Volume 4 (2016) Article in Press

ISSUE 3 − A
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Article Type : Research Article
Title : Analysis of Successive Occurrence of Digit 0 in Prime Numbers till 1 Trillion
Country : India
Authors : Neeraj Anant Pande

Abstract: All primes less than $1$ trillion are analyzed for successive occurrence of digit $0$ in them. Multiple successive occurrences of $0$'s are examined. The first and last instances of successive occurrence of all possible repetitions of $0$'s are determined within initial $12$ ranges of increasing powers of $10$.

Keywords: Prime numbers, digit $0$, successive occurrences.

Neeraj Anant Pande
Associate Professor, Department of Mathematics \& Statistics,Yeshwant Mahavidyalaya (College), Nanded, Maharashtra, India.
E-mail: napande@gmail.com


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Article Type : Research Article
Title : Spaces over non-Newtonian numbers
Country : India
Authors : P.Sharma and S.Mishra

Abstract: We construct the spaces of non-Newtonian numbers using some new operations between them. Then we define generalized metric and generalized norm on the set of non-Newtonian numbers which attains the value as a non-negative non-Newtonian real number (depending on system of measurement) rather than non-negative real. Further, we have studied some order and convergence structures on these spaces.

Keywords: Non-Newtonian numbers, Ordered vector space, $*_{\gamma}$-Banach space.

P.Sharma
Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India.
E-mail: pranav15851@mgail.com


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Article Type : Research Article
Title : Fractional Order Model in Generalist Predator--Prey Dynamics
Country : Saudi Arabia
Authors : Moustafa El-Shahed, A. M. Ahmed and Ibrahim M.E.Abdelstar

Abstract: In this paper, we construct the fractional order generalist predator--prey dynamics model. The stability of free and positive fixed points is studied. The Adams-Bashforth-Moulton algorithm has been used to solve and simulate the system of differential equations.

Keywords: Generalist predator, Fractional order, Stability, Limit cycle, Numerical method.

Moustafa El-Shahed
Department of Mathematics, Faculty of Arts and Sceinces, Qassim University, Qassim, Unizah, Saudi Arabia.
E-mail: elshahedm@yahoo.com


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Article Type : Research Article
Title : Commutators of Fractional Integral with Variable Kernel on Variable Exponent Herz and Lebesgue Spaces
Country : P.R. China
Authors : Afif Abdalmonem, Omer Abdalrhman and Shuangping Tao

Abstract: In this paper, we study the boundedness for commutators of the fractional integral with variable kernel on Lebesgue spaecs with variable exponent. Also, we study the boundedness of the fractional integral operator and their commutator generated by BMO function is obtained on those Herz spaces with two variable exponent $p(\cdot), q(\cdot)$.

Keywords: Fractional integral, variable kernel, commutator, variable exponent, BMO function, Lebesgue spaecs, Herz spaces.

Afif Abdalmonem
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, P.R. China.
E-mail: afeefy86@gmail.com


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Article Type : Research Article
Title : Collatz Conjecture for Modulo an Integer
Country : India
Authors : T.Kannan and C.Ganesa Moorthy

Abstract: A function $T_m$ from a set \{1,2,3,...$m$\} into itself defined by \\$T_m(x)=\frac{x}{2},$ for even $x$ and by $T_m(x)=\frac{3x+1}{2}$ (mod $m$), for odd $x$ is considered in this article. The asymptotic behaviour of this function is studied in this article for some cases.

Keywords: Congruence, Collatz conjecture.

T.Kannan
Department of Mathematics, Sree Sevugan Annamalai college, Devakottai, TamilNadu, India.
E-mail: hardykannan@gmail.com


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Article Type : Research Article
Title : Generalization of Common Coupled Fixed Point Theorems in Complex Valued b-Metric Spaces
Country : India
Authors : A.K.Dubey

Abstract: Recently, Azam et al. [1] introduced the complex valued metric space and obtained sufficient conditions for the existence of common fixed points. Rao et al. [20] introduce the notion of complex valued b-metric spaces. In this paper, some common coupled fixed point theorems have been established for a pair of mappings in a complete complex valued b-metric space in view of diverse contractive conditions. Our results extend and improve several fixed point theorems in the literature.

Keywords: Common fixed point, Coupled fixed point, Complete complex valued b-metric space, Complex-valued metric spaces.

A.K.Dubey
Department of Mathematics, Institute of Technology, Bhilai House, Chhattisgarh, India.
E-mail: anilkumardby70@gmail.com


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Article Type : Research Article
Title : Snakes Related Sum Perfect Square Graphs
Country : India
Authors : S.G.Sonchhatra and G.V.Ghodasara

Abstract: Let $G = (V, E)$ be a simple $(p,q)$ graph and $f:V(G)\rightarrow\{0,1,2,\ldots, p-1\}$ be a bijection. We define $f^{\ast}:E(G)\rightarrow\ \mathbb{N}$ by $f^{\ast}(uv)=(f(u))^{2} + (f(v))^{2} + 2 f(u) \cdot f(v)$, $\forall uv \in E(G)$. If $f^{\ast}$ is injective, then $f$ is called sum perfect square labeling. A graph which admits sum perfect square labeling is called sum perfect square graph. In this paper we prove that several snakes related graphs are sum perfect square.

Keywords: Sum perfect square graphs, triangular snakes, quadrilateral snakes.

S.G.Sonchhatra
Department of Mathematics, Government Engineering College, Rajkot, India.
E-mail: sonchhabdasunil.20@mail.com


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Article Type : Research Article
Title : Balanced Mean Cordial Labeling and Graph Operations
Country : India
Authors : V J Kaneria, M J Khoda and H M Karavadiya

Abstract: Balanced mean cordial labeling is a mean cordial labeling $f$ with \linebreak $|v_{f}(i)- v_{f}(j)|=0$, $|e_{f}(i)- e_{f}(j)|=0$, $\forall$ $i,j\in \{0,1,2\}$. In this paper, we investigate mean cordial labeling for P($t\cdot H$), where H be any graph and $t\equiv 0$(mod $3$). We also investigate balanced mean cordial labeling for TP($t\cdot H$), G$^{*}$, P$_{t}$$\times G$, C$_{t}$$\times G$, where H and G both are balanced cordial graphs.

Keywords: Path Union, Mean Cordial, Balanced mean cordial.

M J Khoda

E-mail: mjkmaths@gmail.com


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