iosr-Jm   Volume-3 ~ Issue-6

Abstract :Reliability analysis of time dependent stress strength system is carried out by considering each of stress variables are deterministic and strength variables are random – fixed and vice versa for different distributions .Reliability computations were done for different cycle lengths for different distributions. The number of cycles in any period of time 't' is assumed to be deterministic , stress and strength follows Exponential distribution and Rayleigh distribution , it is observed that the reliability of the system is decreased when the number of cycles increased and system reliability rapidly change in Rayleigh distribution than the Exponential distribution. In the deterministic stress and random fixed strength and vice versa, for various parameter values, reliability is computed.

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23, pp:355-366.

Abstract :We know that for any numerical method to be efficient and computational reliable, it must be convergent, consistent, and stable. This paper adopted the method of interpolation of the approximate solution and collocation ofits differential system at grid and off grid points to yield a continuous linear multistep method with a constant step size. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected grid and off grid points to yield a discrete block method. The basic property of this method is verified to be convergent consistent and satisfies the conditions for stability. The method was tested on numerical examples and found to compete favorably withthe existing methods in term of accuracy and error variation.
Keywords: interpolation, IVP, ODEs, colocation, approximate solution, independent solution, block method, convergent.

[1] Areo, E.A, Ademiluyi, R.A and Babatola, P.O. (2011). "Three-step hybrid linear multistep method for the solution of first order initial value problems in ordinary differential equations", J.N.A.M.P,19,261-266 [2] Awoyemi, D.O, Ademiluyi, R.A and Amusegham,(2007). "Off-grid points exploitation in the development of more accurate collocation method for solution of ODEs", J.N.A.M.P. 12, 379-386 [3] Badmus, A.M and Mishehia, D.W (2011), "Some uniform order block methods for the solution of first ordinary differential equation", J. N.A.M. P, 19, 149-154 [4] Fatokun, J, Onumanyi, P and Serisena, U.V (2005), "Solution of first order system of ordering differential equation by finite difference methods with arbitrary". J.N.A.M.P, 30-40. [5] Ibijola, E.A, Skwame, Y anKumleng G. (2011). "Formation of hybrid method of higher step-size, through the continuous multistep collation, American J. of Scientific and Industrial Research, 2(2), 161-1732) [6] Salmon H. Abbas (2006). Derivation of a new block method similar to the block trapezoidal rule for the numerical solution of first order IVPs.Science Echoes, 2 10-24 [7] Salmon H. Abbas (2006). Derivation of a new block method similar to the block trapezoidal rule for the numerical solution of first order IVPs.Science Echoes, 2 10-24 [8] Yahaya, Y.A and Kimleng, G.M. (2007). "Continuous of two-step type method with large region of absolute stability", J.N.A.M.P, 11, 261-268 [9] Zarina B.I., Mohamed, S., Kharil, I and Zanariah, M (2005). "Block method for generalized multistep method Adams and backward differential formulae in solving first order ODEs, MATHEMATIKA, 25-33 [10] Zarina B.I., Mohamed, S., Kharil, I and Zanariah, M (2005)."Block method for generalized multistep method Adams and backward differential formulae in solving first order ODEs, MATHEMATIKA, 25-33

Abstract :It is of interest in this work to analyze the sufficient conditions of Starlike and Convex functions using the geometric approach. The domains are preserved by the Conformal Mapping Principle.Furthermore, we established subordination properties for functions of the class T   n   using our new approach.
Keyword: Convexity, Starlikeness, Univalent, Unit disk,

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[2] Babalola, K.O. (2005). Some new results on a certain family of analytic functions defined by the Salagean derivative.Ph.D
Thesis.Department of Mathematics, University of Ilorin.
[3] Babalola, K.O. and Opoola T.O, Iterated Integral transformsof Caratheodory function and their applications to analytic and
univalent functions. Tamkang J. Math., 37(4)(2006), 355-366
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Mariner Publishing Co. Inc. Tampa, Florida).
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[9] Duren, P.L. (1983). Univalent functions. Springer-Verlag, New York.
[10] Goodman, A.W. (1983). Univalent functions. Mariner Publishing Co. Inc. Tampa, Florida.

Abstract :The extended star graph with cross-connections ESC (n, k) is a relatively new interconnection network topology, that has a hierarchical and recursive network that combines the versatility and robustness of star graph architectures. In this paper we have discussed some combinatorial results to find the number of nodes and edges of ESC (n, k).
Keyword: Network, star graphs, extended star graphs.

[1] A. Anto Kinsley, S. Somasundaram and C.Xavier, "Fault- tolerant Hierarchical Network of Star Graphs", Computer Science and
Informatics, Vol. 29(1), March 1999,20-35.
[2] K.Day and A. Tripathi, "A Comparative Study of Topological Properties of Hypercubes and Star Graphs", IEEE Transactions on
parallel and distribution systems Vol.5 (1), January 1994, 31-38.
[3] S. Pious Missier, M. Evangeline Prathibha and A. Anto Kinsley, April 2012, "Combinatorial results on the Extended Star Graph
Topology ES (n, k)", Outreach, Vol. 5, 2011, 79-82.