iosr-Jm   Volume-13 ~ Issue-3 ~ May-June 2017

Abstract: The present theory of consistent estimators of the parameters of statistical structures of homogeneous Gaussian fields can be used, for example, in the reliability predication of different engineering designs. In the paper there are discussed Gaussian homogeneous fields statistical structuresE S i I i , , ,  in Banach space of measures. We prove necessary and sufficient conditions for existence of such estimators.

Keywords: Consistent estimators, orthogonal, weakly separable, strongly separable statistical structures. Classification 62HO5, 62H12

[1]. Ibramhalilov A. Skorokhod. Consistent estimates of parameters of random processes. Naukova Dumka. Kiev (1980)
[2]. T. Jech. Set Theory. Springer, Berlin (2003),
[3]. A. Kharazishvili Topological aspects of measure theory. Naukova Dumka. Kiev (1984)
[4]. Z. Zerekidze. On weakly divisible and divisible families of probability measure. Bull Acad.Sci.Georgian SSR 113(2) 273-275
(1984)
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University. Vol. 2 215-220 (1969)

Abstract: The exponential distribution is perhaps the most widely applied statistical distribution in reliability. Anew continuous bivariate distribution called the bivariate beta-exponential distribution (BBE) that extends the bivariate exponential distribution are proposed. We introduce a new bivariate beta-exponential distributions (BBE) based on some types of copulas. Parametric and semiparametric methods are used to estimate the parameters of the models. Finally, Simulation is studied to illustrate methods of inference discussed and examine the satisfactory performance of the proposed distributions.

Keywords: Beta exponential distribution, beta G distribution, bivariate beta exponential distributions; Maximum likelihood method; copula;

[1]. Abd Elaal, M. K. Adham, S. A., and Malaka, H. M. (2017). Goodness of fit tests for some copulas an application for gene data. Advances and Applications in Statistical Sciences accepted.
[2]. Abd Elaal, M. K., Mahmoud,M. R., El-Gohary, M.M., and Baharth,L.A. (2016). Univariate and bivariate Burr Type X distributions based on mixtures and copula. International Journal of Mathematics and Statistics, 17(1),113-127. [3]. Adham, S. A., Abd Elaal, M. K., and Malaka, H. M. (2016). Gaussian copula regression application. Journal International Mathematical Forum,11, 1053-1065.
[4]. Adham, S. A., and Walker, S. G. (2001). A multivariate Gompertz-type distribution. Journal of Applied Statistics, 28(8), 1051–1065.
[5]. Adham, S. A., AL-Dayian, G. R., El Beltagy, S. H., and Abd Elaal, M. K. (2009). Bivariate half- logistic-type distribution. Academy of Business Journal, AL-Azhar University, 2, 92–107.

Abstract: Network analysis is an essential tool used in transport sector, information sector and also for the flow of matter and energy. Thus, choosing efficient route is essential for businesses and industries which aid distribution of goods and services optimally. This research addresses the problem of Dominion Paints Nig. Ltd in transporting their products from their production plant to stores of sales by presenting analysis of the shortest path using Dijkstra's Algorithm and it was concluded that the best paths found from the analysis will save the company less distance in transporting the paints and minimize time and cost of fueling their vehicles. The analysis shows that the best route which provides the shortest distance will be from node 1 – 3 – 5 – 8 ( Aluu – Rumuosi – Location – Mile 3), when transporting from Aluu (the production location) to Mile 3 the company's major sales point with a total distance of km. A TORA software (version 2006) was used in the analysis.

Keywords: Directed Network, node, activity, Dijkstra's Algorithm,Permissible route

[1]. Ahmat, K. A. (n.d.). Graph Theory and Optimization Problems for Very Large Networks. New York: City University of New York/Information Technology.
[2]. Brendan, H. a. (2005). Generalizing Dijkstra's Algorithm and Gaussian Elimination for solving MDPs. International Conference on Automated Planning and Scheduling/Artificial Intelligence Planning System, (pp. 151 - 160).
[3]. Chen, K. M. (2009). A real-time wireless route guidance system for urban traffic management and its performance evaluation. Papers of the 70th Vehicular Technology Conference Anchorage VTC, (pp. 1 -5).
[4]. Ebrahimnejad, S. A. (2011). Find the Shortest Path in Dynamic Network using Labelling Algorithm. Journal of Business and Social Science.
[5]. Goldberg, A. V. (n.d.). Point - to - Point Shortest Path Algorithms with Pre-processing. Silicon Valley:MicrosoftResearch.

Abstract: In this paper, for a marketing organization consisting of multi grades subject to the depletion of manpower (wastages) due to policy decisions with high or low attrition rate, is considered. An important system characteristic namely the mean time to recruitment is obtained for a suitable policy of recruitment when (i) wastages are independent and identically distributed exponential random variable and (ii) threshold for each grade has single component with exponential distribution and (iii) the inter-policy decisions form an order statistics.

Keywords: Hyper exponential, Loss of manpower(wastage),Order Statistics, Mean time to recruitment, Threshold with single components, Two types of policy decisions with high or low attrition rate

[1]. Sridharan.J, Parameswari.K and Srinivasan.A, A stochastic model on time to recruitment in a two grade man power system based on order statistics, International Journal of Mathematical Sciences and Engineering Applications 6(5) (2012):23-30.
[2]. Sridharan.J, Parameswari.K and Srinivasan.A, A stochastic model on time to recruitment in a two grade man power system involving extended exponential threshold based on order statistics, Bessel Journal of Mathematics 3(1) (2013):39-49.
[3]. Sridharan.J, Parameswari.K and Srinivasan.A, A stochastic model on time to recruitment in a two grade man power system involving extended exponential and exponential threshold based on order statistics, Archimedes Journal of Mathematics 3(1) (2013):41-50
[4]. Sridharan.J, Parameswari.K and Srinivasan.A, A stochastic model on time to recruitment in a two grade man power system based on order statistics when the threshold distribution having SCBZ property, Cayley Journal of Mathematics 1(2) (2012): 101-112
[5]. Parameswari.K ,Sridharan.J, and Srinivasan.A, Time to recruitment in a two grade manpower system based on order statistics , Antarctica Journal of Mathematics 10(2) (2013 ):169-181.

Abstract: In this paper, we have suggested a new technique to solve a MOLFPP by using new geometric averaging method. An algorithm is suggested for its solution. We have used some other techniques such as arithmetic averaging, geometric averaging, and new arithmetic averaging method to solve the same problem. New geometric averaging method gives better result than all those methods..

Keywords: Linear Fractional Programming Problem, Statistical average method, Arithmetic average, geometric average

[1]. Sen, Chandra., "A new approach for multi objective rural development planning", The Indian Economic Journal, Vol.30, pp.91-96.
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[5]. Sulaiman, N.A. and Othman, A.Q., "Optimal transformation Technique to solve multi-objective linear programming problem",
Journal of University of Kirkuk, Vol.2. No. 2, 2007

Abstract: In this note we propose that Dark Matter belongs to the complex space of the exceptional lie Algebra E6.This is why it has not been observed, but does have a fundamental frequency f .

Keywords: E6, Equiharmonic Lattice, Quarks, Hessian Polyhedron.

[1]. Arvanitaki, The Dark Matter signal, Weblog /2016/ 03. Online
[2]. J.A.de Wet, What are Quarks? IOSR-JM , Vol. 13 (2017)
[3]. Bruce Hunt, The Geometry of some Special Arithmetic Constants, Lecture Notes in Mathematics , Springer (1637)

Abstract: Inventory models play a major role in analysing the situations arising at places like food, vegetable markets, ware houses, textile markets, etc. In this paper we consider an inventory model for deteriorating products having demand which is function of a non linear function of time. and the cycle length of successive replenishments is a variable in the planning period. It is assumed that the cycle length in each cycle decreases in Arithmetic Progression. Shortages are allowed and are completely backlogged. The instantaneous state of inventory with shortages is derived. The total cost function of the horizon is obtained with suitable costs. The optimal pricing and ordering policies of the model are derived...............

Keywords: Perishable Inventory, Cycle Length, Demand Rate and Cost Function, Optimal Ordering Policies and Sensitivity Analysis.

[1]. Nahmias, S. (1982), "Perishable inventory theory: A review", Operations Research, Vol. 30, pp. 680 – 708.

[2]. Rafat, (1991), "Survey of Literature on Continuously Deteriorating Inventory Models", Journal of the Operational Research Society, Vol. 42, No. 1, pp. 27 – 37.
[3]. Giri ,B.C, Goyal, S. K. (2001), "Recent trends in modelling of deteriorating inventory", European Journal of Operations Research, Vol. 134, No. 1, pp. 97 – 112.
[4]. Roy, T. & ChaudhuriI, K. S. (2007), "An inventory model for a deteriorating item with price-dependent demand and special sale", International Journal of Operational Research, Vol. 2, No. 2, pp. 173 – 187.
[5]. Pal, M. & Ghosh, S. K. (2008), "An Inventory Model with Stock Dependent Demand and General Rate of Deterioration under Conditions of Permissible Delay in Payments", Opsearch, Vol. 44, No. 3, pp. 227 – 239.