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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[2] Kecheng Shen(1988) : On the relation between component failure rate and stree – strength distributional charecterstics , Micro
Electronics Reliability , vol. 28 , pp:801-812.
[3] M.N.Gopalan and P.Venkateswarlu(1982) : reliability analysis of time dependent cascade system with deterministic cycle t imes ,
Micro Electronics Reliability , vol. 22, pp:841-872.
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[8] M.N.Gopalan and P.Venkateswarlu(1983) : Reliability analysis of time dependent cascade system with random cycle times , vol.
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,

[1] Alexander, J.W. (1915). Function which map the interior of the unit circle upon simple regions.Annals of Mathematics. (17), 12-22.
[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.

Abstract :The present paper concentrates on the theory of dominator coloring in graphs and focuses on resolving the dominator chromatic number of interval graphs. Some categorized interval graphs are selected in this process of study. To facilitate the study and to establish the results, emphasis is given to the analogy between the nature and coherence of the intervals, which in turn played an essential role in determining the dominator chromatic number of the interval graphs. An interval graph is a circular- arc graph that can be represented with a set of arcs that do not cover the entire circle. A dominator coloring of a graph G is an assignment of colors to the vertices of G such that no two adjacent vertices are assigned with the same color and every vertex dominates all vertices of at least one color class, where a color class is the set of all vertices, having the same color. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G and is denoted by χd(G). Mathematics Subject Classification: 05C15
Keyword: Chromatic number, dominator chromatic number, interval graphs

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Abstract :Analysis of count data is widely used in medical studies, epidemiology, ecology and many research of interest. Basically negative binomial (NB) will used when Poisson data lead to heterogeneity or over dispersion. Thus, when a Poisson data proof of over dispersion phenomenon exists NB will be replaced for that purpose. We modeled categorical age of death rate cases as the dependent variable comparing a NB and Poisson regression. To con- duct this purpose; SAS was used by using PROC GENMODE procedure. To estimate parameter according categorical age of death rate, we did standardization of rate via NB and Poisson distribution. The objective of this study was to compare Negative Binomial Death Rate (NBDR) and Poisson Death Rate (PDR).
Keyword: negative binomial, Poisson death rate, count data

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Abstract :In the present paper, we analyses a tow-identical unit deteriorating standby system model having two types of workload i.e. normal and fast. The system works under varying workload. When workload is more the standby also starts operation and the system becomes parallel until the workload decreases. The unit may be repairable under normal and fast repair mode. Using regenerative point's technique different measures of reliability are obtained.
Keyword: Deteriorating, Reliability, Standby, Repair.

[1] P.L. Shinde and M.M. Mahale(2006): On the distribution of the number of failed components in a consecutive k-out-of-n: F
system, 'IAPQR Transaction' Vol. 31, No. 1. , pp-19-26.
[2] Ketan A. Gajjar, K.K. Shah and M.N. Patel (2007): Bayesian Reliability Analysis of certain Types of Systems with Discrete
Failure Time, ' IAPQR Transaction' Vol. 32, No. 1, pp- 75-85.
[3] Gupta, Praveen and Sammerwar, Manish (2001): Stochastic analysis of two Wait power engine models, Ultra Science, V. 12,pp 27-
36.
[4] Gupta, P and Deshmukh, K (2002): Cost analysis of two-identical unit standby system with varying workload and maintenance,
'IAPQR' Transaction, Calcutta, vol 27, no. 2.pp 12-17.
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[6] Bazovsky, I. (1961): Reliability Theory and Practices, Practices Hall, Englewood Cliffs, New Jersey.