iosr-Jm   Volume-2 ~ Issue-6

Abstract :We have endeavoured here to depict an interactive inventory model between producer (supplier) and prospective buyer (vendor) in the presence of an extraordinary purchase and credit period with two parameter weibull deterioration for items with ramp type demand. The case of shortages is also studied.Additonally, we deal with the problem of a supplier disposing a large inventory level through an offer to a prospective buyer in the form of a credit period. From our model we confirm that the behaviour of replenishment period and trade credit period and change of the total variable cost observed from numerical evidence should be interpreted with caution in any business organisation.
Keywords: credit period, ramp type demand , shortages, Weibull deterioration

[1] WU Kun-Shan, An EOQ inventory model for items with weibull distribution deterioration, ramp type demand rate and partial backlogging, Production Planning and control, 12(2001), 787-793.
[2] Sanjay Jain and Kumar Mukesh ,An EOQ Inventory model with ramp type demand, weibull distribution deterioration and starting with shortage, OPSARCH Vol.44(2007), 240-250.
[3] T.Chakrabarty, B.C. Giri,. and K.S.Chaudhury, An EOQ Inventory Model for items with weibull distribution deterioration, shortages and trended demand: An extension of Philip's model, Computers and Operations Research, 25(1998), 649-657.
[4] A.K.Jalan, R.R.Giri,.a nd K.S.Chaudhuris, EOQ model for items with weibull distribution deterioration, shortages and trended demand, International Journal of system science, 27(1996), 851-856.
[5] N.H.Shah, and Y.K.Shah, A Discrete-In-Time Probabilistic Inventory Model for Deteriorating Items under conditions of Permissible delay in Payment, International Journal of System Science, 29(1998), 121-126.
[6] S.P.Aggarwal, and C.K.Jaggi, Ordering policies of Deteriorating items under conditions of permissible delay in payments. Journal of operational research society, 46(1995), 658-662.
[7] Manisha Pal, And K.Sanjay Ghosh, An Inventory model with stock dependent demand and general rate of deterioration under conditions of permissible delay in payments,vol.44( 2007), OPSEARCH, 227-239.
[8] S. Hardik., J.Shah, Bhavin and H.Shah Nita.: An EOQ model for deteriorating items with progressive payment sheme under DCF approach, Vol.43(2006), OPSEARCH, 238-257.
[9] A.M.M. Jamal, B.R Sarkar, S.Wang, Optimal payment time for a retailer under permitted delay payments by the wholesaler. International Journal of Production Economic 66(2000), 59-66.
[10] G.Padmanabhan, and P.Vrat, EOQ model for permissible items under stock dependent selling price, European Journal of operational Research, 8.

Abstract:In this paper we study about the prime square dominating graph and we observe that a prime dominating graph need not be prime square dominating graph, but every prime square dominating graph is prime dominating graph. In this paper we got interesting characteristics theorems such as if a graph contains an odd cycle then it is not a prime square dominating graph, if graph is bipartite then it is a prime square dominating graph. Moreover we discussed about minimal prime square dominating graph and provide necessary examples.
Keywords: Dominating graph, Prime dominating graph, Prime Square Dominating graph, minimal dominating, minimal prime square dominating graphs.

[1]. Harary, "Graph Theory", addition weslely 1969.
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[4]. S.R. Sudarshan Iyangar, Somindu C.R and Swathi Srivatsan, "Discrete Mathematics and its Applications", Narosa Publication, New Delhi, 2006. PP169-174.
[5]. Satyanarayana Bhavanari and Syam Prasad K., "Discrete Mathematics and Graph Theory", Printice Hall of India, New Delhi, 2009.
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Abstract: Number Theory is one of the oldest branches of mathematics, which inherited rich contributions from almost all greatest mathematicians, ancient and modern. Nathanson [1] was the pioneer in introducing the concepts of Number Theory, particularly, the "Theory of Congruences‟ in Graph Theory, thus paving way for the emergence of a new class of graphs, namely "Arithmetic Graphs". Inspired by the interplay between Number Theory and Graph Theory several researchers in recent times are carrying out extensive studies on various Arithmetic graphs in which adjacency between vertices is defined through various arithmetic functions.
Keywords: Arithmetic graph, Domination, Total domination, Independent domination, Connected domination.

[1]. Nathanson, Melvyn B. - Connected components of arithmetic graphs, Monat. fur. Math, 29, 1980. 219 – 220.
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Abstract: In this paper consider a classical model of stellar explosion ,in a conducting gas of self gravitating gas propagating in a non uniform atmosphere. Similarity principle has been used to reduced the equation governing the flow to ordinary differential equation . Analytical solution of this classical model have been investigated .

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[2]. J. Sedov ; Similarity and dimensional methods in mechanics
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[4]. Singh, J.B. and Srivastava ; Anexially symmetric explosion model in magnetogasdynamics, Astrophy and Space Sci. 79 :355,
(1981).
[5]. Vishwakarma, J.P. & Yadav, A.K ; Eur. Phys. J.B. 34,25: 247, (2003)
[6]. Chakrabarti,S.K.&Mandal S; Astrophys. Space Sci. 309:163-166, (2007)
[7]. Singh, L.P. and Hussain: An analytical study of strong non planer shock waves in magnetogasdynamics, J. Adv. Theor. App. Mech., 3 no 6 :291, (2010)

Abstract: In this paper, the order,size and degree of the nodes of the isomorphic fuzzyhypergraphs are discussed. Isomorphism between fuzzy hypergraphs is proved to be an equivalance relation.
Keywords - Fuzzy hypergraph, co-weak isomophismr, weak isomorphism, equivalence relation

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Abstract: The aim of the present paper is to establish Mellin transform of the product concerning Fox's Hfunction and the multivariable H-function. The result established here are quit general in nature and a large number of known and new integrals can be obtained by specializing the parameters suitably of the various functions involved in them. The present integral generalizes most of the infinite integrals derived earlier by various authors.

[1] P. Anandani and H. S. P. Srivastava: On Mellin transform of product involving Fox‟s H -function and a generalized function of two
variables, Comment. Math. Univ. St. Pauli. XXI-2 (1972), 35-42.
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[5] U. C. Jain: On an integral involving the H-function, The Journal of the Australian Mathematical Society, VIII-2 (1968), 373-376.
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[8] P. Skibińiski: Some expansion theorems for the H-functions, Ann. Polon. Math, 23 (1970), 125-138.
[9] H. M. Srivastava, K.C. Gupta and S. P. Goyal: The H-functions of one and two variables with applications, South Asian Publishers,
New Delhi-Madras, 1982.

Abstract: In this paper, we define and study k-derivations and symmetric bi-k-derivations on a -Banach algebra. We also define and study hk-derivation d on the projective tensor product V V / p  for the h- and k-derivations 1 d and 2 d on -Banach Algebras V(F) and ( ) / V Frespectively.
AMS subject classification Code: 17D20 (γ, δ)
Key words: k-derivation, symmetric bi-k-derivation, centroid.

[1] C.Selvaraj and S.Petchimuthu, On strongly Prime Gamma Rings, International J. of Algebra, 2(2008), 933-943.
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[6] M. Ali Ozturk and Young Bae Jun, On the Centroid of the prime Gamma rings, Comm. Korean Math. Soc., 15 (2000), 469-479.
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[8] N.B.Okelo, M.O. Okongo and S.A. Nyoukiti, On projective Tensor Norm and Norm-Attainable - derivation, Int. J.Contemp. Math. Sciences, 5 (2010), 1969-1975.
[9] S.Chakraborty and A.Ch. paul, On Jordan k-derivation of 2-torsion free prime N  -Rings, Journal of Mathematics, 40 (2008), 97-101
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