## Issue 4Volume 5 (2017)

ISSUE 4 − A ISSUE 4 − B ISSUE 4 − C ISSUE 4 − D ISSUE 4 − E ISSUE 4 − F
 Authors : P. Chella Pandian Title : On Covering Radius of Codes Over $R=\mathbb Z_2+u\mathbb Z_2,$ where $u^2=0$ Using Bachoc Distance Volume, Issue, Year : 5(4−C)(2017) Pages : 277−282

Abstract: In this paper, we give lower and upper bounds on the covering radius of codes over the ring $R=\mathbb Z_2+u\mathbb Z_2,$ where $u^2=0$ with bachoc distance and also obtain the covering radius of various Repetition codes, Simplex codes of $\alpha$-Type code and $\beta$-Type code. We give bounds on the covering radius for MacDonald codes of both types over $R=\mathbb Z_2+u\mathbb Z_2.$

Keywords: Covering radius, Codes over finite rings, Simplex code, MacDonald code.

 Authors : Aliya Naaz Siddiqui Title : Contact CR-submanifold with $\eta$-parallel $F$-structure Volume, Issue, Year : 5(4−C)(2017) Pages : 283−287

Abstract: The purpose of this paper is to prove that a contact CR-submanifold of a Sasakian-space-form is a contact CR-product submanifold, by using $\eta-$parallel $F$-structure. At last, we shall derive cyclic parallelism of contact CR-submanifold and hence obtain some inequalities based on the second fundamental form $h$.

Keywords: Contact CR-submanifold, Sasakian-space-form, Contact CR-product submanifold mappings.

 Authors : D. Premalatha and A. Vethamanickam Title : Intersection Operator Graph of a Group Volume, Issue, Year : 5(4−C)(2017) Pages : 289−292

Abstract: Let $(G,*)$ be a group with binary operation $\lq*\rq$. The Intersection Operator graph $\ig(G)$ of $G$ is a graph with $V(\ig(G)) = G$ and two distinct vertices $x$ and $y$ are adjacent in $\ig(G)$ if and only if $\langle x\rangle \cap \langle y\rangle \subseteq \langle x*y\rangle$. In this paper, we want to explore how the group theoretical properties of $G$ can effect on the graph theoretical properties of $\ig(G)$. Some characterizations for fundamental properties of $\ig(G)$ have also been obtained. Finally, we characterize certain classes of Intersection Operator Graph corresponding to finite abelian groups.

Keywords: Intersection operator graph, complete graph, star graph.

 Authors : Tapas Lowha Title : Meromorphic Functions and its Sharing Properties Volume, Issue, Year : 5(4−C)(2017) Pages : 293−296

Abstract: In this paper, we study partial sharing of meromorphic functions and its derivatives.Our results improve or generalize the results of K.S. Karak and B.Lal [7] and Yang and Yi [1].

Keywords: Meromorphic function, shared values, differential polynomials, uniqueness.

 Authors : S.Vijayakumar and C.V.R.Harinarayanan Title : Alternating Group in Symmetric Group of Degree Five Volume, Issue, Year : 5(4−C)(2017) Pages : 297−299

Abstract: Let $S_5$ be a finite non abelian group of symmetric group. Then $S_5$ containing $5! = 120$ elements. First, we observe the maltiplication table of $S_5$. In this paper find out elements of alternating group of symmetric group $S_5$.

Keywords: Symmetric Group-perumutation.

 Authors : M.Parimala, R.Jeevitha and A.Selvakumar Title : A New Type of Weakly Closed Set in Ideal Topological Spaces Volume, Issue, Year : 5(4−C)(2017) Pages : 301−312

Abstract: In this paper we introduce the notation of $I_{\alpha\psi}$ closed sets in ideal topological spaces and investigate some of their properties. Further we study the weakly $I_{\alpha\psi}$ closed sets and $I_{\alpha\psi}$ normal space and derive some of their properties.

Keywords: $I_{\alpha\psi}$ closed set, weakly $I_{\alpha\psi}$ closed sets and $I_{\alpha\psi}$ normal space.

 Authors : Surendra Kumar Tiwari and Kaushik Das Title : T-Hardy Rogers Contraction and Fixed Point Results in Cone Metric Spaces with c-Distance Volume, Issue, Year : 5(4−C)(2017) Pages : 175−179

Abstract: In this paper, we introduce the T-Hardy-Rogers's contraction under the concept of c-distance in cone metric spaces and prove the existence and uniqueness fixed point results. The presented theorem extends and generalizes several well known comparable results in literature.

Keywords: Cone metric space, complete cone metric space, c-distance, fixed point, T-Hardy¨CRogers contraction.

 Authors : V.Vinoba and S.Sridevi Title : A Bargaining Cooperative and Non-cooperative Game Theory in Wireless Sensor Networks Volume, Issue, Year : 5(4−C)(2017) Pages : 321−330

Abstract: A Bargaining Cooperation and non-cooperation has been recognized as an important mechanism to enhance connectivity and throughput in multi-hop wireless networks, especially under varying channel conditions. One major problem of cooperation and non-cooperation is t incurs energy and possibly delays costs. To a rational and selfish node these costs are worth incurring only if it receives at least comparable returns in the long term. In light of this, we propose a new incentive mechanism called bandwidth exchange (BE) where a node can delegate a portion of its bandwidth to another node in exchange for relay cooperation and non-cooperation. a n-node wireless network over a fading channel and use a Cooperative and non-cooperative game Nash Bargaining Solution (CANGNBS) mechanism to study the benefits of BE in terms of rate and coverage gains. In this paper we specifically study BE in the simple form of exchanging orthogonal frequency bands to provide incentives for relaying in a wireless network. Other forms of exchanging bandwidth such as delegation of time-slots or using spreading codes of different lengths are also possible. Using a Nash Bargaining framework, we explore the advantage of BE in both static and fading channels.

Keywords: Bargaining cooperative game, Wireless Sensor Network, Power Control, Bargaining Non-Cooperative Game.

 Authors : Ashwinkumar Raosaheb Chavan and Uttam P. Dolhare Title : On Completion of Normed Vector Space and Contraction Mapping Volume, Issue, Year : 5(4−C)(2017) Pages : 331−334

Abstract: In this paper we will discuss in detail, the concept of completion of metric space and its application to completing normed vector space. Further if the necessity of a condition of a mapping being contraction is loosen, then the mapping may not have a fixed point.

Keywords: Contraction mapping principle, Fixed point theorem, Normed vector space, Complete Metric Space.

 Authors : Dhruba Jyoti Bora and Munindra Borah Title : Regional Maximum Annual Rainfall Estimates Using TL-moment and LQ-moment: A Comparative Case Study for North East India Volume, Issue, Year : 5(4−C)(2017) Pages : 335−346

Abstract: Rainfall data of the North East region of India has been considered for selecting the best fit model for rainfall frequency analysis. The five extreme probability distributions, namely Generalized extreme value (GEV), Generalized Logistic (GLO), Pearson type 3 (PE3), Generalized Log normal (GLO) and Generalized Pareto (GPA) distributions have been fitted using LQ-moment. Also three probability distributions namely Generalized extreme value (GEV), Generalized Logistic(GLO) and Generalized Pareto (GPA) distributions have been fitted using TL-moment. Both TL-moment and LQ-moment analysis show that GPA distribution is the best fitting distribution for the North Eastern Region. Relative root mean square error (RRMSE) and RBIAS are employed to compare between the results found from TL-moment and LQ-moment analysis. It is found that the TL-moment method is significantly more efficient than LQ-moment for maximum rainfall estimates of North East India. The rainfall frequency model for the region has been developed by using the identified robust distribution for the region.

Keywords: TL-moments, LQ-moments, Mone curlo simulation.

 Authors : V. Ramachandran Title : (1, N)-Arithmetic Labelling in Multimedia and Network Technology Volume, Issue, Year : 5(4−C)(2017) Pages : 347−351

Abstract: A graph G is said to be $(1, N)$-Arithmetic (where N is a positive integer) if there is a function f from the vertex set of G to $\{0,1,N,(N + 1),2N,(2N + 1),\dots,N(q-1),N(q-1) + 1\}$ in such a way that (i) f is $1-1$ (ii) f induces a bijection $f^{\ast }$ from the edge set of G to $\{1,N + 1,2N + 1,\dots,N(q-1) + 1\}$ where $f^{\ast }(uv)=|f(u)-f(v)|$. In this paper we investigate the experimental results and point out that the new image scrambling method established on $(1, N)$-Arithmetic labelling of tree can deliver a high level security owing to the strong anomaly of sorting transformation.

Keywords: Graceful, $(1, N)$-Arithmetic, image scrambling.

 Authors : V.M.Riya and D.Jayanthi Title : On Intuitionistic Fuzzy $\gamma^{\ast}$ Generalized Connectedness Volume, Issue, Year : 5(4−C)(2017) Pages : 353−360

Abstract: In this paper we have introduced the intuitionistic fuzzy $\gamma^{\ast}$ generalized connected space, intuitionistic fuzzy $\gamma^{\ast}$ generalized super connected space and intuitionistic fuzzy regular $\gamma^{\ast}$ generalized open set. We investigated some of their properties. Also we characterized the intuitionistic fuzzy $\gamma^{\ast}$ generalized super connected space.

Keywords: Intuitionistic fuzzy topology, intuitionistic fuzzy $\gamma^{\ast}$ generalized closed set, intuitionistic fuzzy $\gamma^{\ast}$ generalized continuous mapping, intuitionistic fuzzy $\gamma^{\ast}$ generalized connected space.

 Authors : U. M. Prajapati and R. M. Gajjar Title : Some Labeling Techniques of Braided Star Graph Volume, Issue, Year : 5(4−C)(2017) Pages : 361−369

Abstract: This paper aims to defined a new graph, Braided Star Graph. and to focus on some labeling methods of Braided Star Graph. We investigate Braided Star Graph with six types of labeling; Cordial, H-cordial, Prime, Total prime, Vertex prime, Difference cordial.

Keywords: Graph Labeling, Braided Star Graph, Cordial Labeling, Prime Labeling.

 Authors : Mohammed Elnagi M. Elsanosi Title : Second-Order Boundary Value Problem With Set of the Associated Green's Function May Have Zeros Volume, Issue, Year : 5(4−C)(2017) Pages : 371−376

Abstract: We consider the nonlinear second-order boundary value problem \begin{align*} &u''+\kappa^{2}u=f(t, u(t)), \ \ \ \ t\in (0, T),T>0,\\ &u(0)=u(T),u'(0)= u'(T), \end{align*} where $0<\kappa<\frac{\pi}{T}$,\,$f:[0, T]\times[0,\infty)\to [0,\infty]$ is continuous. We use the sets of the associated Green's function may have zeros at some interior points. In particular, we study the problems where the associated Green's function may have zeros. The proof is based on the fixed point theorem in cones.

Keywords: Second-order, Positive solutions, Sets of associated Green's function zeros, Fixed point theorem in cones.

 Authors : I. Rajasekaran, M. Meharin and O. Nethaji Title : On Nano $g \beta$-closed Sets Volume, Issue, Year : 5(4−C)(2017) Pages : 377−382

Abstract: In this paper, we introduced nano $g \beta$-closed sets and use some properties relation between nano $g \beta$-closed sets.

Keywords: Nano semi-open set, nano $\beta$-open set and nano $g \beta$-open set.

 Authors : V. Muthulakshmi and S. Pavithra Title : Oscillatory Behavior of Fractional Differential Equation with Damping Volume, Issue, Year : 5(4−C)(2017) Pages : 383−388

Abstract: In this paper, we establish some oscillation criteria for a fractional differential equation with damping term using Riccati transformation technique. Here we use the Riemann-Liouville fractional derivative of order $\alpha\in (0,1)$. We give some examples to illustrate our main results.

Keywords: Oscillation, Riemann-Liouville fractional derivative, Riccati technique.

 Authors : G. Uthra, K. Thangavelu and S. Shunmugapriya Title : Ranking Generalized Institutionistic Pentagonal Fuzzy Number by Centroidal Approach Volume, Issue, Year : 5(4−C)(2017) Pages : 389−393

Abstract: In this paper we define a Generalized Institutionistic Pentagonal fuzzy number and propose a new ranking formula which includes the area of both membership and non membership parts of the fuzzy number. The membership and the non membership area of the fuzzy number is splitted into three plane figures and centroid of the centroids of these plane figures are calculated. The ranking formula is calculated by finding the area of this centroid from the origin. The advantage of this paper is that the ranking GIPFN by this approach yields better solution when compared with ranking by Accuracy function. This approach is illustrated with numerical examples.

Keywords: Generalized Pentagonal fuzzy number, Institutionistic fuzzy number, centroid.

 Authors : Renny and Susha Title : The Spectrum of Two New Corona of Graphs and its Applications Volume, Issue, Year : 5(4−C)(2017) Pages : 395−406

Abstract: In this paper we introduced two notions of corona products of graphs such as Duplication vertex corona and Duplication add vertex corona. Here we mainly determine the adjacency, Laplacian and signless Laplacian spectra of the new corona products of two graphs and we prove that the Duplication vertex corona and Duplication add vertex corona are cospectral graphs. In addition to that the Kirchhoff index and number of spanning trees of the new graph corona products were also calculated. Lastly, we focus on the classification of new class of integral graphs.

Keywords: Spectrum, duplication graph, corona of graphs, integral graphs, Kirchhoff index, spanning tree.

 Authors : Amit Kumar, Pardeep Porwal and V.H.Badshah Title : An Epidemic Model with Immigration and Non-Monotonic Incidence Rate Under Treatment Volume, Issue, Year : 5(4−C)(2017) Pages : 407−420

Abstract: The present mathematical model deals with the study of SIRS epidemic model with immigration and under treatment function type. We start from formulation of model and analyze it. The equations depend on treatment function system. The system is established. If $R_{0}<1$ the DFE (Disease Free Equilibrium) is globally stable and if $R_{0}>1$ then the endemic equilibrium is obtained which is globally stable. An example also provides to justify the stability.

Keywords: Mathematical Model, Equilibrium Point, Stability Analysis, Saturated incidence.

 Authors : C. Loganathan, Annakkodi and S. Rangasamy Title : Fuzzy Clustering Analysis of Selected IT Companies in India Volume, Issue, Year : 5(4−C)(2017) Pages : 421−427

Abstract: This paper applies fuzzy clustering algorithm in classifying IT companies in India according to some general financial indexes, such as Equity capital, Earning per Share, Price to book value, net profit margin and dividend payout. By constructing and normalizing initial partition matrix, getting fuzzy similar matrix with Minkowski metric and gaining the transitive closure, the dynamic fuzzy clustering analysis for IT companies is shown clearly that different clustered results change gradually with the threshold reducing, and then, it's shown that there is similar relationship with the prices of those companies in the stock market. In this way, it is greatly valuable in contrasting the IT companies financial conditions in order to identify some good opportunities of investments.

Keywords: Fuzzy clustering algorithm, Data Mining, Financial Analysis.