iosr-Jm   Volume-11 ~ Issue-5 ~ Sep-Oct 2015

Abstract: A general description of the cut method is presented and an overview of its applications in a benzenoid graph is given. The Wiener index, the Szeged index and the hyper-Wiener index of a benzenoid graph is calculated based on the consideration of the elementary cuts and the pair of elementary cuts of the corresponding benzenoid graph.

Keywords: Benzenoid graph, cut method, hyper-Wiener index, Szeged index, Wiener index.

[1] S. Klavzar, I. Gutman and B. Mohar, Labeling of benzenoid systems which reflects the vertex–distance relations, J. Chem. Inf. Comput. Sci. 35 (1995) 590–593.
[2] I. Gutman and S. Klavzar, A method for calculationg Wiener numbers of benzenoid hydro-carbons and phenylenes, ACH Models Chem. 133 (1996) 389–399.
[3] D. Djokovic, Distance preserving subgraphs of hypercubes, J. Combin. Theory Ser. B 14 (1973) 263–267.
[4] P. Winkler, Isometric embeddings in products of complete graphs, Discrete Appl. Math. 7 (1984) 221–225.
[5] I. Gutman and S. Klavzar, An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons, J. Chem. Inf. Comput. Sci. 35 (1995) 1011–1014.
[6] M. Randic, Novel molecular descriptor for structure-property studies, Chem. Phys. Lett. 211 (1993) 478–483.
[7] D.J. Klein, I. Lukovits and I. Gutman, On the definition of the hyper-Wiener index for cycle-containing structures, J. Chem. Inf. Comput. Sci. 35 (1995) 50–52.

Abstract: The aim of this paper is to introduce and study some properties of supra topological spaces. We introduce the concepts of supra Q*g closed sets ,Supra Q*g open sets,Supra Q*closed sets and supra Q*open sets.
Keywords : supra Q*g closed sets, supra Q*g open sets, supra Q*closed sets, supra Q* open sets.

[1]. R.Devi, S.Sampathkumar, M.Caldas, On supra ∝- open sets and S ∝- continuous functions, General Mathematics, 16(2)(2008), 77-84.
[2]. N.Levine, Generalized closed sets in Topology, Rend. Circ. Palermo, 19(2)(1970), 89-96.
[3]. A.S.Mashhour, A.A.Allam, F.S.Mohmoud and F.H.Khedr, On Supratopological spaces, Indian J. Pure and Appl.Math., 14(4)(1983), 502-510.
[4]. M. Murugalingam and N. Lalitha, " Q* sets ", Bulletin of pure and applied sciences, Volume 29E issue 2 (2010), 369-376.
[5]. Pauline Mary Helen, Veronica Vijayan, PunithaTharani, " on supra g* closed sets ", International journal of Computer application, vol1( feb2013), 18-27.
[6]. P.Padma and S.Udayakumar, " Q*g closed sets in topological space ", international journal of Advance Research in Engineering and Applied Sciences. Vol.2, No.1( January 2015 ), 97 -105.

Abstract: In this paper we define the Srivastava functions H(n)B and H(n)C of matrix arguments in complex case,which are the generalization of the Hb and Hc Functions.

[1]. Mathai A. M. (1992): Jacobians of Matrix Transformations-I, Center for Mathematical Sciences, Trivandrum, India.
[2]. Mathai, A.M. (1993): Jacobians of matrix Tranoformations . Publication No. 23, Centre for Mathematical Sciences, Trivandrum, India.
[3]. Mathai A. M. (1993): Hypergeometric functions of Several Matrix Arguments, Center for Mathematical Sciences, Trivandrum, India.
[4]. Mathai A. M. (1993) : A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Oxford University Press, Oxford.
[5]. Mathari A.M. (1993) : Appell's and Humbert's Functions of Matrix Arguments, Linear Algebra and its Applications ; 183, pp. 201-221.
[6]. Mathai A.M. (1993) : Lauricella Functions of Real Symmetric Positive Definite Matrices, Indian J. Pure Appl. Math., 24(9), 513-531.

Abstract:In this paper we have introduced some new integrals involving multivariate polynomials suggested by Jacobi and Laguerre polynomials of real, symmetric and positive definite matrix (or complex symmetric matrix). All the results of this paper are new and have a wide range of application in the field of Mathematics Science.

[1]. Constantine A.G. (1963) : Some nonoental distribution problems in multivariate analysis, Ann. Math
Statist. 34, p.p. 1270-1285.
[2]. James A.T. (1961) : The distribution of non-central means with known covariance, Ann. Math. Statist.,
32, 874-882.
[3]. Subrahmaniam K. (1976) : Recent trends in multivariate normal distribution theory: On the Zonal
polynomial and other function of matrix argument, The India Journal of Statistics, 38 Ser. A, Pt. 3, 221-
258.
[4]. Mathai A.M. (1995a) : Special function of matrix argument I. Nat. Aca. Sci. India, Vol LXV Sec. A .
part III, p.p. 121 - 144 .
[5]. Mathai A.M. (1995b) : Special function of matrix argument II. Nat. Aca . Sci. India , Vol LXV, SecA.
Part IV, p.p.227 - 246 .

Abstract: Weibull distribution is a life data analysis, have been developed for failure rate, it is often used to analyse the field or test failure data to understand how items are failing. In this paper, we have studied an inventory model for two parameter Weibull distribution deterioration with selling price demand rate, in which shortages are allowed and are partially backlogged
Keywords: Deterioration Products, Partial Backlogging, Selling price demand, Shortage, Time varying Holding Cost, Weibull Distribution.

[1]. R.Amutha and Dr.E.Chandrasekaran "An Inventory Model for Deteriorating Products with Weibull Distribution Deterioration,
Time-Varying Demand and Partial Backlogging" ISSN [2229-5518], Vol.3,N0.10, (2012), pp.1-4
[2]. Azizul Baten and Anton Abdulbasah Kamil "Analysis of inventory-production systems with Weibull distributed deterioration",
International Journal of Physical Sciences, Vol.4, No.11, (2009), pp 676-682
[3]. R.Begum, S.K.Sahu and R.R.Sahoo "An EOQ Model for Deteriorating Items with Weibull Distribution Deterioration, Unit
Production Cost with Quadratic Demand and Shortages", Applied Mathematical Sciences, Vol.4,No.6, (2010), pp.271 -288
[4]. S.K.Ghosh and K.S.Chaudhuri "An Order-Level Inventory Model for A Deteriorating Item with Weibull Distribution Deterioration,
Time-Quadratic Demand and Shortages", AMO-Advanced Modeling and Optimization, Vol.6, No.1, (2004)
[5]. S.K.Goyal and B.C.Giri "Recent Trends in Modelling of Deteriorating Inventory", European Journal of Operational Research,
Vol.134, (2001), pp. 1-16

Abstract: In this paper we developed a new way of construction of digital signature and its verification. A new public key cryptosystem is also developed in this paper. All these public systems are based on discrete logarithm problem over finite extension field of the field Fp. These cryptosystems have all features of public key cryptosystems. The securities of these systems are based on the difficulty of finding discrete logarithms over 𝐹𝑝𝑛 with sufficiently large n.

Keywords: Digital Signature, Discrete Logarithm Problem, Hash Function,, Polynomials over Finite Fields, Primitive Polynomial, Public key cryptosystem.

[1]. Digital Signature Standard, Federal Information Processing Standards Publication 186, May 1994.
[2]. Lilly P.L., Saju M.I., A method of designing a public- key cryptosystem based on discrete logarithm problem, IRJPA-4(11), 2014, 628-630.
[3]. Saju M.I., Lilly P.L., A public key Cryptosystem based on discrete logarithm problem over finite fields Fpn, IOSR Journal of Mathematics(IOSR-JM)-Vol.11(1), 2015, 01-03.
[4]. Saju M.I., Lilly P.L., A method of designing block cipher involves a key bunch matrix with polynomial entries over F2, IOSR Journal of Mathematics(IOSR-JM)-Vol.11(2), 2015, 01-04.
[5]. Odlyzko A.., Discrete logarithms: The past and the future; Designs, Codes and Cryptography, (2000), 129-145.
[6]. McCurley K., The discrete logarithm problem, Proceedings of Symposia in Applies Mathematica, Vol.42, 1990, 49-74.

Abstract: Hydromagnetic and thermal radiation effects on unsteady free convective flow of a viscous incompressible flow past an exponentially accelerated infinite isothermal vertical plate with variable mass diffusion has been considered. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised to w T and the concentration level near the plate is raised linearly with time.

[1]. 1. Basant Kumar Jha, Ravindra Prasad and Surendra Rai , Mass transfer effects On the flow past an exponentially accelerated
vertical plate with constant heat flux- Astrophysics and Space Science, 181 (1991), 125-134.
[2]. 2. U.N. Das, R.K. Deka, V.M. Soundalgekar, Radiation effects on flow past an impulsively started vertical infinite plate. J. Theo.
Mech.1.(1996), 111-115.
[3]. 3. W.G. England , A.F. Emery , Thermal radiation effects on the laminar free convection boundary layer of an absorbing gas. J. Heat
Transfer.91(1969), 37-44.
[4]. 4. M.A. Hossain, H.S. Takhar, Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat and
Mass Transfer.31(1996), 243- 248.
[5]. 5. A. Raptis , C. Perdikis, Radiation and free convection flow past a moving plate, Int. J. App. Mech. Engg.4 (1999), 817-821.
[6]. 6. A.K. Singh, Naveen Kumar, Free convection flow past an exponentially accelerated vertical plate, Astrophy. Space Sci. 98
(1984), 245-258.

Abstract: In this paper, the recent developments of topology contributed by various authors are mentioned and definitions cited by them are also presented and rg*b-closed sets, and rg*b-continuous functions are studied in Supra Topological Spaces.

Keywords: rg*bμ –closed set, rg*bμ –open set

[1]. R. Devi, S. Sampathkumar and M. Caldas, On supra α-open sets and sα-continuous maps, General Mathematics, 16(2) (2008), 77-84.
[2]. M. Kamaraj, G. Ramkumar and O. Ravi, Supra sg-closed sets and supra gs-closed sets, International Journal of Mathematical Archive,2(11) (2011), 2413-2419.
[3]. N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo. 19(2)(1970), 89- 96.
[4]. A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F. H. Khedr, On supra topological spaced, Indian J. Pure and Appl. Math., 14(4) (1983), 502-510.
[5]. N. Palaniappan and K. C. Rao, Regular generalized closed sets, Kyungpook Math 33(2)(1993), 211- 219.
[6]. O. Ravi, G. Ramkumar and M. Kamaraj, On supra g-closed sets, International Journal of Advances in Pure and Applied Mathematics, 1(2)(2011), 52-66.
[7]. O. R. Sayed and T. Noiri, On subra b-open sets and supra b-continuity on topological spaces, European J. Pure and Applied Math., 3(2) (2010), 295-302.

Abstract: In this paper, we introduce the concept of some new kinds of connected domination number of a fuzzy graphs. We determine the domination numbers lsc , rsc and the total domination number of tcs, 
tds for several classes of fuzzy graphs and obtain bounds for the same. We also obtain the Nordhaus – Gaddum type result for these parameters.
Keywords: Fuzzy graphs, fuzzy domination , connected strong domination, disconnected strong domination, total connected strong domination, total disconnected strong domination, left semi connected domination, right semi connected domination.

[1]. C.Y.Ponnappan, P.Surulinathan, S.BasheerAhamad,(2014). The strong split domination number of fuzzy graphs. International
Journal of Computer &Organisation Trends, 3(1).
[2]. Harary, E., 1969. Graph Theory. Addison Wesley, Reading, MA. McAlester, M.L.N., 1988. Fuzzy intersection graphs. Comp.
Math. Appl. 15(10), 871-886.
[3]. Haynes, T.W., Hedetniemi S.T. and Slater P.J. (1998). Domination in Graphs : Advanced Topics, Marcel Dekker Inc. New York,
U.S.A.
[4]. Haynes, T.W., Hedetniemi S.T. and Slater P.J. (1998). Fundamentals of domination in graphs, Marcel Dekker Inc. New York,
U.S.A.
[5]. Kulli, V.R. and Janakiram B. (1997). The split domination number of graph. Graph Theory notes of New York. New York
Academy of Sciences, XXXII, pp. 16-19.
[6]. Kulli, V.R. and Janakiram B. (2000). The non-split domination number of graph. The Jounral of Pure and Applied Math. 31(5). Pp.
545-550.

Abstract: Let 𝑅 be a ring. A map 𝐹:𝑅→𝑅 is called left multiplicative generalized derivation if 𝐹 𝑥𝑦 =𝑑 𝑥 𝑦+𝑥𝐹(𝑦) is fulfilled for all 𝑥,𝑦 in 𝑅.Where 𝑑:𝑅→𝑅 is any map (not necessarily derivative or an additive mapping).The following results are proved:

Key words: Semi prime ring, Multiplicative generalized derivation, Left multiplicative generalized derivation.

[1] Anderson, F.w.:Letures on noncommutative rings. University of Oregon, Oregon (2002).

[2] BasudebDhara and Shakir Ali: On multiplicative (generalized)-derivations in prime and semiprime rings .Aequat. Math.86 (2013).

[3] Bresar, M.: On the distance of the composition of two derivations to the generalized derivations.Glasgowmath.J.(33), 89-93 (1991).

[4] Daif, M.N.:When is a multiplicative derivation additive. Int. J. Math. Math. Sci.14(3),615-618(1991).

[5] Daif, M.N.,Tammam EI-Sayiad, M.S.: Mulplicative generalized derivations which are additive.East-West J.Math.9(1), 31-37(1997).