## Issue 3 − BVolume 4 (2016)

ISSUE 3 − A ISSUE 3 − B
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 Article Type : Research Article Title : Supra $\alpha$-Locally Closed Sets and Supra $\alpha$-Locally Continuous Functions in Supra Topological Spaces Country : India Authors : S.Dayana Mary and N.Nagaveni

Abstract: The aim of this paper is to introduce a new type of sets called supra $\alpha$-locally closed sets and new type of functions called supra $\alpha$-locally continuous functions. Furthermore, we obtain some of their properties.

Keywords: S-$\alpha$-LC sets, S-$\alpha$-LC* sets, S-$\alpha$-LC** sets, S-$\alpha$-L-continuous and S-$\alpha$-L-irresolute.

S.Dayana Mary
Department of Mathematics, Coimbatore Institute of Technology, Tamilnadu, India.
E-mail: dayanamaryv@gmail.com

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 Article Type : Research Article Title : Reliability Importance of Components in Health Care System Country : India Authors : M.Reni Sagayaraj, A.Merceline Anita, A.Chandra Babu and A.Jeno

Abstract: In Today's Scenario, it's very rare to find an healthy person and the number of patients are increasing rapidly, reflecting recent life style changes. One of the Most Common disease in the World is Diabetes Mellitus. In this paper, we discuss the Diabetes Mellitus disease and the study of Reliability importance helps to take preventive measures from its disease. The knowledge of System Reliability helps the System in Health Care to be more perfect and improve its status for the betterment of the Society. Here, we deal with Series-Parallel-Series (SPS) Configuration Systems and using Fault Tree Analysis Approach we determine the Reliability of Cure for the treatment of Diabetes in a Diabetic Health Centre.

Keywords: System Reliability, Reliability Importance, Series-Parallel-Series Configuration System, Fault Tree Analysis Approach.

A.Merceline Anita
Department of Mathematics, Sacred Heart College, Vellore, Tamilnadu, India.
E-mail: mercelineanita@gmail.com

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 Article Type : Research Article Title : Cost Analysis for a Telecommunication System with Standby Transmitter Country : India Authors : Dr.Neelam Yadav and Amit Kumar

Abstract: This paper deals with the Cost analysis for telecommunication system with standby transmitter. The failure and repair rates of the subsystems follow the exponential distribution. One Standby control unit has been taken to improve system performance. Supplementary variables techniques have been used for mathematical formulation of the model. The steady state availability expression has been derived using normalizing conditions. Laplace transform is being utilized to solve the mathematical equations. Some particular cases and asymptotic behavior of the system have also been derived to improve the practical utility of the model. Cost function and availability of the system have been computed. The findings of the present paper will be highly useful to the telecommunication system to enhance system performance.

Keywords: Reliability function, Supplementary variables, Perfect Switching, Standby redundancy, Availability and cost function.

Department of Mathematics, L.S.Raheja College of Arts and Commerce, Santacruz (W), Mumbai, Maharastra, India.
E-mail: neelam.yd83@gmail.com

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 Article Type : Research Article Title : On Semi $\alpha$-Regular Pre-Semi Closed Sets in Bitopological Spaces Country : India Authors : T.Shyla Isac Mary and A.Subitha

Abstract: In this paper, we introduce a new class of closed sets and open sets in bitopological spaces, namely, $\tau_{1} \tau_{2}$-$s\;\alpha rps$-closed sets and $\tau_{1}\tau_{2}$-$s\;\alpha rps$-open sets and characterize the properties of this sets.

Keywords: $\tau_{1} \tau_{2}$-$s\;\alpha rps$-closed, $\tau_{1} \tau_{2}$-$s\;\alpha rps$-open and $\tau_{1}$-$\alpha rps$-open.

A.Subitha
Department of Mathematics, Nesamony Memorial Christian College, Marthandam, India.
E-mail: subithaaus@gmail.com

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 Article Type : Research Article Title : Radial Variation of Axial and Radial Velocity of Blood in Stenosed Artery in the Presence of Body Accelerations Country : India Authors : Neeta D.Kankane and N.S.Bodke

Abstract: The paper studies the flow of blood through a stenosed artery in the presence of body accelerations. The mathematical model is constructed by considering blood to be a Newtonian fluid. The artery is assumed to have axisymmetric shape. The shape of stenosis is time dependent. The present paper calculates both radial and axial velocities. The governing blood flow equations are solved using finite difference approximation numerically and radial variation of axial and radial velocities is discussed. These velocities are plotted for different times.

Keywords: Axial velocity, radial velocity, Body acceleration.

N.S.Bodke
Department of Mathematics, Dr.B.N.P.Arts, S.S.G.G.Commerce \& Science College, Lonavla, Pune, India.
E-mail: bodke.nitin@gmail.com

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 Article Type : Research Article Title : Edge Geodetic Domination Number of a Graph Country : India Authors : P.Arul Paul Sudhahar, A.Ajitha and A.Subramanian

Abstract: In this paper the concept of edge geodetic domination number of a graph is introduced. A set of vertices \textit{S} of a graph is an edge geodetic domination set (\textit{EGD}) if it is both edge geodetic set and a domination set of G. The edge geodetic domination number (\textit{EGD }number)\textit{ }of G\textit{, }$\gamma$\textit{g${}_{e }$}(G) is the cardinality of a minimum \textit{EGD} set. \textit{EGD} numbers of some connected graphs are realized. Connected graphs of order \textit{p }with EGD number \textit{p }are characterized. It is shown that for any two integers \textit{p} and \textit{q} such that 2 $\mathrm{\le}$ \textit{p }$\mathrm{\le}$ \textit{q}, there exist a connected graph G with $\gamma$\textit{g}(G) = \textit{p} and $\gamma$\textit{g${}_{e}$}(G) = \textit{q.} Also it is shown that there is a connected graph G such that $\gamma$(G) = \textit{p}, g${}_{e}$(G) = \textit{q} and $\gamma$\textit{g${}_{e}$} (G) = \textit{p} + \textit{q}.

Keywords: Geodetic number, Edge geodetic number, Geodetic domination number, Edge geodetic domination number.

P.Arul Paul Sudhahar
Department of Mathematics, Rani Anna Government College (W), Tirunelveli, Tamilnadu, India.
E-mail: arulpaulsudhar@gmail.com

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 Article Type : Research Article Title : Unsteady Hydromagnetic Gas Flow Along an Inclined Plane With Indirect Natural Convection in the Presence of Thermal Radiation Country : India Authors : B.Prabhakar Reddy

Abstract: The Numerical solution of an unsteady gravity-driven thermal convection flow of a viscous incompressible, electrically-conducting, absorbing-emitting, optically-thick gray gas along an inclined plane in the presence of thermal radiation and a transverse magnetic field effects are carried out. The Rosseland diffusion flux model is employed to simulate thermal radiation effects. The momentum and energy conservation equations are non-dimensionalzed and solved by using Ritz finite element method. The effects of Prandtl number $(P_{r} )$, Boltzmann-Rosseland radiation parameter $(K_{1} ),$ Hartmann number squared $(M^{2} ),$ porosity parameter $(K),$ Grashof number $(G_{r} ),$ time parameter $t$ and plate inclination $(a)$ on the velocity $(u)$ and temperature $(\theta )$ distributions are studied. Results obtained show that a decrease in the velocity and temperature occurs when Prandtl number and Hartmann number square root are increased. The velocity and temperature enhanced as Boltzmann-Rosseland radiation parameter and Grashof number are increased.

B.Prabhakar Reddy
Department of Mathematics, Geethanjali College of Engineering and Technology, Cheeryal (V), Keesara (M), Telangana, India.
E-mail: prabhakar.bijjula@gmail.com

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 Article Type : Research Article Title : Cordial and Product Cordial Labelings for the Extended Duplicate Graph of Kite Graph Country : India Authors : B.Selvam, K.Anitha and K.Thirusangu

Abstract: In this paper, we prove that the extended duplicate graph of kite graph is cordial total cordial , product cordial and total product cordial labeling.

Keywords: Graph labeling, Cordial labeling, Product cordial labeling, Kite graph.

B.Selvam
Department of Mathematics, S.I.V.E.T. College, Gowrivakkam, Chennai, India.
E-mail: kbmselvam@gmail.com

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 Article Type : Research Article Title : Correction to the Number of Homomorphisms From Quaternion Group into Some Finite Groups Country : China Authors : Bo Shang and Jinke Hai

Abstract: Using only elementary group theory, we determine the number of homomorphisms from quaternion group into some finite groups.

Keywords: The dihedral group, the quaternion group, the modular group, homomorphisms.

Jinke Hai
College of Mathematics and Statistics, Qingdao University, Qingdao, China.
E-mail: haijinke2002@aliyun.com

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 Article Type : Research Article Title : Divisor Cordial Labeling for Vertex Switching and Duplication of Special Graphs Country : India Authors : G.V.Ghodasara and D.G.Adalja

Abstract: A divisor cordial labeling of a graph $G$ with vertex set $V$ is a bijection $f$ from $V$ to $\{1,2,\ldots,| V |\}$ such that an edge $e = uv$ is assigned label 1 if $f(u) | f(v)$ or $f(v) | f(u)$ and label 0 otherwise, then $|e_f(0)-e_f(1)| \leq 1$. A graph which admits divisor cordial labeling is called divisor cordial graph. In this paper we prove that vertex switching of gear graph, shell graph, flower graph are divisor cordial. We also prove some result on divisor cordial labeling for the graphs resulted from the duplication of graph elements.

Keywords: Divisor cordial graph, Vertex switching, Duplication of graph.

Department of Mathematics, Marwadi Education Foundation, Rajkot, Gujarat, India.

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 Article Type : Research Article Title : Cryptographic Protocol Country : India Authors : Dr.S.Vasundhara

Abstract: Theoretical research in number theory has a long tradition. Since many centuries the main goal of these investigations is a better understanding of the abstract theory. Numbers are basic not only mathematics, but more generally for all sciences, a deeper knowledge of their properties is fundamental for further progress. Remarkable achievements have been obtained. Among the unexpected features of the recent developments in technology are the connections between classical arithmetic and on the one hand, and new methods for reaching a better security of data transmission on the other. In this paper we illustrate the aspect of the subject by showing the modern cryptography and its types like public key cryptography and private key cryptography its properties.

Keywords: Number theory, Cryptography.

Dr.S.Vasundhara
Department Mathematics, G.Narayanamma Institute of Technology \& Science For Women, Shaikpet, Hyderabad, India.
E-mail: vasucall123@gmail.com

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