iosr-Jm   Volume-10 ~ Issue-3 ~ May-June 2014

Abstract: In this paper, we analyze the application of Simulation in Queueing model in tollgate are discussed. We visualize the activities of each lane is discussed. The main aim of this paper is, the management can easily find which system are busy and which system is ideal and the movement of each type of vehicles in each lane is simulated by the arrival and departure time. The numerical studies for various aspects are discussed.
Keywords: Mathematical model, Quantitative model, M/M/1 Queueing model, Simulation, Probability distribution.

[1]. ^Benedettini,O., Tjahjono, B.(2008). "Towards an improved tool to facilitate simulation modeling of complex manufacturing systems". International Journal of Advanced Manufacturing Techology 43 (1/2): 191-9.doi:10.1007/s00170-008-1686-z.
[2]. ^a b c Sundarapandian, V.(2009). "7.Queueing Theory". Probability, Statistics and Queueing Theory. PHI learning. ISBN 8120338448.
[3]. ^a b J.Banks, J Carson, B. Nelson, D.Nicol (2001). Discrete-Event System Simulation. Prentice Hall.p.3.ISBN 0-13-088702-1.
[4]. ^Also spelled queueing.askoxford.com. Retrived 2009-4-29.
[5]. ^Sokolowski, J.A., Banks, C.M (2009). Principles of Modeling and Simulation. Hoboken,NJ:Wiley.p.6.ISBN 978-0-470-28943-3.
[6]. Abbas-Turki, A., O.Grunder and A. Elmoudni. 2001. "Simulation and optimization of the public transportation connection system", In Proceedings of the 13th European Simulation Symposium, October 18-20, Marseille, France,pp.435-439

Abstract: In many econometric studies, especially those based on cross-sectional data, the assumption of a constant variance for the disturbance term is unrealistic. For example in consumer budget studies (micro consumption function), the residual variance about the regression function is very likely to increase with income. Also, in cross-sectional studies of firms the residual variance probably increases with the size of the firm. In a simple relation the dependent variable Y is explained by Z. Thus we assume y  f (z)  e.In this formulation y e Z2 var( )  var( )  . Using i i Z X just gives us a way of formulating the assumption about i i e Z2 var( )  in a fairly general manner. To make this assumption operational and general, it is convenient and quite plausible to specify the form of association g i i e Z2 var( )  where g is< the strength of heteroscedasticity, the lower the magnitude of g, the smaller the difference between the< individual variances. When g =0, the model is homoscedastic otherwise g  2 generally. This paper proposes a generalization of consistent standard error (CSE) estimators denoted by HC5.Comparison of this proposed estimator and other CSE estimators using various strength of sizes 25, 30, 35, 40, 45, and 50 was done The OLS estimator remains unbiased and the results showed that the developed estimator is indeed a generalization of all and produces a consistent and asymptotic efficient.
Keywords: Generalization, Heteroscedasticity Consistent Standard Error Estimator, Monte Carlo Simulation simple linear regression model, Error terms, weighting factor.

[1]. EICKER, F. (1967). Limit theorems for regression with unequal and dependent errors. In L. M. Le Cam &J. Neyman (Eds.),
Proceedings of the fifth Berkeley symposium on mathematical statistics and probability. Berkeley, CA: University of California
Press.
[2]. HUBER, P. J. (1967). The behavior of maximum likelihood estimation under nonstandard conditions. In L. M. Le Cam &J.
Neyman (Eds.), Proceedings of the fifth Berkeley symposium on mathematical statistics and probability. Berkeley, CA: University
of California Press.
[3]. HINKLEY, D. V.(1997). Jacknifing in unbalanced situations. Technometrics, 19, 285-292.
[4]. MACKINNON, J. G., &WHITE, G. P. (1985).Some hetreoskedasticity consistent covariance matrix estimators with improved
finite sample properties. Journal of Econometrics, 29, 305-325.
[5]. DAVIDSON, R., &MACKINNON, J. G.(1993). Estimation and inference in econometrics. Oxford:Oxford University Press.

Abstract: The present paper introduces a new class of separation axioms called α-generalized separation axioms using α-generalized open sets and also includes the study of the connections between these separation axioms and the existing α-separation axioms. Also, here, the concept of   - closed set has been coined and then   - separation axioms have been framed w.r.t   -open sets.
Key Words: α-open sets,   -closed sets, α g-closed sets, α-continuous &   - continuous / irresolute functions,  -Tk(k = 0,1,2) and αg- Tk(k= 0,1,2).

[1]. N. Levine, Generalized Closed Sets In Topology, Rend.Circ.Mat. Palermo(2) 19(1970),89-96 .
[2]. N.Levine, Semi-Open Sets And Semi- Continuity In Topological Spaces, Amer.Math. Monthly 70(1963),36-41.
[3]. O.Njasted, On Some Classes Of Nearly Open Sets, Pacific J. Math15(1965), 961-970.
[4]. K.Balachandran,P.Sundran, and H.Maxi, On Generalized Continuous Maps In Topological Spaces. Mem. Fac.Sci. Kochi Univ., ser.
A. math.,12, 5-13(1991).
[5]. R.Devi, H.Maki,&K. Balachandran, Semi-Generalised Closed Maps And Generalized Semi-Closed Maps, Mem. Fac. Sci. Kochi
Univ. Ser. A. math.,14,41-54(1993).

Abstract: Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. In this paper, we proposed the definition of T-product of intuitionistic fuzzy soft matrices with examples. Finally, We extend our approach in application of these matrices in decision making problem, by using medical diagnosis.
Keywords: Soft set, Fuzzy soft set(FSS), Fuzzy soft matrix, T-product of fuzzy soft matrix, Intuitionistic fuzzy soft set(IFSS), Intuitionistic fuzzy soft matrix.

[1] Atanassov .K.T,‟ Intuitionistic fuzzy set ",Fuzzy sets and systems,Vol.20(1), 1986, pp:86 -87.
[2] Cag man.N, Enginoglu.S,‟Soft set-Theory and uni-int Decision Making", European Journal of Operational
Research,207(2010),pp:848- 855.
[3] Cheitia.B and Das.P.K, ‟Some results of intuitionistic fuzzy soft matrix theory", Advances in applied Science Research(2012),3(1),
pp:412-423.
[4] De.S.K, Biswas.R and Roy.A.R,(2001),‟An Application of Intuitionistic fuzzy sets in Medical diagnosis", Fuzzy sets and
sytems,117,pp:209-213.
[5] Jalilul Islam Mondal.Md, Tapan Kumar Ray, ‟ Some Properties on Intuitionistic fuzzy soft matrices", International journal of
Mathematics Research,Volume5,Number2(2013),pp:267-276.

Abstract: A method of constructing a smallest congruence relation that is larger than a given equivalence relation on a lattice is explained. A method of constructing a congruence relation in which equivalence classes contain all least upper bounds and all greatest lower bounds for subsets of equivalence classes is explained; and this method constructs a smallest congruence relation with this property which is also larger than a given congruence relation in a lattice.
Keywords: Cardinal number, Transfinite induction principle, Congruence relation.

[1] G.Birkoff, Lattice Theory, Amer. Math. Soc., New York, 1948.
[2] T.S.Blyth, Lattices and ordered structures, Springer, London, 2005.
[3] F.Wehrung, A solution to Dilworth's congruence lattice problem, Advances in Mathematics, 216(2007)610-625.

Abstract: In most of the deteriorating items inventory model, demand rate has considered as a constant function. But in realistic situation these cost varying according to time. So in this paper, we developed a deterministic deteriorating inventory model with inflation in which demand rate are quadratic function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged. The model is solved numerically by minimizing the total inventory cost for cycle.
Keywords: inventory, deteriorating items, shortages, time dependent demand, partial backlogging, constant holding cost and inflation.

[1]. Abad, P. (1996). Optimal pricing and lot-sizing under conditions of perishability and partial backordering. Management Science ,42,1093–1104.
[2]. Abad, P. (2001). Optimal price and order-size for a reseller under partial backlogging. Computers and Operation Research 28,53–65.
[3]. Alamri, A. and Balkhi, Z. (2007). The effects of learning and forgetting on the optimal production lot size for deteriorating tems with time varying demand and deterioration rates. International Journal of Production Economics,107,125–138.
[4]. Buzacott, J.A., 1975. Economic order quantities with inflation. Operational Research Quarterly,26: 553-558.
[5]. Chang, C.T. (2004): An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. International Journal of Production Economics, 88, 307-316.

Abstract: In this paper, spherically symmetric space-time is studied with bulk viscous fluid in the context of Rosen's Bimetric Theory of Relativity. Here it is shown that the bulk viscous fluid does not exist in this theory.
Keywords: Spherically symmetric, bulk viscous fluid, Bimetric Relativity AMS Code-83C05 (General relativity)

[1]. Rosen N. (1940) General Relativity and Flat space I. Phys. Rev.57, 147.
[2]. Rosen N. (1973) A bimetric theory of gravitation I Gen. Rela. Grav. 04, 435-47.
[3]. Takeno H.(1982) Spherically symmetric space-time in general relativity.Prog. Theo.Phys.8,317-26
[4]. Gonner H.,Havas P.(2001) Spherically symmetric space-time with constant curvature J.Maths phys 42,1063
[5]. Shahoo P.K.(2008)Spherically symmetric cosmic string in Bimetric relativity.Int.J.Theo.Phys.47,3029-3034
[6]. Shahoo P.K.(2010) Kantowski-Sachs Cosmic string in Bimetric relativityInt.J.Theo.Phys 49,25-30
[7]. Israelit M(1981)Spherical Symmetric Fields in Rosen's Bimetric Theories of Gravitation, Gen. Rela .Grav.13,681-688
[8]. Bondi H(1999) Spherical Symmetric Model in General Relativity, Gen. Rela .Grav.31,1783-1805