iosr-Jm   Volume-12 ~ Issue-3 ~ May-June 2016

Abstract: Industry sector plays a very important role in the economic growth of the India. Composition & production of goods from Indian industrial depends on many factors and due to that factors, there may be shortterm (seasonal) and long-term (trend) variations in index if industrial production (IIP) in India. Therefore, the study on the effects of seasonal and trend on IIP in India is the prime objective of the present study. The data set of IIP is from National Data Sharing & Accessibility Policy (NDSAP), Government of India, it comprises of general IIP and 26 sub-sectors of industrial productions................

Keywords: IIP (Index of Industrial Production), Seasonal, Trend, ARIMA, Forecast

[1]. Wikipedia, Index of Industrial Production,Retrieved from https://:en.wikipedia.org/wiki/index_of_industrial_production dated 30/04/2016.

[2]. CSO, Study on internal consistency of all India index of industrial production (IIP) data. Ministry of Statistics & Programme Implementation, GoI.

[3]. India-All Economic Indicators, available in“ https://www.quandl.com/collections/india-economy-data” retrieved on 26th April, 2016.

[4]. World Bank (2015), GDP and its breakdown at current price in US Dollar, United Nations Statistics Division.

[5]. Economic Reforms in India: Task Force Report. University of Chicago, 2013, p 9-12

Abstract: IIn this paper we study the queueing system of unreliable server of production system which causes server breakdowns. The analysis of a finite-capacity N queueing system with a single server where service rule is FIFO has been done. A customer, on arrival to an idle server, is immediately taken for service; or else he joins the tail of the queue. During the service of a customer, one or more breakdowns may occur. It takes a random amount of time to clear the interruption. We consider a queueing system with troubled and non-troubled server breakdowns.............
Keywords: Queuing systems of finite capacity, server vacations, server breakdowns, FIFO

[1]. Avi-ltzhak, B. and Naor, P. (1963). "Some queueing problems with the service station subject to breakdowns". Operations Research, Vol 11, pp: 303-320.
[2]. Choudhury, G., Ke, J. C. and Tadj, L. (2009). "The N -policy for an unreliable server with delaying repair and two phases of service". Journal of Computational and Applied Mathematics, Vol 231, pp: 349-364.
[3]. D. Gaver Jr. (1962). "A waiting line with interrupted service, including priorities". Journal of the Royal Statistical Society, Vol. B24, pp: 73–90.
[4]. H. Masuyama and T. Takine. (2003). "Stationary queue length in a FIFO single server queue with service interruptions and multiple batch Markovian arrival streams". Journal of the Operations Research Society of Japan, Vol. 46(3), pp: 319–341.
[5]. H. White and L. Christie. (1958). "Queuing with preemptive priorities or with breakdown". Operation Research, Vol. 6(1), pp: 79–95.

Abstract: In this paper, generalized Hat functions operational matricesare proposed and combined with the method of steps to solve linear and nonlinear delay differential equations of fractional order. We convert the delay differential equationsof fractional order to non-delay differential equationsof fractional orderon a given intervalby apply the method of steps, and then apply the operational matrices for generalized Hat function on the obtained non-delay differential equationsof fractional order to transform linear and nonlinear non-delay differential equationsof fractional order into a system of algebraic equations and then find the solution.Two illustrative examples will be presented to show the accuracy and efficiencyof the proposed method. .................
Keywords: Fractional calculus, Delay differential equations, Fractional delay differential equations, Hat functions, Method of steps.

[1]. Loverro, A., “ Fractional Calculus: History, Definitions and Applications for theEngineer”, Department of Aerospace and Mechanical Engineering, University ofNotre Dame, Notre Dame, IN 46556, USA, May 8, 2004.

[2]. KolowankarK. M. and Gangal, “ Fractional Differentiability of no-where differentiable functions and dimensions ”, CHAOS V.6, No.4, American Institute of Physics, 1996.

[3]. PodlubnyI .,“ Fractional Differential Equations ” , Mathematics in Science and Engineering V198, Academic Press, 1999.

[4]. Wang Z., Huang X., Li N. and Song X., Chin. Phys. B, 5 050506(2012)

[5]. KilbasA. A., Srivastava H. M. and Trujillo J. J. , Theory and Applications of Fractional Di fferential Equations. Elsevier, Amsterdam(2006).

Abstract: This paper deals with an approximation theorem on proximate orders and this result is followed by some additional asymptotic properties of these functions. Finally proximate order is constructed for a class of GBSP,𝐹(𝛼,𝛽) regular in open hyper sphere of radius R under certain conditions, 𝜇1 .
Keywords: GBSP, Proximate order, Analytic function,

[1]. Juneja,O.P and Kappor, G.P., Analytic functions-growth aspects, research notes in mathematics:104, Pitamn advanced publishing program, Boston, London and Melbourne,1985.
[2]. Kasana, H.S., On the existence of proximate order for analytic functions, Ukrain, Mat. Zh.(kiev), 40(1988)
[3]. Levin, B. Ja., Distribution of zeroes of entire function, monographs, Amer. Math. Soc. Traslations, Vol.5(1968), revised edition (1980).
[4]. McCoy, P.A., Approximation of generalized biaxisymmetric potentials, J.Approx. Theory (1979), 125-137.

Abstract: A theoretical model, regarding the time dependence of several cosmological parameters, has been constructed in the framework of generalized Brans-Dicke theory, using its field equations for spatially flat FRW metric. An empirical expression of the scalar field parameter, written in terms of the scale factor, has been substituted into the field equations to obtain expressions of Brans-Dicke dimensionless parameter (𝜔) and the density of matter (𝜌), in terms of several relevant cosmological parameters. The dark energy, which is regarded as responsible for the accelerated expansion of the universe, is assumed to have generated from matter..........
Keywords: Densities of matter and dark energy, Time dependence of Brans-Dicke parameter and scalar field, Relative proportions of matter and dark energy, Dependence of cosmic expansion upon matter content, Time dependence of gravitational constant, Cosmology.

[1]. S. Perlmutter et al., Measurements of Omega and Lambda from 42 High-Redshift Supernovae, The Astrophysical Journal, 517,
1999, 565-586.
[2]. A. G. Reiss et al., Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and
Constraints on Dark Energy Evolution, The Astrophysical Journal, 607, 2004, 665-687.
[3]. T. Padmanabhan, Cosmological Constant-the weight of the vacuum, Physics Reports, 380, 2003, 235-320.
[4]. V. Sahni, The Cosmological Constant Problem and Quintessence, Classical and Quantum Gravity, 19, 2002, 3435-3448.
[5]. R. G. Vishwakarma, A Machian Model of Dark Energy, Classical and Quantum Gravity, 19, 2002, 4747-4752

Abstract: We develop a model for deteriorating item with linear demand and partial backorder. Often customers want to buy multiple items in one order, especially when delivery cost is high and there are alternative sellers available to turn to. In this situation, the rate of purchase for one inventory item is influenced by stock outs of another inventory items that were requested together. In this inventory model for a set of inter-dependent inventory items whose purchases are partially interdependent, we find an optimal solution for ordering terms and fill rate that minimize the costs of lost sales, backordering, ordering, and holding inventories. We find that purchase dependency influences the behavior of cost function, making it very different from the typical cost functions reported in previous research.

[1]. Bijvank, M. and I. F.A.Vis (2011) Lost-sales inventory theory: A review, European Journal of Operational Research 215, 1-13. [2]. Ghare, P. M. and Scharder, G. F. (1963) A model for exponentially decaying inventories.Jour. Ind. Engg., 14 : 238-243.
[3]. Federgruen, A, H. Groenevelt, and H.C. Tijms (1984) Coordinated replenishments in a multi-item inventory system with compound Poisson demands, Management Science 30(3) 344-357.
[4]. Lee K.Y. and Seo, J. (2007) A case study on the inventory management using the data mining. Journal of the Society of Korea Industrial and Systems Engineering (in Korean), 30(3), 20-27.
[5]. Liu, L. and Yuan, X. (2000) Coordinated replenishments in inventory systems with correlated demands, European Journal of Operational Research∗ � 1123, 490-503.

Abstract: In this paper we apply the notion of IR*-closed sets to present and the study a new class of function called contra IR*-continuous & almost contra IR*-continuous functions in ideal topological space. The relationship between their new sets and other sets of functions are established and some properties are discussed. .
Keywords: IR*-continuous functions, contra IR*-continuous functions, almost contra IR*- continuous functions, IR*-𝑇1 space, IR*-𝑇2space, IR*-𝑇12 space

[1]. S.P Arya and R.Gupta "on strongly continuous mappings" Kyunpook Math., J.14 (1974), 131-143.
[2]. J. Bhuvaneswari, A. Keskin, N.Rajesh, contra–continity via Topological Ideals.,J.Adv.Res.Pure Math.,3(1)(20),4051
[3]. Cameron D.E, Properties of S-closed spaces, Proc.amer.Math.Soc.72 (1978), 581-586
[4]. J.Dontchev contra-continuous functions and strongly S-closed spaces, Internal J.Math.Math.Sci.,19(1996),303-310
[5]. J.Dontchev On generalizing semi pre opensets, Mem. Fac. Sci. Kochi. Univ. Ser. A. Math 16(1995), 35-48.

Abstract: The present paper pursuit significantly analyses the free convection flow of viscous incompressible fluid bounded by two vertical plates filled with the porous matrix in the presence of transverse magnetic field with periodic temperature at one plate is discussed when both the plates are moving in opposite directions. The non-dimensional governing equations are analytically solved by applying the homotopy perturbation technique. The effect of various physical parameters is discussed in the flow field numerically, and presented by figures.1 .
Keywords: Free convection, Porous matrix, Suction, Skin-friction, Nusselt number, Viscous dissipation, Suction

[1]. Gersten, K. and Gross, J.F., Flow and Heat Transfer along a Plane Wall with Periodic Suction, Z. Angew. Math. Phys. 25 (3), 399-408, (1974).
[2]. Gulab, R. and Mishra, R.S., Unsteady Flow Through Magneto Hydrodynamic Porous Media, Ind. J. Pure Appl. Math. 8, 637-642, (1977).
[3]. Kaviany, M., Laminar Flow Through a Porous Channel Bounded by Isothermal Parallel Plates, Int. J. Heat Mass Transfer, 28, 851-858, (1985).
[4]. Attia, H.A. and Kotb, N.A., MHD Flow between Two Parallel Plates with Heat Transfer, Acta Mech., 117, 215-220, (1996).
[5]. Chamkha, A.J., Unsteady Hydro Magnetic Natural Convection in a Fluid Saturated Porous Medium Channel, Advances Filtra. Sep. Tech., 10, 369-375, (1996).

Abstract: This work is focused on the modeling of oil exports and non-oil exports in Nigeria. The value of R2 indicates that 73% is the proportion of variation in the observed values that is explained by the fitted model. The residuals of the model are uncorrelated. In the study only oil export is significant (P< 0.05) in the regression model. Hence, the fitted model is given as: 𝑌 = 201403.56+0.808𝑥1+ 0.083𝑥2. It is the basis for forecasting of the series of the first independent variable (𝑥1), oil export and second independent variable (𝑥2), non- oil export.1 .
Keywords: Multiple regression, oil export, non- oil export, Nigeria.

[1]. Kalu E. Okore (2009). College Statistics: A focus on hypothesis Testing. EL' Demak (Publishers) Enugu State Nig.
[2]. Suma'ila Idi Ningi (2013). An Analysis of banks of non-oil exports in Nigeria. American Journal of Contemporary Research. 3(1)
[3]. Emerole Gideon, Edeoga Georgina (2013). Empirical Analysis of the problems and prospects of export marketing of non-oil Agricultural product in Nigeria. 5(23)
[4]. Oliver Ike Inyama&Okpe Innocent Ikechukwu (2015). Crude oil production, prices, export and foreign exchangerate. Do they interact?. International Journal of Developing and emerging Economics. 3(2): 24-37.
[5]. NwankwoOdi (2015). Diversification of non-oil export product as a precondition accelerated real economic growth in Nigeria. Journal of Managerial Studies and Research. 3(7): 104-112.

Abstract: This study applied discriminant function to discriminate between tourists with high intention and low intention to revisit a tourist destination in Plateau State. Researches have shown that ecotourism destinations in Plateau state have lost their attractions due to lack of effective management, hence the need to identify the factors that could discriminate a tourist's intention to revisit. It is expected that a satisfied tourist would usually have high intention to revisit and could influence first time visitors positively at no cost to the park, through word of mouth publicity...............
Keywords: Ecotourism, Discriminant Function, Tourists, Destination Management and Public-Private-Partnership

[1]. Achieng, D. O., Hayombe, P. O., & Agong, S. G. (2014). Positioning ecotourism destinations in Kisumu County: Cultural Diversity Perspective. IOSR Journal of Computer Engineering (IOSR-JCE), 16-26.
[2]. Aigbavboa, C., & Thwala, W. (2013). A Theoretical Framework of Users‟ Satisfaction/Dissatisfaction Theories and Models. 2nd International Conference on Arts, Behavioral Sciences and Economics Issues, (pp. 48-53). Thailand.
[3]. Ajala, O. (2008). Employment and Income Potentiality of Tourism Development in Amhara Region Ethiopia. Ethiopian Journal of Environmental Studies and Management Vol.1 No.2 , 74-82.
[4]. Amati, C. (2013). "We all voted for it": experiences of participation in community-based ecotourism from the foothills of Mt Kilimanjaro. Journal of Eastern African Studies, 650-670.
[5]. Aniah, E. J., Eja, E., Otu, J., & Ushie, M. (2009). Resort Potentials as a Strategy for Sustainable Tourism Development in Plateau State, Nigeria . Journal of Sustainable Development Vol. 2 No.2, 73-79.

Abstract: Full Bayesian Significance Test (FBST) was derived by Pereira and Stern for testing a sharp (precise) null hypothesis. The evidence measure of this test has similar interpretation as the p-value of the frequentist significance test. However, it does not suffer from the drawbacks of the p-value. Pereira and his associates argued that full posterior distribution be used to obtain the evidence measure. One of the advantages of the Bayes procedure is that it can handle nuisance parameters easily by integrating this parameter from the posterior distribution...............
Keywords: Full Bayesian Significance Test, lognormal distribution, power of the test, p-value

[1] C. A. B. Pereira, and J. M. Stern, Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses, Entropy, 1, 1999, 99-110.
[2] M. R. Madruga, C. A. B. Pereira, and J. M. Stern, Bayesian evidence test for precise Hypotheses, Journal of Statistical Planning and Inference, 117, 2003, 185-198.
[3] C. A. B. Pereira, J. M. Stern, and S. Wechsler, Can a significance test be genuinely Bayesian? Bayesian Analysis, 3 (1), 2008, 79-100.
[4] C. A. B. Pereira, and J. M. Stern, Full Bayesian significance test for Coefficient of Variation, In Bayesian Methods with Applications to Science, Policy, and Official Statistics, EI George (editor), Creta, Greece: ISBA, 2001, 391-400.
[5] C. A. B. Pereira, and J. M. Stern, Model Selection: Full Bayesian approach, Environmetrics, 12(6), 2001, 559-568.

Abstract: double dominating set of 𝑮 is a restrained double dominating set of 𝑮 if for each 𝒙 𝝐 𝑽 𝑮 \ 𝑺 there exists𝒚 𝝐 𝑽 𝑮 \ 𝑺 such that𝒙𝒚 𝝐 𝑬 𝑮 . This paper, characterized the restrained double dominating sets in the lexicographic product of two graphs and determine sharp bounds for the restrained double domination numbers of these graphs.................
Keywords: Domination, lexicographic, restrained double domination, total domination

[1] Frank Harary and Teresa W. Haynes, Double domination in graphs,Arts Combin., 55, 2000, 201-213.

[2] Frank Harary and Teresa W. Haynes, Norhdhaus-Gaddum inequalities for domination in graphs, Discrete Mathematics, 155, 1996, 99-105

[3] J.A. Telle, Vertex partitioning problems: characterization, complexity and algorithms on partial k-trees, Ph.D. Thesis, University of Oregon, CIS-TR-94-18.

[4] G.S. Domkeet. al., Restrained Domination in Graphs, Discrete Mathematics, 203, 1999, 61-69.

[5] R. Kala and T.R. Nirmala Vasantha, Restrained double domination number of a graphs, AKCE J. Graphs. Combin., 5(1),2008, 73-82.

Abstract: In this paper we study the further properties of multivariable generalized Mittag-Leffler function E z j l j q j
j p j , , , ,    associated with Weyl fractional integral and differential operators.A new integral operator z j l j p j j q j w
, , , , , ,      depending on Weyl fractional integral operator and containing E z j l j q j j p j , , , ,    in its
kernel is defined and studied, namely,its boundedness. Also, composition of Weyl fractional integral and differential operators with the new operator z j l j p j j q j w , , , , , ,      is established................
Keywords: ...............

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201.MR1555014.JFM36.0471.01.
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