iosr-Jm   Volume-11 ~ Issue-3 ~ May-June 2015

Abstract: In this paper, we introduce the concept of zeroid in PO-ternary semirings. We study whether the algebraic structure of (T, [ ]) may determine the order structure of (T, +) and vice-versa. Throughout this chapter unless otherwise mentioned T is a po-ternary semiring in which (T, +) is a zeroid. The zeroid of a po-ternary semiring is denoted by Z. We also study the properties of zeroid PO-ternary semirings and ordered zeroid PO-ternary semirings. We prove that in a PO-ternary semiring every odd power of x is a zeroid if x is a zeroid. We also prove that in a zeroid PO-ternary semiring which is also zero cube Po-ternary semiring, then T3 = {0}.

[1] Arif Kaya and Satyanarayana M. Semirings satisfying properties of distributive type, Proceeding of the American Mathematical
Society, Volume 82, Number 3, July 1981.
[2] Chinaram, R., A note on quasi-ideal in ¡¡semirings, Int. Math. Forum,3 (2008), 1253{1259.
[3] Daddi. V. R and Pawar. Y. S.Ideal Theory in Commutative Ternary A-semirings, International Mathematical Forum, Vol. 7, 2012,
no. 42, 2085 – 2091.
[4] Dixit, V.N. and Dewan, S., A note on quasi and bi-ideals in ternarysemigroups, Int. J. Math.Math.Sci. 18, no. 3 (1995), 501-508.
[5] Dutta, T.K. and Kar, S., On regular ternary semirings, Advances in Algebra, Proceedings of the ICM Satellite Conference in
Algebra and RelatedTopics, World Scienti¯c, New Jersey, 2003, 343{355.

Abstract: Certain classes of graphs obtained from paths are super vertex graceful. In this paper, such classes of derived graphs like twig graphs, spider graphs, regular caterpillars and fire crackers are analysed under super vertex graceful mapping.
Keywords - fire crackers, graceful graphs, regular caterpillars, super vertex graceful graphs, spider graphs, and. twig graphs.

[1]. Joseph A. Gallian, A Dynamic survey of Graph Labeling, 2008.
[2]. Sin – Min – Lee, Elo Leung and Ho Kuen Ng, On Super vertex graceful unicyclic graphs, Czechoslovak mathematical Journal, 59 (134) (2009), 1- 22.
[3]. Murugesan. N, Uma. R, A Conjecture on Amalgamation of graceful graphs with star graphs, Int.J.Contemp.Math.Sciences, Vol.7, 2012, No.39, 1909-1919.
[4]. Murugesan. N, Uma.R, Super vertex gracefulness of complete bipartite graphs, International J.of Math.Sci & Engg. Appls, Vol.5, No.VI (Nov, 2011), PP 215-221.
[5]. Murugesan. N, Uma. R, Graceful labeling of some graphs and their subgraphs, Asian Journal of Current Engineering and Maths1:6 Nov – Dec (2012) 367 – 370.

Abstract: We develop an integrated production model for a deteriorating item in a two-echelon supply chain. The supplier's production batch size is restricted to an integer multiple of the discrete delivery, lot quantity to the buyer. Exact cost functions for the supplier is developed. It leads to the determination of individual optimal policies.
Keywords : Inventory, Graded mean Integration Representation, Lagrangean method

[1]. Changyuanyan, Avijit Banerjee, Liangbin Yang → An integrated production – distribution model for a deteriorating inventory item.
[2]. Bhunia, A.K.Maiti, M., 1998.Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on
inventory level.
[3]. Misra, R.B., 1975.Optimal production lot size model for a system with deteriorating inventory.International Journal of Production
Research 15, 495.
[4]. Wee, H.M. 1995 A deterministic lot – size inventory model for deteriorating items with shortages and a declining market.
Computers & operations Research New York 22(3), 345.

Abstract: The main aim of this paper is to introduced and study notion of Poisson Size-biased Quasi Lindley distribution. Besides deriving its p.m.f., some of its properties and the expressions for raw and central moments, coefficient of skewness and kurtosis, coefficient of variation, index of dispersion have been obtained. The problem of parameter estimation by using method of moments has been also discussed.

Keywords: Compounding; size-biased distribution; Poisson-Lindley distribution; size-biased Quasi Poisson-Lindley distribution; Estimation of parameters.

[1] T. R. Adhikari, T. R. and R. S. Srivastava, "A Size-biased Poisson-Lindley Distribution", International Journal of Mathematical Modeling and Physical Sciences, 01(3), 2013, 1-5.
[2] T. R. Adhikari and R. S. Srivastava, "Poisson- Size-biased Lindley Distribution", International Journal of Scientific and Research Publication, 04(3), 2014, 1-6.
[3] P. Dutta And M. Borah, "Some properties and application of size-biased Poisson-Lindley distribution", International Journal of Mathematical Archive-5(1), 2014, 89-96.
[4] P. Dutta and M. Borah, "Zero-modified Poisson-Lindley distribution", Journal of Assam Statistical Review, to be published.
[5] P.Dutta and M. Borah, "On certain recurrence relations arising in different forms of size-biased Poisson-Lindley distribution", Mathematics Applied in Science and Technology-7(1), 2015, 1-11.

Abstract: This paper has proposed a bivariate stochastic model for finding the share allocations in risky and non-risky portfolios of an investment business. Linear birth, death and migration processes have been considered for getting the bivariate processes of risky assets and non-risky assets within the portfolio. Joint probability function for number of units in the above said two groups are derived using differential difference equations. Several statistical measures are derived from the developed model and sensitivity analysis is carried out with numerical illustrations for better understanding of the model.

Keywords - Stochastic Modelling, Portfolio Management, Linear birth and death processes, Differential-difference equations.

[1]. Black.F. and Scholes. M. (1973), ―The Pricing of Options and Corporate Liabilities‖, Journal of Political Economy, 81, 637-54.
[2]. John C. Cox, Stephen A. Ross & Mark Rubinstein (1979), ―Option Pricing: A Simplified Approach*‖, Journal of Financial
Economics 7 (1979) 229-263. North-Holland Publishing Company.
[3]. Alexander J.McNeil, Jonathan P. Wendin, ―Bayesian inference for generalized linear mixed models of portfolio credit risk‖ Journal
of Empirical Finance, Volume 14, Issue 2, March 2007, Pages 131–149.
[4]. Neil Shephard, Torben G. Andersen, ―Stochastic Volatility: Origins and Overview‖, Handbook of Financial Time Series, 2009, pp
233-254.
[5]. Huai Zhao, Ximin Rong, Weiqin and Ma, Bo Gao ―Optimal Investment Problem with Multiple Risky Assets under the Constant
Elasticity of Variance (CEV) Model‖, Modern Economy-Scientific Research, 2012, 3, 718-725.

Abstract: J.Antony Rex Rodrigo and P.Mariappan introduced the characterizations and properties of g#-closed sets in ideal topological space. In this paper, we introduced 𝑇𝐼𝑔#-space,𝑇𝐼𝑔#∗ -space, strongly 𝐼𝑔#-continuous maps, perfectly 𝐼𝑔#-continuous and 𝐼𝑔#-compactness.

Keywords:𝑇𝐼𝑔#-space,𝑇𝐼𝑔#-space, 𝑇𝐼𝑔#∗ -space, Strongly 𝐼𝑔#-continuous maps, Perfectly 𝐼𝑔#-continuous , 𝐼𝑔#-compactness. Subject classification:Primary 54A05; Secondary 54D15,54D30.

[1]. D.Jankovic and T.R.Hamlett, New topologies from old via ideals, Amer.Math.Monthly 97(1990), no 4,295-310.
[2]. H.Maki,R.Devi and K.Balachandran, Associated topologies of generalized 𝛼-closed sets and 𝛼-generalized closed sets, Mem.Fac.Sci., Kochi Univ., Ser.A.Math., 15, 51-63(1994).
[3]. J.Antony Rex Rodrigo and P.Mariappan, g#-closed sets in ideal topological spaces, International Journal of Mathematical Archive-5(10),2014, 225-231.
[4]. K.Kuratowski, Topology, Vol. 1, Acadamic Press, New york, 1966

Abstract: Recently product warranty and technological development are closely related in this world. Every product company makes a policy about warranty claims because of setting up an appropriate product price. But find out the approximate failure number is very difficult work due to the censoring information about usage or age or both. In this paper, increasing failure rate and linear model based on age and usage for finding the approximate failure numbers are applied. For this purpose, this paper contains the application of different use rate to make the incomplete data due to censored information as complete information's. Using two-dimensional warranty scheme, it is found that the approximate failure number and compared with age based forecasting through a brief simulation.

Keywords: Warranty Policy, Censoring, Increasing Failure Rate (IFR), Month-in-Service (MIS).

[1] Condra, L.W. (1993). Reliability Improvement with Design of Experiments. 2nd Ed., New York: Marcel Dekker, Inc.
[2] Jiang, R. and Jardine, A.K.S. (2006). Composite scale modeling in the presence of censored data. Reliability Engineering and System Safety. 91(7), pp.756–764.
[3] Blischke, W. R., Karim, M. R., and Murthy, D. N.P.,(2011). Warranty Data Collection and Analysis, New York: Springer.
[4] Blischke, W.R. and Murthy, D.N.P.(1994). Warranty Cost Analysis, New York: Marcel Dekker, Inc.
[5] Alam, M.M. and Suzuki, K. (2009).Lifetime estimation using only information from warranty database. IEEE Transactions on Reliability.
[6] Alam, M.M., Suzuki, K. and Yamamoto, W. (2009). Estimation of lifetime parameters using warranty data consisting only failure information. Journal of Japanese Society for Quality Control (JSQC). 39(3), pp. 79-89.

Abstract: In this paper, we investigate that for each p, 1 p , space ℓp , equipped with the normed topology, is both (i) B-reflexive, and (ii) inductively reflexive. We also discuss that the locally convex spaces ℓp [s(ℓq)] , where 1 p and 1/p + 1/q =1, are semi-reflexive ( and so polar semi-reflexive) and the locally convex space ℓ1 [k(c0)] is inductively semi-reflexive. Keywords- Bornological, B-reflexive, inductively reflexive, normed topology, polar reflexive, sequence space.0.

[1]. G. Köthe, Topological vector spaces I ( Springer-Berlin Heidelberg New Yark , 1983).
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[5]. Atarsingh Meena, G.C. Dubey, Various reflexivities in locally convex spaces , Int. J. Pure.Appl. Math.Sci., Vol.8, No.1(2015), 31-36.

Abstract: A total coloring of a graph G is a proper coloring with additional property that no two adjacent or incident graph elements receive the same color. The total chromatic number of a graph G is the smallest positive integer for which G admits a total coloring. Here, we investigate the total chromatic number of some cycle related graphs.
Keywords: Middle graph, One point union of cycles, Shadow graph, Total coloring, Total chromatic number, Total graph.D30.

[1] G. Chartrand and L. Lesniak, Graphs and Digraphs (4/e, Florida, Chapman and Hall/ CRC, 2005).
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Abstract: Waiting on a queue is not usually interesting, but reduction in this waiting time usually requires planning and extra investments. Queuing theory was developed to study the queuing phenomenon in the commerce, telephone traffic, transportation, etc [Cooper (1981), Gross and Harris (1985)]. The rising population and health-need due to adverse environmental conditions have led to escalating waiting times and congestion in hospital Emergency Departments (ED). It is universally acknowledged that a hospital should treat its patients, especially those in need of critical care, in timely manner.

[1]. Adeleke, R. A., Ogunwale, O. D., & Halid, O. Y. (2009). Application of Queuing Theory to WaitingTime of Out-Patients in Hospitals". Pacific Journal of Science and Technology , 10(2):270-274.
[2]. Blake, F. I. (1978). An Introduction to Probability Models. USA: John Wiley and Sons Inc.
[3]. Bailey N. T. J. (1952).. A study of queues and appointment systems in hospital out- patient departments, with special reference to waiting-times. Journal of the Royal Statistical Society. Series B (Methodological), 14(2):185–199,
[4]. Churchman, G. W., Ackoff, R. C., & Arnoff., F. C. (1957). Introduction to Operation Research. New York, NY: John Willey and Sons:.
[5]. Gross, D., & Harris, C. M. (1985). Fundamentals of Queuing Theory. New York.: 2nd edition John Wiley.

Abstract: In this paper. Gauss Legendre quadrature have been applied for numerical solution of the integral of the form 𝑥𝑘 10𝑓 𝑥 𝑑𝑥, where k is real number. We compare the numerical solutions with J. Ma, V. Rokhlin, S. Wandzura. et al. [8]. The performance of the method is illustrated with numerical examples. Key words: Finite element method , Numerical Integration, Gauss Legendre Quadrature

[1]. O .C. Zienkiewicz, The Finite Element Method, 3rd. Edition, Mcgraw - Hill Inc., New York (1977).
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Abstract: We have extended the susceptible – infected – removed epidemic model to susceptible – exposed – infected – removed epidemic model by dividing into two cases. One is the number of susceptibles decreases and the number of exposed persons increases each by one and another is the number of exposed persons decreases and the number of infected persons increases each by one. AMS classification: 60G05, 62P10, 92B05, 92D30. Keywords: Epidemics, susceptible, exposed, infected.

[1]. Bailey, N.T., The mathematical theory of infectious diseases, Second Edition, Griffin, London, 1975.
[2]. Burghes, D.N. and Borrie, M.S., Modeling with differential equations, Ellis Horwood Ltd., 1981.
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John Wiley, New York, 2000.
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[5]. Hethcote, H.W., "Three basic epidemiological models." In S.A. Levin, editor, Lect. Notes in Biomathematics, Springer-Verlag,
Heidelberg, 100 (1994), 119-144.
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Abstract: The study main objective is to examine the multidimensional aspects of poverty in one Kenya's culturally diverse region of the Lake Victoria basin. The analysis using data collected by IUCEA researchers in 2007 and also the 2009 census on households in Kenya. This study investigates statistical models based on factors that characterize the demographic characteristic of individuals, in determining the predictors of poverty for better policy formulation.. The research findings indicate that poverty measures do overlap to capture a percentage of the sample as poor. The analysis shows that education, gender (being male), marital status, assets (livestock, water sources, and wall materials) and age of the head of the family have statistically positive effects on the likelihood of an individual falling into poverty.

Keywords: Poverty, Demography, Augmented, Logistic, Assets

[1]. World Bank (WB), "World development indicators 2010," Technical report License: CC BY 3.0 IGO, World Bank, Washington,
DC, 2010. Available at: https://openknowledge.worldbank.org/handle/10986/4373.
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vol. 61, no. 3, pp. 385–408, 1999.
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Abstract: Zadeh defined a Z-number associated with an uncertain variable X as an ordered pair of fuzzy numbers,(A,B). The first component represents the value of the variable while the second component gives a measure of certainty. Computations with Z-numbers is a topic which is both interesting and useful. In this paper we explain the computational technique and illustrate with examples how sum and product of Z-valuations can be computed.

Keyword: Fuzzy event probability ,Restriction, Zadeh's Z-numbers ,Z-valuation

[1]. L.A.Zadeh, A note on Z-numbers, Information Science 181, 2923-2932 (2011).
[2]. Ronald R. Yager, On a View of Zadeh Z-numbers, pp. 90-101,2012.
[3]. S.K.Pal etal;. An Insight Into The Z-number Approach To CWW, Fundamental Informatica 124 (2013) 197-229.
[4]. L.A.Zadeh,Probability measures of fuzzy events, Journal of Mathematical Analysis and applications,10,421-427(1968).
[5]. L.A.Zadeh.The concept of a linguistic variable and its application to approximation reasoning, Part I: Informatiom Science 8 (1975).