iosr-Jm   Volume-2 ~ Issue-3

Abstract: Coefficient inequalities and distortion theorems are obtained for certain subclass of meromorphic starlike univalent functions with alternating coefficients. Further class preserving integral operators are obtained. 2000 Mathematics subject classification: 30 C 45.
Keywords: Regular, meromorphic, starlike, distortion theorem.

[1] F. M. Al – Oboudi, On univalent functions defined by a generalized salagean operator, Internat J. Math. Math. Sci., 27(2004), 1429-1436.
[2] M. K. Aouf and H. M. Hossen, New criteria for meromorphic p – valent starlike functions, Tsukuba J. Math. 17(2)(1993), 481- 486.
[3] M. K. Aouf and H. E. Darwish, Meromorphic starlike univalent functions with alternating coefficients, Utilities Math. 47(1995), 137-144.
[4] M. Darus, S. B. Joshi and N. D. Sangle, Meromorphic starlike functions with alternating and missing coefficients, General Mathematics (2006), 113 – 126.
[5] H. E. Darwish, Meromorphic p-valent starlike functions with negative coefficients, Indian. J. Pure Appl. Math. 33(7), 2002, 967-976.
[6] M. L. Mogra, T. R. Reddy and O. P. Juneja, Meromorphic univalent functions with positive coefficients, Bull. Austral. Math. Soc, 32(1985) 161-176.
[7] T. Ram Reddy and P. Thirupathi Reddy, Meromorphic p-valent
[8] starlike functions with alternating coefficients, Bull. Pure Appl.Math. Vol 3,(2009),254-262.
[9] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51(1975), 109-116.
[10] B. A. Uralegeddi and C. Somanatha, New criteria for meromorphic starlike univalent functions, Bull. Austral. Math. Soc. 43(1991), 137-140.

Abstract: In the most primitive times our ancestors employed the principle of one-one correspondence for counting purposes. In those days when the shepherd came back in the evening from the grazing fields he used to count his sheep by pebbles (or sticks) in his bag and he was satisfied if he had as many sheep as pebbles in his bag. Later on different vocal sounds were developed as word tally against the number of obstacles and later on symbols were evolved to stand for these numbers. In this way it took many thousands of years to come to 1, 2, 3,4, 5,…… which are called natural numbers "ℕ". The properties of natural numbers were developed from a few of simpler properties known as Peano's Axioms after the Italian Mathematician Guiseppe Peano(1858-1932) who gave these axioms in 1899.We thus find that the operations of addition and multiplication are fully defined in the set of natural numbers and then union , intersection in different sets. After a long struggle we have been able to form a well-decorated set ℝ, the set of real numbers. This ℝ contains all kind of numbers namely natural numbers, negative integers, zero, rational numbers and irrational numbers. There are infinitely many real numbers in ℝ. Every real number has a specific name. In my research work, I would like to convey the concerned readers that every real number takes a new name when we consider that real number on different sets.
Key words: Enigmatic, visualization, Neighbourhood, real numbers, belongs to, traditional, various, cases

[1] Real Analysis, P.N. Chatterji, page-34[2000]
[2] Real Analysis, B.K. Lahari and K.C. Roy, page-47[1988]
[3] Lattices and Boolean algebras by V.K Khanna, page-3
[4] P.N. Chatterji, page-68[2000]
[5] Lattices and Boolean algebras by V.K Khanna, page-11
[6] Lattice Theory, George Gr tzer, page-2, 1970
[7] Lattice Theory, George Gr tzer, page-3, 1970
[8] Real Analysis, P.N. Chatterji, page-59, 2000
[9] Biscuits of Number Theory, Arthur T.Benjamin, Ezra Brown, page-39, 2009
[10] Biscuits of Number Theory, Arthur T.Benjamin, Ezra Brown, page-53, 2009

Abstract: In this paper we have developed a continuous review inventory model for deteriorating items with time dependent demand rate. Deterioration rate is increasing with time. Each cycle has shortages, which have been partially backlogged. The backlogging rate is taken to be inversely proportional to the waiting time for the next replenishment. Fuzziness is introduced by considering demand rate and partial backlogging parameter to be fuzzy numbers . The maximum total profit and optimal order quantity are derived by defuzzifying the total profit through the signed distance method. Finally, the crisp model and fuzzy model are illustrated with the help of numerical example. A sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the fuzzy model.
Keywords: Demand, Deterioration, Partial backlogging, Fuzzy inventory model, signed distance method

[1] U.Dave , L.K. Patel, (T,𝑆𝑖) Policy inventory model for deteriorating items with time proportional demand,Journal Of Oprational Research Society,32,1981,137-142.
[2] R. S. Sachan , On (T,𝑆𝑖) inventory policy model for deteriorating items with time proportional demand "Journal Of Oprational Research Society, 35,1984,1013-1019,
[3] G. C. Mahata and A. Goswami, Fuzzy EOQ Models foe Deteriorating Items with Stock Dependent Demand & Nonlinear Holding Costs ,International Journal of Mathematical and Computer Science ,5:2. 2009,94-98
[4] Kuo-Lung Hou ,An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting,European Journal of Operational Research ,168, 2006,463–474
[5] N. K. Sahoo, C.K. Sahoo, S.K.Sahoo, An Inventory Model for Constant Deteriorating Items with Price Dependent Demand and Time-varying Holding Cost, International Journal of Computer Science & Communication , 1(1), January-June 2010, 267-271
[6] T. Chakrabarti, B.C.Giri, K.S. Chaudhuri, An EOQ Model for Items With Weibull Distribution Deterioration, Shortages and Trended Demand: an Extension of Philip's Model,Computers and Operations Research,25(7/8), 1998, 649-657
[7] C. K. Tripathy , U. Mishra, An Inventory Model for Weibull Time-Dependence Demand Rate with Completely Backlogged Shortages, International Mathematical Forum, 5(54), 2010, 2675 – 2687
[8] S. K. Manna and , K.S. Chaudhuri,An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages, European Journal of Operational Research 171 ,2006,557–566
[9] H.J. Chang , C.Y.Dye, An EOQ Model for Deteriorating Items with Exponential Time-Varying Demand and Partial Backlogging, Information and Management Sciences, 10(1),1999, 1-11
[10] Chung-Yuan Dye , Liang-Yuh Ouyang, An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging, European Journal of Operational Research , 163 ,2005,776–783

Abstract: This paper is intended to explore the application of the logit model in the Soekarno-Hatta Malang bridge traffic jam. Logit model is a model which uses regression technique to estimate the probability that an event occurs or not. The data which is used in this paper is the vehicles data. The vehicles are classified by heavy vehicles (trucks, buses, etc), light vehicles (sedan, pick-up, etc), motorcycles, and unmotorcycles. The result of this research is 66.8% of motor vehicle will cause traffic jam and 66.9% of unmotor vehicle will cause traffic jam. Keywords: - logit model, traffic jam, congestion

[1] Hosmer, D.W. dan S. Lemeshow. (2000). Applied Logistic Regression, 2nd edition. John Wiley and Sons.
[2] Agresti, A. (1996) Introduction to Categorical Data Analysis. John Wiley.
[3] J. S. Cramer (2003). "The Origins and Development of the Logit Model". Cambridge UP.

Abstract: A real quadratic family functions f(x) = k x ( 1 – x ), k  R, has indicated that even the simplest looking functions may have the complicated dynamics. This logistic map exhibits the properties like topological transitivity, sensitivity dependence on initial conditions and density of periodic points. The cubic family functions f : R → R, f(x) = x3 + x,   R, are no exceptions. The dynamics of this family is 'controlled' for an interval of values of , but it becomes more complicated as the value of  decreases from -1.5. At λ = -3, f(x) is chaotic on the interval [-2,2]. In this paper, we shall see that the chaotic behaviour of f(x) = x3 + x is even more complex for  < -3.
Key words: Dense periodic points, Domain of chaos, Dynamics of a function, Fractal, Sensitivity dependence on initial conditions

[1.] Steven H. Strogatz , Nonlinear Dynamics and chaos : With applications to Physics, Biology, Chemistry and Engineering.
[2.] Michel Vellekoop ; Raoul Berglund , On intervals, Transitivity = Chaos, American Mathematical Monthly, Volume 101, Issue
[3.] Devaney R. L., An introduction to Chaotic Dynamical Systems, Second Edition, Addition Wesley, Redwood city, 1989
[4.] Kathleen T. Alligood, Tim D. Sauer, James A. Yorke , CHAOS – An introduction to dynamical systems, Springer Verlag, New Y
[5.] Saber N. Elaydi, Discrete Chaos , CHAPMAN & HALL/CRC, 2000
[6.] Michael Brin & Garrett Stuck , Introduction to dynamical systems, Cambridge University Press, 2002
[7.] Robert Gilmore & Marc Lefranc, The topology of Chaos, John Wiley & Sons. Inc. New York, 2002
[8.] Tien-Yien Li and James A. Yorke, 'Period three implies Chaos' American Mathematical Monthly, 1975.
[9.] E. J. Barbeau , Polynomials, Page 164
[10.] www.mathworld.wolfram.com

Abstract: In this paper, a group acceptance sampling plan using weighted binomial is developed for a truncated life test when the lifetime of an item follows Inverse Rayleigh and Log – Logistic distributions. The minimum number of groups required for a given group size and the acceptance number is determined when the consumer's risk and the test termination time are specified. The operating characteristic values according to various quality levels are obtained. The results are explained with examples.
Keywords: Inverse Rayleigh distribution, Log – Logistic distribution, Group acceptance sampling using weighted binomial, consumer's risk, Producer's risk, truncated life test.

[1] Aslam, M., and Jun, C.-H. (2009): A group acceptance sampling plans for truncated life tests based on the inverse Rayleigh and log-logistic distributions. Pakistan Journal of Statistics 25, 1-13.
[2] Epstein, B. (1954): Truncated life tests in the exponential case. Annals of Mathematical Statistics 25, 555-564.
[3] Jun, C.H., Balamurali, S. and Lee, S.-H. (2006): Variables sampling plans for Weibull distributed lifetimes under sudden death testing. IEEE Transactions on Reliability 55, 53-58.
[4] Kantam, R.R. L., Rosaiah, K. and Srinivasa Rao, G. (2001): Acceptance sampling based on life tests: Log-logistic models. Journal of Applied Statistics 28, 121-128.
[5] Radhakrishnan R. and Alagirisamy K. (2011): Construction of group acceptance sampling plan using weighted binomial distribution. International Journal of Recent Scientific Research 2(7), 229-231.
[6] Rosaiah, K. and Kantam, R.R.L. (2005): Acceptance sampling based on the inverse Rayleigh distribution. EQC 20, 277-286.
[7] Rosaiah, K., Kantam, R.R.L. and Pratapa Reddy, J. (2007): Economic reliability test plan with Inverse Rayleigh Variate. Pakistan Journal of Statistics 24, 57-65.

Abstract: In this paper Bianchi type-I cosmological model are presented in scalar tensor theory of gravitation proposed by Saez and Ballester [1] in the presence of viscous fluid. Some physical and geometrical properties of the model are also discussed. Keywords: Bianchi type-I, Saez-Ballester scalar tensor theory, viscous fluid

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Abstract: With the development of digital electronic computers and calculators the mathematical operations have become easier and faster but there is always a limitation of retaining the number of digits in the results of the operations. One has to see the retained number of digits in the result produce how much error in the other quantities which are computed using them. But it is a fun to retain all the digits in the result of square of a number of any sizes. Sometimes all the digits in the result may be required for some accurate scientific investigations when computers fail to provide the same. The author has developed this method of squaring any number retaining all the digits in the result.

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