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-