimum replacement time and the effectiveness of the same is illustrated by an example.

Keywords: Intuitionistic Fuzzy Set, Triangular intuitionistic fuzzy number, intuitionistic fuzzy replacement problem.

Authors : R. Pradeep Kumar, D. Soner Nandappa and M. R. Rajesh Kanna
Title : Minimum Dominating Partition Energy of a Graph
Volume, Issue, Year : 5(4−F)(2017)
Pages : 857−865

Abstract: In this paper we compute minimum dominating partition energies of a star graph, complete graph, crown graph and cocktail party graphs. We also establish upper and lower bounds for minimum dominating partition energy $PE_{D}(G)$ of a graph $G$.

Keywords: Minimum dominating set, Minimum dominating partition matrix, Minimum dominating partition eigenvalues, Minimum dominating partition energy of a graph.

Authors : R. Rathika, S. Subramanian and R. Balakumar
Title : Age Group of Men Medical Representatives Affected by Stress in Pharmaceutical Company in Thanjavur and Kumbakonam City of Tamil Nadu Using Intuitionistic Fuzzy Soft Matrix
Volume, Issue, Year : 5(4−F)(2017)
Pages : 867−874

Abstract: The Paper Comprises of a case study which is done on men medical representatives in the age group of 25 to 58 years. Stress is a most persisting factor in professional and modern life. It is a natural and unavoidable feature of life experienced at one time or another by the vast majority of those engaged in professional work. Our objective of this paper to find out the peak age of men medical representatives gets stress in Thanjavur and Kumbakonam workers. For that we have studied the job stress among men workers. It has been classified into seven symptoms as don't sleep well, Muscle pain, frequent headache, Restlessness, Hair loss, Stomach pain, Wake-up tried. The concept of Intuitionistic fuzzy soft Matrix is applied to identify the age group of men medical representatives (based on age) worst affected.

Keywords: Soft Set, Fuzzy soft set, Intuitionistic Fuzzy soft set, Intuitionistic fuzzy soft Matrix.

Authors : K.Dhurai and A.Karpagam
Title : New Membership Function and New Ranking Function on Heptagon Fuzzy Number
Volume, Issue, Year : 5(4−F)(2017)
Pages : 875−878

Abstract: The Fuzzy set theory has been applied in many fields such as management, Engineering etc. In this paper, a new membership function and new ranking function introduce on Heptagon fuzzy number and a new ranking method based on heptagon fuzzy numbers used to a Travelling Salesman problems.

Keywords: Membership function, Ranking Function, Heptagon Fuzzy numbers, Travelling Salesman problem.

Authors : Manju Sharma and Rajvir Singh
Title : Study of Retrial Chain with Non Continued Clients Along with Orbital Search
Volume, Issue, Year : 5(4−F)(2017)
Pages : 879−891

Abstract: In this paper, we expand the search approach to a syntactically complicated alone server retrial queueing specimen with non consistent clients. We account a retrial queueing prototype with circular search in which an identifying subscriber after some failed retrials allocates up further repetitions as well as abdicates the mechanism (Almasi, \cite{1}). Let $I_{p}$ be the liability that after the pth approach fails, a consumer will make the $(p+1)^{th}$ one. The set of chances $(p+1)^{th}$ is labeled the persistence exercise. We assume that the chance of a call restarts after downfall of a duplicate attempt, does not depend on the count of previous attempts (i.e., $I_{2} = I_{3}= \dots$) algebraic calculations in telephone networks display that this is a realistic accumulation in conduct to such networks. One consequential characteristic of the model below consideration is that, for frequent difficulties, the cases $I_{2}<1$ and $I_{2}<1$ yield centrally asymmetric acquisitions. The case $I_{2} = 1$ can be examined in complete detail whiles the case $I_{2}<1$ is far more complex along with sealed form acquisition is attainable only for exponential service time distribution (Wang et. al., \cite{2}). This paper is arranged as succeeds. In section 2, we explain the algebraic prototype: For the cases $I_{2} = 1$, the simulation is examined in full assembly in section 3. In section 3.1, consistency clause is derived along with in 3.2, the bounding detachment of the mechanism state is acquired based on the supplementary-variable approach. The architecture of the active duration as well as its assertion in clauses of Laplace adapts have been consulted in 3.4 In section 3.5, we assign a direct procedure of algorithm for the first along with second circumstances attendant the busy time. In section 4, the case $I_{2}<1$ is counted along with the locked form solution is acquired for the exponential sustenance time separation in conditions of hyper geometric series. In section 4, we demonstrate many numerical examples to demonstrate the effect of the guidelines on the mechanism activity.

Keywords: Retrial chain, non continued clients, complex retrial.

Authors : M. Kavitha, P. Murugadas and S. Sriram
Title : Computing the Greatest X-eigenvector of Fuzzy Neutrosophic Soft Matrix
Volume, Issue, Year : 5(4−F)(2017)
Pages : 893−907

Abstract: A Fuzzy Neutrosophic Soft Vector(FNSV) x is said to be a Fuzzy Neutrosophic Soft Eigenvector(FNSEv) of a square max-min Fuzzy Neutrosophic Soft Matrix (FNSM) A if $A\otimes x=x$. A FNSEv x of A is called the greatest X-FNSEv of A if $x \in X=\{x:\underline{x}\leq x\leq \overline{x}\}$ and $y\leq x$ for each FNSEv $y\in X$. A max-min FNSM A is called strongly X-robust if the orbit $x,A \otimes x,A^{2}\otimes x,...$ reaches the greatest X-FNSEv with any starting FNSV of X. We suggest an $O(n^{3})$ algorithm for computing the greatest X-FNSEv of A and study the strong X-robustness. The necessary and sufficient condition for strong X-robustness are introduced and an efficient algarithm for verifying these conditions is described.

Keywords: Fuzzy Neutrosophic Soft Set (FNSS), Fuzzy Neutrosophic Soft Matrices(FNSMs), Fuzzy Neutrosophic Soft Eigenvectors(FNSEv), Interval vector, max-min Fuzzy Neutrosophic Soft Matrix(FNSM).

Authors : J. Paulraj Joseph and N. Shunmugapriya
Title : Total Resolving Number of Power Graphs
Volume, Issue, Year : 5(4−F)(2017)
Pages : 909−913

Abstract: Let $G = (V, E)$ be a simple connected graph. An ordered subset $W$ of $V$ is said to be a resolving set of $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $W.$ The minimum cardinality of a resolving set is called the \textit{resolving number} of $G$ and is denoted by $r(G).$ As an extension, the total resolving number was introduced in \cite{F} as the minimum cardinality taken over all resolving sets in which $\left\langle W \right\rangle$ has no isolates and it is denoted by $tr(G).$ In this paper, we obtain the bounds on the total resolving number of power graphs. Also, we characterize the extremal graphs.

Keywords: Resolving number, total resolving number, power graph.

Authors : P. Jayalakshmi and N. Ramya Priya
Title : Homeomorphism of Fuzzy Topological Graph
Volume, Issue, Year : 5(4−F)(2017)
Pages : 915−922

Abstract: This paper provides solid theoretical foundation for studying Fuzzy Topological Graph theory. The concepts such as subdivision, homeomorphism and connectedness of a fuzzy topological graph is established. In addition to this an attempt is made to study about planar and minimal non planar fuzzy topological graphs. These concepts are illustrated through examples.

Keywords: Homeomorphism, Fuzzy Topological Graph, Subdivision, Planar Fuzzy Topological Graph, Minimal Non Planar Fuzzy Topological Graph, Connectedness of Fuzzy Topological Graph.

Authors : K.K.M. Sarma and Yohannes Gebru
Title : Fixed Point Theorems for Generalized $(\psi,\phi)$-contractive Mappings in a Complete Strong Fuzzy Metric Space
Volume, Issue, Year : 5(4−F)(2017)
Pages : 923−938

Abstract: In this paper, we introduce generalized $(\psi,\phi)$-contractive mapping in strong fuzzy metric spaces and prove fixed point theorems to this class of maps. Further we introduce a generalized $(\psi,\phi)$-contractive mapping $f$ with respect a mapping $g$ and prove common fixed point theorems. We provide examples in support of our results.

Keywords: Strong fuzzzy metric space, generalized $(\psi,\phi)-$contractive mappings, generalized $(\psi,\phi)-$ contractive for a pair of mappings.

Authors : Lakhan Nagar, Pradeep Porwal, V.K. Gupta and S.K. Tiwari
Title : A Tuberculosis Mathematical Model with Infected Population and Vaccination
Volume, Issue, Year : 5(4−F)(2017)
Pages : 939−943

Abstract: Tuberculosis is an infectious disease that usually affects the lungs. World Health Organization has declared that tuberculosis Disease can cause global warming. So, TB must be solved especially in prediction and vaccination. In this model the infected population is divided into two groups, namely infectious infected and noninfectious infected population. This paper explains about the equilibrium point, and analyzing the stability model.

Keywords: Basic reproduction number, vaccination, tuberculosis, stability.