Issue 1 − C Volume 4 (2016)

ISSUE 1 − A ISSUE 1 − B ISSUE 1 − C ISSUE 1 − D
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Article Type : Research Article
Title : I-Convergence Difference Sequence Classes of Fuzzy Real Numbers Defined By Sequence of Modulus Functions
Country : India
Authors : Manmohan Das || Sanjay Kr. Das

Abstract: In this article our aim to introduce some new I- convergence difference sequence classes of fuzzy real numbers defined by sequence of modulus functions and studies some topological and algebraic properties. Also we establish some inclusion relations.

Keywords: Fuzzy real number, I- convergence, modulus function, difference sequence.

Manmohan Das
Department of Mathematics, Bajali College (Gauhati University), Assam, India.
E-mail: mdas.bajali@gmail.com


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Article Type : Research Article
Title : Soft Pre Generalized Closed Sets With Respect to a Soft Ideal in Soft Topological Spaces
Country : India
Authors : V.Chitra || V.Inthumathi || K.Nirmaladevi

Abstract: In this paper, we extend the concept of soft pre generelized closed sets due to J. Subhashini and C. Sekar [15] to soft pre generalized closed sets with respect to a soft ideal and study some of their basic properties.

Keywords: Soft sets, Soft topological spaces, Soft pg-closed set, soft g-closed set, Soft $I_g$-closed set and Soft $I_{pg}$-closed set.

K.Nirmaladevi
Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore, Tamilnadu, India.
E-mail: nirmalamaths8@gmail.com


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Article Type : Research Article
Title : On Relaxed Skolem Mean Labling For Four Star
Country : India
Authors : V.Balaji|| D.S.T.Ramesh || M.Elakkiya

Abstract: In this paper, we prove that if $\ell $= m $<$ n, the four star K${}_{1, }$${}_{\ell }$${}_{ }$$\cup$ K${}_{1, }$${}_{\ell }$${}_{ }$$\cup$ K${}_{1, m }$$\cup$ K${}_{1, n}$ is a relaxed skolem mean graph if $|m-n|\, \le \, 2\ell \, +6$ for $\ell $= 2, 3, 4, . . . ; m = 2, 3, 4, . . . and $2\ell +m\, \le n\, \le \, 2\ell \, +\, m\, +6$.

Keywords: Skolem mean graph and star.

V.Balaji
Department of Mathematics, Sacred Heart College, Tirupattur, India.
E-mail: pulibala70@gmail.com


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Article Type : Research Article
Title : Some Types of Generalized $H^h$-Recurrent in Finsler Spaces
Country : Yemen
Authors : Fahmi Yaseen Abdo Qasem || Adel Mohammed Ali AL-Qashbari

Abstract: The purpose of this paper is to develop some properties of generalized $H^{h}$-recurrent affinely connected space, P2-like generalized $H^{h}$-recurrent space and $P^{\ast}$-generalized $H^{h}$-recurrent space for Berwald curvature tensor $H_{jkh}^{i}$ which satisfies the condition $H_{jkh\vert l}^{i}=\lambda_{l}H_{jkh}^{i}+\mu_{l}(\delta _{h}^{i} g_{jk}-\delta_{k}^{i} g_{jh})$, where $\vert l$ is h-covariant differentiation, $\lambda_{l}$ and $\mu_{l}$ are non-null covariant vectors field is introduced and such space is called as a generalized $H^{h}$-recurrent space and denote it briefly by $G H^{h}$-$R F_{n}$. Some theorems and conditions have been pointed out which reduce a generalized $H^{h}$-recurrent space $F_{n}(n>2)$ into a Finsler space of curvature scalar.

Keywords: Finsler space, Generalized H-recurrent space, affinely connected space, P2-like space and $P^{\ast}$-space.

Adel Mohammed Ali AL-Qashbari
Department of Mathematics, Faculty of Education, University of Aden, Khomaksar, Aden, Yemen.
E-mail: Adel_ma71@yahoo.com


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Article Type : Research Article
Title : On a Generalized K^h- Birecurrent Finsler Space
Country : Yemen
Authors : Fahmi Yaseen Abdo Qasem || Wafa'a Hadi Ali Hadi

Abstract: In the present paper, a Finsler space whose curvature tensor $K^i_{jkh}$ satisfies $K^i_{jkhÐ\ell Ðm}{\rm =\ }{\ a}_{\ell m}K^i_{jkh}+{\ b}_{\ell m}\left({\delta }^i_kg_{jh}-{\delta }^i_hg_{jk}\right)\ ,K^i_{jkh}\ne $ 0 , where ${\ a}_{\ell m}$ and ${\ b}_{\ell m}\ $are non-zero covariant tensor fields of second order called recurrence tensor fields, is introduced, such space is called as a generalized $K^h-$birecurrent Finsler space . The associate tensor $K_{jrkh}$ of Cartan's fourth curvature tensor $K^i_{jkh}$ , the torsion tensor $H^i_{kh}$ ,the deviation tensor $K^i_h$, the Ricci tensor $K_{jk}$, the vector $H_k$ and the scalar curvature $K$ of such space are non-vanishing. Under certain conditions, a generalized $K^h-$birecurrent Finsler space becomes Landsberg space . Some conditions have been pointed out which reduce a generalized $K^h-$birecurrent Finsler space $F_n(n>2)$ into Finsler space of scalar curvature.

Keywords: Finsler space; Generalized K^h-birecurrent Finsler space; Ricci tensor; Landsberg space; Finsler space of scalar curvature.

Wafa'a Hadi Ali Hadi
Department of Mathematics , Community College-Aden, Dar Saad , Aden, Yemen.
E-mail: wf_hadi@yahoo.com


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Article Type : Research Article
Title : Some Results for Semi Derivations of Prime Near Rings
Country : India
Authors : Meram Munirathnam

Abstract: Let $R$ be a prime near ring. By a semi-derivation associated with a function $g:R \rightarrow R$ we mean an additive mapping $f: R \rightarrow R$ such that $ f (xy) =f (x)g(y) + xf (y) = f (x)y + g(x)f (y)$ and $f (g(x)) = g(f (x)) $ for all $x, y \in R$. In this paper we try to generalize some properties of prime rings with derivations to the prime near rings with semi-derivations.

Keywords: Semi derivation, Prime ring, Commuting mapping, Characteristic of a ring.

Meram Munirathnam
Ad-hoc Lecturer, Dept. of Mathematics, RGUKT, R.K.Valley, Idupulapaya(vi),Vempalli (md), Kadapa(Dt), Andhra Pradesh, India.
E-mail: munirathnam1986@gmail.com


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Article Type : Research Article
Title : Some Unified and Generalized Kummer's Second Summation Theorems with Applications in Laplace Transform Technique
Country : India
Authors : M.I.Qureshi || M.S.Baboo

Abstract: Some significant hypergeometric summation theorems with suitable convergence conditions, are obtained in the present study; analogous to summation theorems for Gauss function ${_2F_1(\frac{1}{2})}$ presented by Brychkov, Prudnikov {\it et~al.} and derived by Fox, Rakha-Rathie. By means of these summation theorems we also find the Laplace transforms of Kummer's confluent hypergeometric function $_1F_1$ in closed form.

Keywords: Gauss and Kummer hypergeometric functions; Legendre duplication formula; Pfaff-Kummer's linear hypergeometric transformation; Principle of analytic continuation; Laplace transforms.

M.S.Baboo
School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, 201306, India.
E-mail: mesub007@gmail.com


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Article Type : Research Article
Title : Ciric Type Coincidence and Fixed Point Results For Nonexpansive Multi-Valued and Single Valued Maps
Country : India
Authors : Umesh Dongre || R.D.Daheriya || Manoj Ughade

Abstract: In this paper we consider the existence of coincidences and fixed points of nonexpansive type conditions satisfied by multivalued and single valued maps and prove some fixed point theorems for nonexpansive type single and multivalued mappings.

Keywords: Coincidence point; fixed point; non-expansive mappings; compatible mappings; T-orbitally complete; (T, f)-orbitally complete.

Manoj Ughade
Department of Mathematics, Sarvepalli Radhakrishnan University, Bhopal, P.O. Box 462026, India.
E-mail: surajshrivastava70@gmail.com


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Article Type : Research Article
Title : Balanced Cordial Labeling and its Application to Produce new Cordial Families
Country : India
Authors : V.J.Kaneria || K.M.Patadiya || J.R.Teraiya

Abstract: In this paper we have introduced a balanced cordial labeling for a graph G, which is a cordial labeling $ f $ with condition $ e_{f}(0)= e_{f}(1), v_{f}(0)= v_{f}(1). $ We proved that $ P_{n} \times C_{4t}, C_{n} \times C_{4t}$ ($n$ is even) are balanced cordial graphs. We also proved that the corona graph $ G_{1} \odot G_{2} $ is cordial, when $ G_{1} $ a cordial graph and $ G_{2} $ is a balanced cordial graph.

Keywords: Binary vertex labeling, balanced cordial graph, corona graph.

K.M.Patadiya
School of Engineering, RK University, Rajkot, India.
E-mail: kalpesh.patadiya$@$rku.ac.in


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Article Type : Research Article
Title : The Edge Zagreb indices of Circumcoronene Series of Benzenoid
Country : Iran
Authors : M.R.Farahani || M.R.Rajesh Kanna || R.Pradeep Kumar || S.Hosamani

Abstract: In chemical graph theory, we have many invariant polynomials and topological indices for a molecular graph. One of the best known and widely used is the Zagreb topological index of a graph $G$ $M_1(G)$ introduced in 1972 by I. Gutman and N. Trinajstic and is defined as the sum of the squares of the degrees of all vertices of $G$, $M_{1}(G)=\sum\limits_{v\in V(G)} {d_{v}}^2$ (or $=\sum\limits_{e=uv\in E(G)} {d_{u}+d_{v}}$, where $d_{u}$ denotes the degree (number of first neighbors) of vertex $u$ in $G$. Also, the Second Zagreb index $M_2(G)$ is equal to $M_{2}(G)=\sum\limits_{e=uv\in E(G)} {d_{u} \times d_{v}}$. In this paper, we focus on the structure of molecular graph Circumcoronene Series of Benzenoid $H_{k}$ ($k>1$) and its line graph $L(H_{k})$ and counting First Zagreb index and Second Zagreb index of $L(H_{k})$.

Keywords: Circumcoronene Series of Benzenoid, Line graph, Degree (of a vertex), Zagreb Topological Index.

M.R.Farahani
Department of Applied Mathematics of Iran University of Science and Technology (IUST), Narmak, Tehran, Iran.
E-mail: mrfarahani88@gmail.com


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Article Type : Research Article
Title : Some Common Fixed Point Theorems For Nonexpansive Type Mappings In 2-Metric Spaces
Country : India
Authors : Ritu Sahu || P L Sanodia || Arvind Gupta

Abstract: The aim of this paper is to prove some common fixed point theorems for weakly compatible mappings under nonexpansive type conditions in the setting of 2-metric spaces. Our result extend and generalizes corresponding results of Singh, Adiga and Giniswami [9] and Liu and Zhang [7].

Keywords: 2-metric spaces, nonexpansive mapping,compatible mappings compatible mapping of type (A).

Ritu Sahu
Department of Mathematics, People’s College of Research & Technology, Bhopal, India
E-mail: sahuritu00@gmail.com


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Article Type : Research Article
Title : A New Approach For Solving All Integer Linear Fractional Programming Problem
Country : India
Authors : Geeta Modi || Sushma Duraphe || Huma Akhtar

Abstract: In this paper we present a new approach for solving all integer linear fractional programming problem (ILFPP) in which the objective function is a linear fractional function, and where the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon simplex method as well as dual simplex method. A simple example is given to clarify the theory of this new approach.

Keywords: Fractional programming, Simplex method, Dual simplex method, Gomory’s fractional cut method.

Huma Akhtar
Research Scholar, Govt. M.V.M. Bhopal, India.
E-mail: akhtarhuma50@gmail.com


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Article Type : Research Article
Title : Key mortality factors of Scirpophaga incertulas (Rice stem borer) infesting Rice
Country : India
Authors : S.Udayakumar || P.Sujatha || P.Yasotha

Abstract: Scirpophagaincertulaspassed through one generation each during rainy season at Agricultural Engineering College, Kumulur. TrichogrammaJaponicum,Trichogrammabraziliensis, Telenomusbeneficiens, Tetra stichus SP. are egg parasites and BraconChinensis, Stenobraconnicenilles, Tropobracon sp. Platygaster. In addition to the above TrichogrammaJaponicum and playgasterOryzac unidentified as key mortality factors of scirpopherga incertulas. Using the key mortality factors the killing power of k value is decrease by second generation.

Keywords: Rice, Key Mortality factors, Scirpophaga incertulas.

P.Sujatha
Assistant Professor(Maths), Ph.D Research Scholar, Horticultural college and Research Institute (women), Tamil Nadu Agricultural University, Trichy, India.
E-mail:


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Article Type : Research Article
Title : Super Root Square Mean Labeling Of Disconnected Graphs
Country : India
Authors : M.Kannan || R.Vikrama Prasad || R.Gopi

Abstract: Let G be a graph with p vertices and q edges. Let $f:V(G)\to \{1, 2, 3,\dots, p+q\} be an injective function. For a vertex labeling f, the induced edge labeling $f^\ast(e=uv)$ is defined by then f is called a super root square mean if . A graph which admits super root square mean labeling is called super root square mean graph. In this paper, we investigate super root square mean labeling of disconnected graphs.

Keywords: Super root square mean,

M.Kannan
Research & Development Centre, Bharathiar University, Coimbatore – 641 046, India.
E-mail: kannan8383@gmail.com


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Article Type : Research Article
Title : Asymptotic Stability In Impulsive Functional Differential Equations
Country : India
Authors : Sanjay K. Srivastava || Neha Wadhwa || Neeti Bhandari

Abstract: In this paper conditions on Lyapunov functionals $V(t, \phi)$ are improved which ensure asymptotic stability and uniform asymptotic stability.

Keywords: Stability, Asymptotic Stability, Impulsive Functional Differential Equation, Lyapunov functional.

Neha Wadhwa
Department of Applied Sciences, Amritsar College of Engineering and Technology, Amritsar - 143006, Punjab, India.
E-mail: nehawadhwa08@yahoo.com


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Article Type : Research Article
Title : Construction of Two Special Integer Triples
Country : India
Authors : S.Vidhyalakshmi || M.A.Gopalan || E.Premalatha

Abstract: This paper concerns with the study of constructing a special non zero integer triple (a, b, c) such that the product of any two elements of the set added with the other is a perfect square. Also, the product of any two elements of the set added with the square of the other is a perfect square.

Keywords: Integer Triple, system of double equation

E.Premalatha
Department of Mathematics, National College, Trichy, Tamil Nadu, India.
E-mail: premalathaem@gmail.com


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Article Type : Research Article
Title : Parametric Metric Space, Parametric b-metric Space and Expansive Type Mapping
Country : India
Authors : R.D.Daheriya || Suraj Shrivastava || Manoj Ughade

Abstract: In this article, we present some fixed point theorems under various expansive conditions in parametric metric spaces and parametric b-metric spaces. The presented theorems extend, generalize and improve many existing results in \cite{13}. Also we prove a common fixed point theorem, which is generalization of Theorem 2.2 of Jain et al. \cite{24} in the setting of parametric b-metric space. We introduce an example the support the validity of our result.

Keywords: Fixed point, common fixed point, parametric metric space, parametric b-metric space.

Suraj Shrivastava
Department of Mathematics, Swami Vivekanand College of Science and Technology, Bhopal, Madhya Pradesh, India.
E-mail: surajshrivastava70@gmail.com


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Article Type : Research Article
Title : Obscuring Instability In C Language Using Euler's Modified Method
Country : India
Authors : Sonia Shivhare || Yogesh Shukla

Abstract: The solutions of ordinary Differential equations having initial value problems are analyzed numerically. Computationally effective numerical methods, Euler’s method is given meticulously while Euler’s Modified method presented here gives a better exactness. No higher order derivatives are required to be tabulated. Drawbacks and advantages of the methods are discussed here and the results obtained by them have been compared. The idea behind this paper is to illustrate the facts of implementing a small number of steps of Euler's modified method, in addition , how to apply built-in functions available in C++ [1]. Firstly, we use Euler methods to bring in the fundamental thoughts linked with initial value problems (IVP) and then later on, we apply the Euler’s Modified method associated to the built-in C++ . The purpose of this paper is to go from textbook formula on ODE to production software.

Keywords: Euler’s Method, Euler’s Modified Method, C++, ODE.

Yogesh Shukla
Amity University, Madhya Pradesh, India.
E-mail:


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Article Type : Research Article
Title : Lucky Edge Labeling of $K_n$ and Special Types of Graphs
Country : India
Authors : R.Sridevi || S.Ragavi

Abstract: Let G be a simple graph with vertex set V(G) and edge set E(G) respectively. Vertex set V(G) is labeled arbitrary by positive integers and E(e) denote the edge label such that it is the sum of labels of vertices incident with edge e. The labeling is said to be lucky edge labeling if the edge E(G) is a proper coloring of G, that is, if we have $E(e_{1})\neq E(e_{2})$ whenever $e_{1}$ and $e_{2}$ are adjacent edges. The least integer k for which a graph G has a lucky edge labeling from the set $\{1, 2,\dots, k\}$ is the lucky number of G denoted by $\eta(G)$. A graph which admits lucky edge labeling is the lucky edge labeled graph. In this paper, we proved that complete graph $K_{n}$, tadpole graph $T_{m, n}$ and rectangular book $B_{p}^{4}$ are lucky edge labeled graphs.

Keywords: Lucky edge labeled graph, Lucky edge labeling, Lucky number.

S.Ragavi
Research Scholar, Department of Mathematics, Sri S.R.N.M.College, Sattur, Tamilnadu, India.
E-mail: stragavi22@gmail.com


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Article Type : Research Article
Title : Finite Product Topologies Modulo An Ideals
Country : India
Authors : R.Alagar

Abstract: Given a topological space (X,$\tau $) and an ideal$\Im $ in X, a finer topology $\tau $* in X can be associated with $\tau $ and$\Im $. Given two topological spaces (X,$\tau $${}_{1}$), (Y,$\tau $${}_{2}$) and ideals $\Im $, $\vartheta$ in X, Y respectively, an ideal $\Im $x $\vartheta$ in X x Y, called the product ideal of $\Im $and $\vartheta$, in X x Y. We investigate inclusion relations between $\tau $${}_{1}$* x $\tau $${}_{2}$* and ($\tau $${}_{1}$ x $\tau $${}_{2 }$)* and the conditions under which $\tau $${}_{1}$* x $\tau $${}_{2}$* = ($\tau $${}_{1}$ x $\tau $${}_{2 }$)* and we extend the theorem for finite case.

Keywords: Product ideal, Product Topology,$\tau $* - topologies, $\pi \tau _{\alpha } $* - closed.

R. Alagar
Department of Mathematics, R.V. Government Arts college, Chengalpattu – 603 001.
E-mail:


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Article Type : Research Article
Title : Regular And Totally Regular Intuitionistic Fuzzy Hypergraph(IFH)
Country : India
Authors : I.Pradeepa || S.Vimala

Abstract: Regular and totally regular Intuitionistic fuzzy graph was first introduced by Nagoor gani.A and Radha.K. In this paper, we define regular and totally regular Intuitionistic fuzzy hypergraphs and discusses the size and order along with properties of the regular and totally regular Intuitionistic fuzzy hypergraphs. The work has been extended to completeness of Intuitionistic fuzzy hypergraphs.

Keywords: Intuitionistic fuzzy graph, Regular intuitionistic fuzzy graph,Totally Regular intuitionistic fuzzy graph,Degree,Total degree.

I.Pradeepa
Assistant Professor, Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, India.
E-mail: tvimss@gmail.com


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Article Type : Research Article
Title : Adjacent vertex sum polynomial for the splitting graph of Factographs
Country : India
Authors : E.Ebin Raja Merly || A.M.Anto

Abstract: Let $G=(V, E)$ be a graph. The vertex polynomial of the graph $G=(V,E) $ is defined as $V(G,x)=\sum\limits_{k=0}^{\Delta(G)}{v_{k}x^{k}}$, where $\Delta (G)=\max\{d(v)/v\in V\}$ and $v_{k}$ is the number of vertices of degree $k$. The adjacent vertex sum polynomial is defined as $S(G, x)=\sum\limits_{i=o}^{\Delta(G)}{n_{\Delta(G)-i}x^{\alpha_{\Delta (G)-i}}}$, where $n_{\Delta(G)-i}$ is the sum of the number of adjacent vertices of all the vertices of degree $\Delta(G)-i$ and $\alpha_{\Delta(G)-i}$ is the sum of the degree of adjacent vertices of all the vertices of degree $\Delta(G)-i$. In this paper we seek to find the vertex polynomial and the adjacent vertex sum polynomial for the splitting graph of Perfect factograph and the splitting graph of Integral Perfect factograph.

Keywords: Perfect factograph, Integral Perfect factograph, Vertex polynomial, Adjacent vertex sum polynomial, Splitting graph.

A.M.Anto
Research scholar, Department of Mathematics, Nesamony Memorial Christian College, Marthandam, India.
E-mail: antoalexam@gmail.com


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Article Type : Research Article
Title : Prime number generating polynomial $3n^2+3n+23$
Country : India
Authors : Jeevan Maloth

Abstract: A prime number is positive integer which does not divisible by any integers except 1 and itself. Up to now there is no any polynomial which generates all primes. There are few polynomial generate finite primes. In this paper I am giving a new polynomial which generating prime numbers from n= 0 to 21.

Keywords: Prime-generating polynomial.

Jeevan Maloth
Student of the Electrical Department, St. Martin’s Engineering College, Dhulapally, Secunderabad, Telangana, India.
E-mail: jeevannayak777@gmail.com