Issue 4 Volume 5 (2017)

Authors : S. Malathi and S. Nithyanantha Jothi
Title : On Generalized c*-open Sets and Generalized c*-open Maps in Topological Spaces
Volume, Issue, Year : 5(4−B)(2017)
Pages : 121−127

Abstract: The aim of this paper is to introduce the notion of generalized c*-open sets and generalized c*-open maps in topological spaces and study their basic properties.

Keywords: gc*-open sets and gc*-open maps.

Authors : Sanjay Tripathi
Title : Absolute Summability of a Lacunary Fourier Series
Volume, Issue, Year : 5(4−B)(2017)
Pages : 129−131

Abstract: The absolute convergence and absolute summability of Lacunary Fourier series was studied by several authors and obtained many results on it. In this direction ,N.V.Patel \cite{2} has obtained a result on absolute summability of Lacunary Fourier series. In this paper, we have proved a results by considering more general absolute summability under same hypothesis which generalizes the results of N.V.Patel \cite{2}.

Keywords: Absolute CesaroSummability, Lacunary Fourier series, Absolute convergence.

Authors : A. Anto Kinsley and C. Caroline Selvaraj
Title : Interior Domination on Subdivision and Splitting Graphs of Graphs
Volume, Issue, Year : 5(4−B)(2017)
Pages : 133−141

Abstract: A subset D of the vertex set $V(G)$ of a graph G is said to be a dominating set if every vertex in V-D is adjacent to some vertex in $D$. A dominating set D is said to be an interior dominating set if every vertex $v\in D$ is an interior vertex of G. The minimum cardinalities among the interior dominating sets of G is called the interior domination number $\gamma_{Id}(G)$ of G. In this paper we discuss interior domination on the subdivision graph $S(G)$ of various graphs.

Keywords: Interior dominating set, Subdivision graph, Splitting graph.

Authors : L. Pandiselvi, S. Navaneethakrishnan and A. Nagarajan
Title : Twig and Cycle Related Near Mean Cordial Graphs
Volume, Issue, Year : 5(4−B)(2017)
Pages : 143−149

Abstract: Let $G = (V, E)$ be a simple graph. A Near Mean Cordial Labeling of G is a function in $f : V(G) \to \{1, 2, 3,\dots, p-1, p+1\}$ such that the induced map f* defined by \[ f^*(uv) = \left\{ \begin{array}{ll} 1, & \hbox{if $\left(f\left(u\right)+f\left(v\right)\right)\equiv 0\ (mod\;2)$;} \\ 0, & \hbox{else.} \end{array} \right. \] and it satisfies the condition $|e_f(0)-e_f(1)|\le 1$, where $e_f(0)$ and $e_f(1)$ represent the number of edges labeled with 0 and 1 respectively. A graph is called a Near Mean Cordial Graph if it admits a near mean cordial labeling. In this paper, it is to be proved that $Twig\ T(n)$, $\langle C_n : C_{n-1}\rangle$ and $W_n$ (When $n \equiv 0,2,3\ (mod\ 4)$) are Near Mean Cordial graphs. Also, $W_n$ (When $n \equiv 1\ (mod\ 4)$) are not Near Mean Cordial graphs.

Keywords: Cordial labeling, Near Mean Cordial Labeling and Near Mean Cordial Graph.

Authors : Alanur Hussain Laskar and Samira Behera
Title : A Comparative Study of Jacobi Method and Givens Method for Finding Eigenvalues and Eigenvectors of a Real Symmetric Matrices
Volume, Issue, Year : 5(4−B)(2017)
Pages : 151−165

Abstract: The aim of this paper is to compare the Jacobi method and the Givens method for finding the eigenvalues and the corresponding eigenvectors of a real symmetric matrices. Finally, we have seen that with examples Givens method is non iterative and more efficient than Jacobi method, although it requires the given symmetric matrix into a tridiagonal matrix having the same eigenvalues.

Keywords: Eigenvalues and eigenvectors, Jacobi method, Givens method, Symmetric matrix, Bisection method.

Authors : A.K. Ronghe and Sachin Sharma
Title : Some Transformations and Identities for I-Function of Two Variables
Volume, Issue, Year : 5(4−B)(2017)
Pages : 167−174

Abstract: In this paper, some transformations, Summation formulae and identities for I-function of two variables have been evaluated. Many new as well as known relations may be derived as particular cases, which are known by identities.

Keywords: Hypergeometric function, I-function of two variables, known integrals.

Authors : V.R.Kulli
Title : On the Product Connectivity Reverse Index of Silicate and Hexagonal Networks
Volume, Issue, Year : 5(4−B)(2017)
Pages : 175−179

Abstract: In this paper, we introduce the product connectivity reverse index of a molecular graph. In Chemical Graph Theory, the connectivity indices are applied to measure the chemical characteristics of compounds. We determine the product connectivity reverse index for silicate networks and hexagonal networks.

Keywords: Product connectivity reverse index, silicate network, hexagonal network.

Authors : T. Kavitha
Title : On Mildly B-Normal Spaces and Some Functions
Volume, Issue, Year : 5(4−B)(2017)
Pages : 181−188

Abstract: In this paper, by using Bg-closed sets we obtain a characterization of mildly B-normal spaces and use it to improve the preservation theorems of mildly B-normal spaces.

Keywords: Bg-closed sets, mildly B-normal spaces, characterization of mildly B-normal spaces.

Authors : Najmuddin Ahmad and Vimal Pratap Singh
Title : A New Iterative Method for Solving Nonlinear Equations Using Simpson Method
Volume, Issue, Year : 5(4−B)(2017)
Pages : 189−193

Abstract: In this paper, we introduced the new iterative method for solving nonlinear equations. This method based on the combination of mid-point with Simpson quadrature formulas and using Newton's method. The convergence analysis of our method are discussed. It is established that the new method has convergence order three. Numerical tests shows that the new method is comparable with the well-known existing single step iterative methods and provides better results.

Keywords: Nonlinear equations, iterative methods, Simpson method, Newton's method, convergence.

Authors : Pablo I. Pucheta
Title : An Extended Wright Function
Volume, Issue, Year : 5(4−B)(2017)
Pages : 195−200

Abstract: In this paper we will extend the classical function Wright $W_{\alpha, \beta}(z)$ $\rightarrow$ $W_{\alpha, \beta}^{\lambda, \xi}(z)$ using the relationship between Euler beta function with the symbol Pochhammer $\frac{B(\lambda+n,\xi-\lambda)}{B(\lambda,\xi-\lambda)}=\frac{(\lambda)_{n}}{(\xi)_{n}}$. Some basic properties are studied and Laplace transform is evaluate \cite{1,3}. We will study the Riemann-Liouville fractional integral and fractional derivative arbitrary order $v$ of $W_{\alpha, \beta}^{\lambda, \xi}(z)$.

Keywords: Fractional Calculus, Laplace Transform, Wright Function, Extended Mittag-Leffler function.

Authors : Shibaji Halder
Title : Time Derivative of Vector and Mathematical Objects in Tensor Calculus and its Application to Newtonian Equation of Motion
Volume, Issue, Year : 5(4−B)(2017)
Pages : 201−204

Abstract: We represent a vector as the contravariant components with respect to covariant basis and we derivative it with respect to time. Now if we put it in the left side of Newtonian equation of motion for acceleration (time derivative of velocity), we get equation of motion in tensorial form. Now finding the acceleration components in spherical polar coordinate system and get the contravariants components of acceleration and changing it to the physical components. Again if we consider two different coordinate system and using the covariant basis formula we get it tensorial rank does not change this type of differentiation.

Keywords: Time rate of change of contravariant vector, Newtonian Mechanics.

Authors : Sneha K. Patel
Title : Random Number and Combination Based Encryption and Decryption
Volume, Issue, Year : 5(4−B)(2017)
Pages : 205−209

Abstract: For secure communication, cryptography has been used for thousands of years. Encryption and decryption are the process of transforming plaintext into the ciphertext and vice versa. There are three types of encryption and decryption algorithms exist which are classified as symmetric key cryptography, asymmetric cryptography algorithm and hash function. This paper presents an algorithm for data encryption and decryption which is based on random number generation, combination and MOD operation. This algorithm uses random number and combinations, generate a key to encrypt or decrypt the data.

Keywords: Encryption, Decryption, Random number, MOD operator, Symmetric key cryptography.

Authors : Srinivas Maripala and N. Kishan
Title : Micropolar Nanofluid Over a MHD Heat Transfer Porous Shrinking Sheet
Volume, Issue, Year : 5(4−B)(2017)
Pages : 211−217

Abstract: This analysis investigated with the boundary layer flow and heat transfer aspects of a micropoloar nanofluid over a porous shrinking sheet with thermal radiation. The boundary layer equations governed by the partial differential equations are transformed in to a set of ordinary differential equations with the help of suitable local similarity transformations. The coupled nonlinear ordinary differential equations are solved by the implicit finite difference method along with the Thamous algorithm. Dual solutions of dimensionless velocity, angular velocity, temperature and concentration profiles are analyzed by the effect of various controlling flow parameters viz., Lewis number Le, thermophoresis Nt, Brownian motion parameter Nb, Radiation parameter R, Prandtl number Pr, material parameter K, mass suction parameter S, magnetic parameter M.

Keywords: MHD, micropolar fluid flow, thermal radiation, nanofluid, shrinking sheet.

Authors : Waikhom Rojen Singh, Surendra Kumar Srivastava and Jyoti Ratlia
Title : Application of Markov Chain in Predicting Change in Opening Stock Price
Volume, Issue, Year : 5(4−B)(2017)
Pages : 219−223

Abstract: The objective of this present paper is to predict the prompt future change in opening stock price and to find steady state transition probability matrix. The opening stock price of National Stock Exchange NIFTY 50 of India from January to July 2017 was studied and opening price of Stock was scrutinized as following Markov chain. This method is widely applied in Stock Exchange and Business area.

Keywords: Markov Process, Transition Matrix, Steady State, Initial state probability distribution.

Authors : K. Meenakshi and M. Syed Ali
Title : T-S Fuzzy Stochastic Discrete-Time Neural Networks with Time-Varying Delays
Volume, Issue, Year : 5(4−B)(2017)
Pages : 225−233

Abstract: In this chapter, we intend to investigate the stability problem for discrete-time T-S fuzzy stochastic systems with time-varying delay. For a given T-S fuzzy stochastic system, our attention is focused on obtaining the sufficient conditions assuring its asymptotic stability controller for the unstable systems. By using a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the delayed neural networks to be globally. A numerical example is presented to show the effectiveness of the proposed method.

Keywords: Discrete-time neural network, Linear matrix inequality.

Authors : M.S.Khan, D.Dhamodharan, R.Krishnakumar and A.H.Ansari
Title : Cone $\mathcal{C} $-class Function on Some Common Fixed Point Theorems for Contractive Type Conditions in Random Cone Metric Space
Volume, Issue, Year : 5(4−B)(2017)
Pages : 235−245

Abstract: In paper we discuss the some common fixed point theorems for contractive type conditions in random cone metric space via Cone $\mathcal{C} $-class function.

Keywords: Common fixed point, random cone metric space, $C$-class function.

Authors : A. K. Dutta, D. K. Basnet, K. D. Choudhury and S. R. Barbhuiya
Title : Direct Product of General Doubt Intuitionistic Fuzzy Ideals of $BCK/BCI$-algebras with Respect to Triangular Binorm
Volume, Issue, Year : 5(4−B)(2017)
Pages : 247−257

Abstract: In this paper, we introduced the concept of $(\in,\in\vee q_k)$- doubt intuitionistic fuzzy subalgebra and $(\in,\in\vee q_k)$-doubt intuitionistic fuzzy ideals in BCK-algebra with respect to triangular binorm by using the combined notion of not quasi coincidence $(\overline q) $ of a fuzzy point to a fuzzy set and the notion of triangular binorm. We define direct product of $(\in,\in\vee q_k)$-doubt intuitionistic fuzzy sets and direct product of $(\in,\in\vee q_k)$-doubt intuitionistic fuzzy subalgebras/ideals of $BCK/BCI$-algebras and investigate some related properties.

Keywords: $BCK$-algebra, Doubt fuzzy ideal, $(\in,\in\vee q_k)$-doubt fuzzy subalgebra,$(\in,\in\vee q_k)$-doubt fuzzy ideal, $(\in,\in\vee q_k)$- doubt intuitionistic fuzzy subalgebra,$(\in,\in\vee q_k)$- doubt intuitionistic fuzzy ideal, Direct product.

Authors : M.G.Ashok Kumar and E.Krishnan
Title : Affine Semigroups in an Algebra
Volume, Issue, Year : 5(4−B)(2017)
Pages : 259−263

Abstract: In this paper, we consider certain affine subspaces of an algebra, which are also multiplicative subsemigroups of the algebra. We characterize those lines in an algebra which consists solely of idempotents and which turn out to be subsemigroups of algebra. Also, any such line, if not a semigroup, generates a subsemigroup which is a plane. We also characterize those planes which arise as semigroups generated by such lines and also, those subsemigroups which are generated by such lines.

Keywords: Affine Space, Semigroup, Rectangular Band, Idempotent.

Authors : Sanjay Madhukarrao Deshpande
Title : Basics of Development of Integration and Series in India
Volume, Issue, Year : 5(4−B)(2017)
Pages : 265−270

Abstract: Most of the Indian Mathematicians form the period of Aryabha?a knows the arithmetic progression (AP) and sum of terms in AP. The present paper discusses the idea of Sama-gh\={a}ta-sa\.{n}kalita in Yukti-bh\={a}\d{s}a and Varasa\.{n}kalita in Ga\d{n}ita Kaumud\={i}. These ideas create the basic development of Integration and infinite series India. This work leads to evaluate integration as the summation of series.

Keywords: Ga?ita Kaumud\={i}, Naraya?a Pa??ta, Sama-gh\={a}ta-sa\.{n}kalita, Yukti-bh\={a}\d{s}a, Jye\d{s}\d{t}hadeva, Arithmetic Progression.

Authors : B. Anandh and R. Arimalar
Title : An Intuitionistic Fuzzy Meet Semi L-Ideal
Volume, Issue, Year : 5(4−B)(2017)
Pages : 271−276

Abstract: Intuitionistic fuzzy meet semi L-ideal of intuitionistic fuzzy meet subsemilattice is introduced in this Paper. Intuitionistic fuzzy meet semi L-ideal is defined and examples are given. The properties of intuitionistic fuzzy meet semi L-ideal are discussed. Intuitionistic fuzzy level meet semi L-ideals are defined, examples and properties are established.

Keywords: L-ideal, Intuitionistic fuzzy meet semi L-ideal, Subsemilattice.