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

Abstract: In this paper an attempt has been made to present a unified theory of the classical statistical distributions associated with generalized beta and gamma distributions of one variable. The probability density function is taken in terms of the Multivariable H-function. In particular, the characteristic function and the distribution function are investigated. .

[1]. Carlson, B. C.: Special functions of Applied Mathematics, Academic Press, NewYork, 1977. 7
[2]. Erdelyi, A. et. al. Higher Transcendental Functions, Vol. 1 McGraw-Hill, New York, 1953. 6
[3]. Erdelyi, A.: Higher Transcendental Functions, Vol.II, McGraw-Hill, New York, 1953. 5
[4]. Exton, H. Handbook of Hypergeometric Integrals, Ellis Horwood Ltd., Chichester, 1978. 3
[5]. Mathi, A. M. & Saxena, R. K.: On a generalized hypergeometric distribution, Metrika 11 (1966), 127-131. 1

Abstract: In this paper, we will discuss the further properties of some new types of set which have been defined with the help of ideal. We also characterize these sets, generalized continuities and - extremally disconnectedness in ideal topological spaces.

Keywords: t-I-set, - open set, weakly I-locally closed set, -set.

[1] A. Acikgoz and S. Yuksel, Some new sets and decompositions of -continuity, -I-continuity, Continuity via Idealization, Acta Math. Hungar., 114(1-2)(2007), 79 - 89.
[2] D. Andrijevic, On b-open sets, MATHEMAT, 48 (1996), 59 - 64.
[3] D. Andrijevic, On the topology generated by preopen sets, Mathemathhkh Bechhk, 39 (1987), 367 – 376.
[4] G. Aslim, A. C. Guler and T. Noiri, On decompositions of continuity and some weaker forms of continuity via idealization, Acta Math. Hungar., 109(3) (2005), 183 – 190.
[5] C. Bandyopadhyay and S. Modak, A new topology via -operator, Proc. Nat. Aca. Sci.India, 76(A), IV(2006), 317 - 320.

Abstract: in the conventional one-dimensional mathematical modelling of fibre-reinforced thin-walled structures it is assumed that fibres have negligible thickness and they are perfectly flexible. Consequently, the constitutive equation forfinite deformations of fibre-reinforced elastic solids involves no natural length. Based on incorporatingfibre bending stiffness into a continuum theory, asymmetric linearised elasticity theory that takes into consideration the effects of fibres bending stiffness, has been produced in[1]. Relatively, an accurate 2d thin-walled structures modeling has been presented in............

Keywords: fiber bending stiffness, beam deflection, couple-stress, asymmetric elasticity, intrinsic material area or length parameter.

[1] Spencer, A.J.M. and K.P. Soldatos, Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness. International Journal of Non-Linear Mechanics, 2007. 42(2): p. 355-368.
[2] Soldatos, K.P., Towards a new generation of 2D mathematical models in the mechanics of thin-walled fibre-reinforced structural components. International Journal of Engineering Science, 2009. 47(11-12): p. 1346-1356.
[3] Farhat, A.F. and K.P. Soldatos, Cylindrical Bending and Vibration of Polar Material Laminates. Mechanics of Advanced Materials and Structures. 22(11): p. 885-896.
[4] K.P. Soldatos and A.F. Farhat, On Reissner's displacement field in modelling thin elastic plates with embedded fibres resistant in bending. IMA Journal of Applied Mathematics, 2016.
[5] Han, S.M., H. Benaroya, and T. Wei, Dynamics of transversely vibrayion beams using four engineering theories Journal of sound and vibration 1999. 225(5).

Abstract: In this paper, an organization subjected to a random exit of personnel due to policy decisions taken by the organization is considered; there is an associated loss of manpower if a person quits the organization. As the exit of personnel is unpredictable, a recruitment policy involving two thresholds, optional and mandatory is suggested to enable the organization to plan its decision on appropriate univariate policy of recruitment. Based on shock model approach, three mathematical models are constructed using an appropriate univariate policy of recruitment................

Keywords: Manpower planning, Shock models, Univariate recruitment policy,Hypo-Exponential distribution, Exchangeable and Constantly Correlated Exponential Random Variables.

[1]. Barthlomew.D.J. and Morris.B.R..1971.Aspects of Manpower Planning, Elsevier Publishing Company. New York.
[2]. Barthlomew.D.J and Forbes.A.F., Statistical Technique for Manpower Planning, John Wiley and Sons(1979).
[3]. Brindha.M &Srinivasan.A.,Stochastic Model on the Time for Recruitment in a Single Graded Manpower System Associated with a Bivariate Policy of Recruitment I, Acta Ciencia Indica(2008),Vol XXXIVM,No.4,pp (1959-1963).
[4]. Brindha.M &Srinivasan.A.,Stochastic Model on the Time for Recruitment in a Single Graded Manpower System Associated with a Bivariate Policy of Recruitment II, Acta Ciencia Indica(2008),Vol XXXIVM,No.4,pp (2005-2009 ).
[5]. Brindha.M &Srinivasan.A.,Stochastic Model on the Time for Recruitment in a Single Graded Manpower System Associated with a Bivariate Policy of Recruitment III, Acta Ciencia Indica(2008),Vol XXXIVM,No.4,pp (2103-2106).

Abstract: Acceptance sampling plans are introduced mainly to accept or reject the lots of finished products. There are several techniques available to control the quality. Some of the techniques are popularly used where testing involves destruction, for instance, in the manufacturing of crackers, bullets, batteries, bulbs and so on, it is impossible to go for 100% inspection. In this paper we optimized CASP-CUSUM Schemes based on the assumption that the continuous variable under consideration follows a Truncated Hyper-Exponential Distribution............. .

Keywords: CASP-CUSUM Schemes, type C, OC Curve, ARL, Truncated Hyper-Exponential Distribution

[1]. Akhtar P.Md.and Sarma K.L.A.P.(2004) "Optimization of CASP-CUSUM Schemes based on Truncated Gamma Distribution." Bulletin of pure and applied sciences, Vol-23E No.2, PP.215-223.
[2]. Beattie,B.W.,(1962), " A Continuous Acceptance Sampling Procedure based upon a Cumulative Sums Chart for number of defectives", Applied Stat5atistics, Vol. 11, No.2, pp. 137-147.
[3]. Hawkins, D.M. , (1992), "A Fast Accurate Approximation for Average Run Lengths of CUSUM Control Charts, Journal of Quality Technology", Vol. 24, No.1, pp. 37-43.
[4]. Jain,M.K. ,Iyengar,S.R.K. and Jain, R.K. "Numerical Methods of Scientific and Engineering Computations", Wiley Eastern Ltd., New Delhi.
[5]. Kakoty, S and Chakraborthy, A.B. , (1990), "A Continuous Acceptance Sampling Plan for truncated Normal distribution based on Cumulative Sums", Journal of National Institution for Quality and Reliability, Vol.2, No. 1, pp. 15-18.

Abstract: Non-standard method is an efficient numerical technique that provides a relatively simple way of creating discrete models that can correctly replicate the solution of physical applications that are modeled by linear and nonlinear differential equations. This method, which involves a transformation of the differential and non-linear components of the difference equations using the non standard rules 2 and 3, has become a very powerful member of the finite difference family with applications to diverse physical phenomena............

Keywords: Non-standard methods, Series circuit, Interpolation functions, Discrete model, Denominator functions

[1]. Anguelov R. and Lubuma J.M.S. (2000). On Mathematical Foundation of the Nonstandard Finite Differential Method, in Fiedler B, Grooger K, Sprekels .J (Eds), Proceeding of the International Conference on Differential Equations, EQUADIFF' 99 Word Scientific, Singapore, 1401-1403.
[2]. Anguelov R. and Lubuma J.M.S. (2003). Nonstandard Finite Difference Method by Nonlocal Approximatio Mathematics and Computers in Simulation 6, 465-475.
[3]. Fatunla S.O. (1988). Numerical Methods for Initial Value Problems in Ordinary Differential Equations, Academic press Inc., London.
[4]. Henrici, P. (1962). Discrete Variable Methods in Ordinary Differential Equations, John Willey & Sons, New York.
[5]. Lambert J.D. (1991). Numerical Methods for Ordinary Differential Systems-The Initial Value Problems. John Willey & Sons, New York. Mickens R.E. (1992). Finite Difference Schemes having the correct Linear Stability Properties for all Finite Step-sizes. Dynamics Systems and Applications 1, 329-340.

Abstract: This paper investigates an inventory model for deteriorating items under cost minimization with Weibull deterioration rate. The model is solved with salvages value associated in the system. A numerical example is taken to discuss the sensitivity of the models using Mathcad software.
Key words: Inventory, perishable, Weibull distribution, Deterioration

[1]. Covert, R. P., and Philip, G.C., (1973), An EOQ model for items with Weibull distribution deterioration. AIIE Transactions, 5,323-326
[2]. Hariga, M. (1996), Optimal EOQ models for deteriorating items with time-varying demand. Journal of Operational Research Society,47,1228-1246
[3]. Deb M and Chaudhuri, K.S. (1986) An EOQ model for items with finite rate of production and variable rate of deterioration. Opsearch, 23,175-181.
[4]. Chung, . and Ting, P. (1993), An heuristic for replenishment of deterioration items with linear trend in demand. Journal of Operational Research Society,44, 1235-1241
[5]. R.M.Bhandari and P.K.Sharma (2000) A single period inventory problem with quadratic demand distribution under the influence of Market policies', Eng. Science Vol. 12. No.2, pp. 117-127.

Abstract: In this paper, conditions under which linear control systems which are completely observable are stabilizable are investigated. Such systems are shown to be stabilizable provided they satisfy special computable conditions.
Keywords: Controllability, Observability, Stabilizability

[1]. W. P. Dayawansa, Asymptotic Stabilization of Low Dimensional systems in Non-linear Synthesis, 9 Birkhauser Boston: Progress in System and Control Theory, 1991.
[2]. J. P. LaSalle, The Stability and Control of Discreet Process, Spriger Velag: Appli Math Sc 62, 1988.
[3]. E. Lee and L. Markus, Foundations of Contol Theory, New York: John Wiley, 1967.
[4]. E. A. Coddington and L. N, Theory of Ordinary Differential Equations, New york: Dover inc, 1995.
[5]. K. A. Furuta, State Variable Methods in Automatic Control, New York: John Wilry, 1998

Abstract: In this paper, it is shown that in a linear control system which can be steered to zero target from different initial points, the ultimate trajectory is unique provided the control function is bang-bang.
Keywords: Bang-bang control Null-controllability, optimal trajectory

[1]. E. N. Chukwu, "On the Null-Controllability of Nonlinear Delay Systems with Rstrained control," J. M. Anal, vol. 78, pp. 283-299, 1990.
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[4]. E. Lee and L. Markus, Foundations of Contol Theory, New York: John Wiley, 1967.
[5]. J. U. Onwuatu, "Null Controllability of nonlinear infinite Neutral systems," Kyber Netica, vol. 29, no. 4, pp. 325-336, 1993

Abstract: This article is a survey on recent studies on middle convolution for linear and nonlinear special functions [J. Phys. A: Math. Theor. 43 (2010), 175204; J. Phys. A: Math. Theor. 42 (2009), 175208; Kumamoto J. Math. 19 (2006), 15–23]. Part of this survey is also based on the joint work with Y. Haraoka [J. Lond. Math. Soc. 76 (2) (2007), 438–450]. After recalling some basic facts concerning linear and nonlinear special functions, we give an overview of the recent results and current studies on middle convolution for special functions.
Keywords: Linear and nonlinear special functions; middle convolution MSC (2010): 34M55.

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Abstract: Irregular fractional factorial designs are widely used in screening experiments. Several analysis methods were proposed for identifying main effects and their interactions in the past twenty years. The goal of this research was to evaluate the performance of two Bayesian and two Frequentist approaches using some real data. The two Bayesian approaches are Bayes screening method and Empirical Bayes method. The two Frequentist approaches are traditional stepwise variable selection method and least angle regression method. The comparison of analysis methods is demonstrated using A & D optimality and A & D efficiency, the results obtained showed that the Frequentist approach is the best..............

Keywords: Bayesian, Frequentist, Irregular, and Screening

[1]. Box, G.E.P. & Meyer, R.D. (1993): Finding the Active Factors in Fractionated Screening Experiments; Journal of Quality Technology.
[2]. Shek, Y. W. (2012): Comparison of Analysis Methods for Non-regular Fractional Factorial Designs; University of California, Los Angeles.
[3]. Woods, D. C. & Lowis S. M. (2015): Model Selection via Bayesian information capacity designs for generalized linear models; Technometrics.
[4]. Jaynes, J., Ding, X., Xu, H., Wong, W.K., & Ho, C.M. (2013). Application of Fractional Factorial Designs to Study Drug Combinations. Statistics in Medicine, 32, 307-318.

[5]. Hongquan, Xu, Frederick K. H. Phoa & Weng Kee Wong (2009): Recent Developments in Nonregular Fractional Factorial Designs; Statistics Surveys. University of California, Los Angeles.

Abstract: Let (X.T) be a topological space.........

Keywords: Complement Topology, Arbitrary Intersections, Chain of Topologies

[1]. Angus E. Taylor and David C. Lay; Introduction to Functional Anal-ysis; Second Edition, John Wiley and Sons, New York, 1980.
[2]. Benjamin T. Sims; Fundamentals of Topology; Macmillan Publish-ing Co., Inc., New York; Collier Macmillan Publishers, London and Canada, 1976.
[3]. Edwards R.E.; Functional Analysis: Theory and Applications; Dover Publications Inc., New York, 1995.
[4]. James R. Munkres; Topology; Second Edition, Prentice-Hall of India Private Limited, New Delhi, 2007.
[5]. Seymour Lipschutz; Theory and Problems of General Topology; Schaum's Series, McGraw-Hill Publications, New York, 1965

Abstract: A compartmental mathematical model is established to study the dynamics of poverty, drug addiction and snatching. In the model, we have compartments, which allow for an approach of government and non-government interventions. The stability analysis in this model holds for an addiction and snatching free equilibrium. We constituted that, the equilibrium is locally asymptotically stable when the reproduction number is less than 1 and unstable when it is greater than 1. Numerical simulations of the systems have been presented to show the variations of the population in different situations...........

Keywords: Compartmental Model, Drug addiction, Intervention, Poverty, Reproduction Number, Snatching, Stability Analysis, ODE.

[1]. Zhao, H., Feng, Z. and Castillo-Chavez, C., The Dynamics of Poverty and Crime, Journal of Shanghai Normal University (Natural
Sciences· Mathematics), 2014, 225-235.
[2]. Oduwole, H. K. and Shehu, S. L., A Mathematical Model on the Dynamics of Poverty and Prostitution in Nigeria, Mathematical
Theory and Modeling, 3(12), 2013, 74-79.
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