iosr-Jm   Volume-9 ~ Issue-1

Abstract: In this communication, we propose useful fuzzy entropy measure and study its particular cases. Some coding theorems have been proved for decipherable codes using Holder's inequalities. Some known results are the particular cases of our proposed measure. Keywords: Fuzzy set, Fuzzy entropy, Holder's inequalities, Decipherable codes. AMS subject Classification: 94A17, 94A24.

[1] M. Aamri and D. El Moutawakil, Common fixed points under contractive conditions in symmetric spaces, Appl. Math. E-Notes 3 (2003), 156–162.

[2] M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), 181–188.

[3]. Duran turkoglu and ishak altun a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying an implicit relation bol. soc. mat. mexicana (3) vol. 13, 2007.

[4] I. Altun, H. A. Hancer and D. Turkoglu, A fixed point theorem for multi-maps satisfying an implicit relation on metrically convex metric spaces, Math. Commun. 11 (2006), 17–23.

[5] T. L. Hicks and B. E Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear Anal., 36 (1999), 331–344.

[6] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771–779.

[7] G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci. (4) (2), (1996), 199–215.

[8] R. P. Pant, Common fixed points of contractive maps, J. Math. Anal. Appl. 226 (1998), 251–258.

[9] R. P. Pant, Common fixed points of sequences of mappings, Ganita 4 (1996), 43–49.

[10] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation,Demonstratio Math. 32 (1) (1999), 157–163.

Abstract: This paper is devoted to derivation of q-analogues of Iterative Methods for solution of algebraic and transcendental equations and comparing accuracy of results with classical methods.

Keywords: Basic, q-special function, q-analogue

[1] F. H. Jackson, A q-form of Taylor's formula, Mess. Math., 38, 1909,62-64.

[2] G. Gasper and M. Rahman, Basic Hypergeometric Series, CambridgeUniversity Press, Cambridge, 1990.

[3] Harold Exton,q-Hypergeometric Functions And Applications

[4] L.J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, London and New York, 1966.

[5] Thomas Ernst, A method for for q-Calculus, Journal of Nonlinear Mathematical Physics, 2003

Abstract: Agricultural planning, drainage pattern and designs for erosion control all depends on how best the design of water management practices are been conducted. This can be, best achieved if there is a prior knowledge of the distribution pattern of rainfall characteristics. The effect of rainfall to man is diverse ranging from designs of agricultural systems to erosion control. This study is aimed at exploring the statistical distribution namely Gamma distribution on quarterly rainfall amount in Zaria. Quarterly rainfall data were been collected for a period of 38 years (1971 – 2008) from Nigeria Meteorological Agency (NMA) quoted in central bank of Nigeria (CBN) bulletin, the Gamma distribution was used to model the distribution of the quarterly rainfall amount. Kolmogorov – Smirnov, One Sample test was used to evaluate the model fit. The Gamma distribution adequately fit the quarterly rainfall data producing a suitable model base on the Kolmogorov – Smirnov One Sample test. The result could be very useful to agricultural planning, erosion control, etc.

Keywords: Chi-square test, Gamma distribution, Likelihood ratio test, quarterly, Rainfall intensity,

[1] P. K.Das, N. Subash, , A. K. Sikka, V. N.Sharda, and N. K. Sharma, Modeling weekly rainfall using gamma probability distribution and Markov chain for crop planning in a sub-humid (dry) climate of central Biar. Indian Journal of Agricultural Science, 76, 2006, 358-361.

[2] H. K. Cho, K. P. Bowman and G. R. North, A comparison of Gamma and Log-normal distributions for characterizing satellite rain rates from the tropical rainfall measuring mission, Journal of Applied meteorology., 43(165) 2004,1586-1597

[3] B. Kedem, H .Pavlopoulos, X. Guan, and D. A. Short, Probability distribution model for Rain rate, Journal of Applied Meteorology, 33, 1994, 486-1493, 1520-0450.

[4] D. Salisu, S. Supiah, and A. Azmi, Modeling the Distribution of Rainfall Intensity Using Hourly Data. American Journal of Environmental Sciences, 6(3), 2010, 238-243.

[5] S. G. K. Adiku,, P. W. A. Dayananda, C. W. Rose and G. N. N. Dowuona, Analysis of within-season rainfall characteristics and simulation of daily rainfall in two Savannah Zones in Ghana, Agric. Forest meteorology., 86(96) 1997, 51-62, 168-1923,14-8.

[6] R. Srikanthan, A multisite daily rainfall data generation model for climate change conditions, 18th World IMACS/MODSIM Congress, Cairns, Australia 13-17 July. 2009. http://mssanz.org.au/modsim09

[7] D. S.Wilks, Adopting stochastic weather generation algorithms for climate change studies, Climate Change, 22, 1992, 67-84.

[8] M. D Zalina, M. N. M. Desa, V. V. Nguyen and A. H. M. Kassim, Selecting a probability distribution for extreme rainfall series in Malaysia. Water Sci. Techno., 45, 63-68, 2002).

[9] S. M. Ross, Introduction to Probability and Statistics for Engineers and Scientists. Third Edition, (London: Elsevier Academic Press 2004).

[10] P. McCullagh, and J. A. Nelder, Generalized Linear Models, Second edition, (London: Chapman and Hall, 1989).

Abstract: Time series analysis and forecasting has become a major tool in different applications for the private sector. Among the most effective approaches for analyzing time series data is the model introduced by Box and Jenkins, ARIMA (Autoregressive Integrated Moving Average). In this study we used Box-Jenkins methodology to build ARIMA model for annual production and utilization of gas from Nigeria National Petroleum Company (N. N. P. C.) for the period from 1970-2004. After the model specification; the best model for production was ARIMA (1, 1, 1) and for utilization was ARIMA (0, 1, 1). These models were used to forecasting the production and utilization of gas for the upcoming 4 years to help decision makers establish priorities in terms of gas demand management. An intervention time series analysis could be used to forecast the peak values of production and utilization data.

Key words: ARIMA, Box-Jenkins, forecasting, production and utilization model, Time series analysis,

[1] A. M. Herzberg and L. Frew, Can public policy be influenced ( Environmetrics, 2003) (14)1-10.

[2] C. K. Lee, Multifractal characteristics in air pollutant concentration time series. (Water, Air, and Soil Pollution., 2002) (135), 389-409.
[3] G.E.P. Box, and G.M. Jenkins, Time Series Analysis: Forecasting and Control. Revised Edn. (Hoden-Day, San Francisco, 1976). http://adsabs.harvard.edu/abs/1976tsaf.conf.....B

[4] V. Walter, Applied time series and Box-Jenkins Models. (Academic Press Inc., Orlando, Florida, 1983)

[4] C. Chatfild, The Analysis of Time Series-an introduction, 5th Edn., ( Chapman and Hall, UK., 1996.)
[4] D.C.Montgomery, and L.A. Johnson, Forecasting and Time Series Analysis. ( McGrow-Hill Book Company, 1967), http://www.abebooks.com/Forecasting-Time-

Abstract: This paper summarizes the findings of causality and long-term relationship between Foreign Direct Investment (FDI), economic growth and other socio-political determinants. Although a considerable literature gives the evidence of relationship between FDI and economic growth. There is a need for a detailed examination of socio-political determinants of FDI. The paper considers economic growth, exchange rate, and level of interest rates, unemployment, and political instability as determinants of the level of FDI inflows for Nigeria over the period 1970 to 2010. Almost all variables are found to have the theoretically expected signs with two-way causality relationship. The present study also estimates an error correction model by ordinary least squares, based on cointegrating VAR (2).

Keywords: causality, co-integration, Determinant, Foreign Direct Investment, Long term

[1] E. Faut and T. Ekrem, locational determinant of foreign direct investment in emerging economy: Evidence from Turkey, Multinational business review 10(1), 2002

[2] J. C Anyanwu, An econometric Investigation of Determinants of FDI in Nigeria: Nigeria Economic Society Annual Conference Publication, Lagos, 1998

[3] A.B Ayanwale, FDI and Economic Growth: Evidence from Nigeria" AERC Bulletin, 2007, 108-112.

[4] Broadman and Sun, The distribution of foreign direct investment in china, The world economy, 20(3) 1997

[5] O. Bajo-rubia and S. sosvilla-Rivera x, An econometrics analysis of foreign direct investment in Spain, Southern Economic journal, 61 (1), 1994, 104-117

[6] P. Tsai, Determinants of Foreign Direct Investment and its Impact on Economic Growth, Journal of Economic Development, 19, 1994, 137-163.

[7] O. G. Wafure,. and A. Nurudeen, Determinants of Foreign Direct Investment in Nigeria: An Empirical Analysis, Global Journal of Human Social Science, 10(1), 2010

[8] H. Masyuki, and f. ivohasina, The Determinants of Direct Investment into japan, Kobe University Economic Review 51, 2005.

[9] A.H. Ekpo, Foreign Direct Investment in Nigeria: Evidence from Time Series Data, CBN Economic and Financial Review, 35(1), 1997

[10] D. Olatunji, , At home Abroad when Titles get in way the Nation Newspapers Tuesday, September, 25, 2001

Abstract: In this paper, flexible job-shop scheduling problem (FJSP) is studied in the case of optimizing different contradictory objectives consisting of: (1) minimizing makespan, (2) minimizing total workload, and (3) minimizing workload of the most loaded machine. As the problem belongs to the class of NP-Hard problems, a new hybrid evolutionary algorithm is proposed to obtain a large set of Pareto-optimal solutions in a reasonable run time. The algorithm utilizes from a local search heuristic for improving the chance of obtaining more number of global Pareto-optimal solutions. The solution method uses from a perturbed global criterion function for guiding the search direction of the hybrid algorithm. Computational experiences show that the hybrid algorithm has superior performance in contrast to previous studies.

Keywords: multi-objective, Pareto optimal, flexible job shop scheduling, evolutionary algorithm, variable neighborhood descent

[1] Baykasoglu, A., Ozbakir, L., Sonmez, A.I., "Using Multiple Objective Tabu Search and Grammars to Model and Solve Multi-Objective Flexible Job-Shop Scheduling Problems." Journal of Intelligent Manufacturing, Vol. 15(6), 2004, pp. 777–785.
[2] Garey, M.R., Johnson, D.S., Sethi, R., "The Xomplexity of Flow Shop and Jobshop Scheduling," Mathematics of Operations Research, Vol. 1, 1976, pp. 117–129.
[3] Bruker, P., Schlie, R., "Job Shop Scheduling with Multi-Purpose Machine", Computing, Vol. 45, 1990, pp. 369– 375.
[4] Xia, W.J., Wu, Z.M., "An Effective Hybrid Optimization Approach for Multiobjective Flexible Job-Shop Scheduling problems," Computers and Industrial Engineering, Vol. 48(2), 2005, pp. 409–425.
[5] Brandimarte, P., "Routing and Scheduling in a Flexible Job Shop by Taboo Search,". Annals of Operations Research, Vol. 41(3), 1993, pp. 157–183.
[6] Paulli, J., "A Hierarchical Approach for the FMS Scheduling Problem," European Journal of Operational Research Vol. 86, 1995,

Abstract: Transportation problem is considered a vitally important aspect that has been studied in a wide range of operations including research domains. As such, it has been used in simulation of several real life problems. Thus, optimizing transportation problem of variables has remarkably been significant to various disciplines. In this paper, three variables will be optimized to reduce transportation cost using four methods which will include: Northwest corner method, least cost method, Vogel method and modi method. This will mainly aim at finding the best and cheapest route on how supply will be used to satisfy demand at specific points. This will imply that, a variable cost of shipping products from suppliers to demand points will be considered.

Key words: optimization techniques, transportation problem, Northwest corner, least cost, Vogel, Modi.

[1] Ahmad, Hlayel Abdallah. "The Best Candidates Method for Solving Optimization Problems." Journal of Computer Science , 2012: 711-715.

[2] Atoum, J. "Solving the traveling salesman problem using new operators in genetic algorithms." Journal of applied sciences, 2009: 1586-1590.

[3] Ech-Cherif, A. "A new machine learning based approach for tuning metaheuristics for the solution of hard combinatorial optimization problems." ournal of applied sciences, 2010: 1991-2000.

[4 ] Soewono, E. "Oil production optimization in a cluster of gas lift wells system." journal of applied sciences, 2010: 1705-1713.

[5] Tlelo-Cuautle, E. "Applications of evolutionary algorithms in the design automation of analog integrated circuitsournal ." journal of applied sicences, 2010: 1859-1872.

[6] Lu, H. "A new particle swarm optimization with a dynamic inertia weight for solving constrained optimization problems." inform technolofy journal of applied sciences, 2010: 1536-1544.

[7] Djebbar, B. "Optimization of a quadratic function under its canonical form." Asian journal of applied sciences, 2009: 499-510.

[8 ] Mahad, D.A. "Modeling of multi-level capacitated lot-size scheduling problem." journal of applied science, 2011: 290-296.

[9] Alimohamadi, A. "Routing of water pipeline using gis and genetic algorithm." Journal of applied science, 2009: 4137-4145.

[10] Chaudhuri, Arindam. "A Comparative study of Transportation Problem under." Journal of mathematics and computer science, 2011: 256-267.

Abstract: The use of technology has a long history in mathematics education. Many societies, for example, introduce arithmetic with an abacus, for two reasons. First, the abacus supports computation. Second, the abacus presents a tangible image of mathematics, which helps students understand difficult concepts. Technology can reduce the effort devoted to tedious computations and increase students' focus on more important mathematics. Equally importantly, technology can represent math in ways that help students understand concepts. In combination, these features can enable teachers to improve both how and what students learn.

[1]. Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking of theories – an approach for exploiting the diversity of theoretical approaches. In B. Sriraman & L. English (Eds.), Theories of mathematics education: seeking new frontiers (pp.483506). New York: Springer.

[2] Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool; instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213-234..

[3] Hoyles, C., & Lagrange, J.-B. (Eds.)(2010). Mathematics education and technology –Rethinking the terrain. NewYork/Berlin:Springer. [4] Kaput, J. (2007). Technology becoming infrastructural in mathematics education. Models & Modeling as Foundations for the Future in Mathematics Education. Mahwah, NJ: Lawrence Erlbaum..

[5] Roschelle, J., Tatar, D. , Shechtman, N., Hegedus, S., Hopkins, B., Knudsen, J., Stroter, A. (2007). Can a Technology-enhanced Curriculum Improve Student Learning of Important Mathematics? Menlo Park, CA: SRI International. Available at: http://math.sri.com/publications/index.html.

[6] Fuglestad, A.B. (2007). Teaching and teachers' competence with ICT in mathematics in a community of inquiry. Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (pp. 2-249 - 2-258). Seoul, Korea.

[7] Kieran, C., & Drijvers, P. (2012). The didactical triad of theoretical framework, mathematical topic, and digital tool in research on learning and teaching. Paper presented at the Colloque Hommage à Michèle Artigue, Paris, May, 31st, 2012.

[8] Ruthven, K. (2007). Teachers, technologies and the structures of schooling. In Pitta-Pantazi,D., & Philippou, G., Proceedings of the V Congress of the European Society for Research in Mathematics Education CERME5 (pp. 52-67). Larnaca, Cyprus: University of Cyprus.

[9] Pea, R. (1987). Cognitive technologies for mathematics education. In A.H. Schoenfeld (Ed.),Cognitive Science and Mathematics Education (pp. 89-122). Hillsdale, NJ: Lawrence Erlbaum.

[10] Monaghan, J. (2005). Computer Algebra, instrumentation and the Anthropological Approach. Paper Presented at the 4th CAME onference, October 2005.

Abstract: There are several approaches in estimating losses caused by the environmental intervention. The common one is to determine the incomes obtained before and after the perturbation where the difference is the net loss or gain. However, the loss sometimes extends to the consumers who have to pay more for the goods affected by the perturbation following the law of demand and supply. Thus, in fisheries, the losses are determined by the differences of producer and consumer surpluses. The forecasting technique using time series data collected in 1992-1997 is used to predict landings after perturbation for the next six years. ARIMA (2,0,2) model is found suitable for the forecasting to perform. It is suggested that in the situation where the landings trend is already decreasing even before the perturbation, forecasting technique is used to discern the losses. The reason being, the decreasing trend after perturbation is likely to be perceived as naturally caused thus does not merit losses claim.

Keywords: Forecasting, ARIMA models, fish landings

[1] A. Marshall, Principles of economics (8 th edition) (Macmillan,London, 1920)

[2] Perunding Utama Sdn. Bhd., Detailed environmental impact assessment for proposed Lekir coastal development. (Desa Kilat Sdn.Bhd (Kuala Lumpur, 1977)

[3] R. S. Pindyck, and D.L. Rubinfeld, Econometric models and economic forecasts. (Irwin/McGraw-Hill,U.S.A., 1998)

[4] P.Jedamus, ; R. Frame and R. Taylor , Statistical analysis for business Decisions (McGraw-Hill Book Company, USA pp. 213, 1976)

[5] R.L. Miller, C. Acton, D.A. Fullerton and J. Maltby, SPSS for social scientists (Palgrave Macmillan, UK, 2002).

[6] LKIM , Laporan kajiansSosioekonomi nelayan 1995 (Kuala Lumpur: Lembaga Kemajuan Ikan Malaysia, Kementerian Pertanian Malaysia, 1998)

[7] D.N. Gujarati,. Basic econometrics (Singapore: McGraw-Hill, Inc., 1995)

[8] A.H Studenmund, Using econometrics: a practical guide. (Addison-Wesley, U.S.A., 1997)

[9] C.P. Wheater, and P.A. Cook, Using statistics to understand the environment (London: Routledge, Taylor & Francis Group, 2003)

[10] G.S. Maddala, Introduction to econometrics. (John Wiley & Sons, Ltd, Chichester, 2001)

Abstract: In this paper we present and study a new class of functions as a new generalization of contra continuity. Furthermore we obtain some of their basic properties and relationship with R*-regular graphs.

Keywords: Contra R*-continuous function, almost contra R*-continuous functions, R*-regular graphs, R*- locally indiscrete. AMS subject classification: 54C08, 54C10

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Abstract:In this paper contains description of certain relations called partial equivalence relations .Moreover ,it includes the formal algorithms for determining the order of relations like partial reflexive, partial symmetric and partial transitive relations .Some examples are also presented for the clarification of these concept.

Key Words:-Partial reflexive, Partial symmetric and Partial transitive .

[1]. J. Klir,George, & A. Floger,Tina ,Fuzzy Sets, Uncertainty and Information ,Prentice-Hall of India Private Limited,2008,P.65-105
[2]. Parhi,S.K ,Das,L, "Generalization of Equivalence Partial Relation" Odisha Mathematical Society Annual Conference abstract of National Conference on Recent Trends in Mathematics,27-28 ,may -2001,P.3
[3]. Parhi,S.K. , Das,L., " Generalization of Equivalence Relation " Submitted to International journal of Fuzzy Information Engineering, China .