iosr-Jm   Volume-8 ~ Issue-5

Abstract: In this paper the quantum aspects are described in-detail with the help of a new type of energy source called latent energy group SU(6) of the super unified theory of SU(11). The thermodynamics of general self gravitating systems created by the energy group SU(6) and some related topics such as complex space-time (i.e. Pseudo-Space-Time) are also briefly discussed. The thermodynamic connection is based on Hawking celebrated application of quantum theory to Black-Hole.

Keywards: finite difference, explicit, diffusion equation, soil moisture.

[1]. Hawking S.W(1984): The quantum state of the universe, Nucl. Phys. B239.257.
[2]. Hoyle F. and Naralikar J.V(1964): A new theory of gravitation. Proc. R. Soc., A282.191.
[3]. Bhadra N.K(2012):The complex Model of the Universe, IOSR-JM, ISSN: 2278-5728, vol.2, 4, pp-20; and The complex model of the quantum universe,vol.4, 1, pp-20.
[4]. Einstein, A. de-Sitter, W. (1932): On the relation between the expansion and mean density of the universe. Proc. Natl. Acad. Sci.,(USA), 18,213.
[5]. Davies, P.C.W. (1974): The Physics of Time Asymmetry(Surrey University Press/ University of California Press) – 1976a Proc. R. Soc. A. 351 139; -1976b Nature 263 377; -1977a Proc. R. Soc. A. 353 499; -1977b Space and Time in the Modern University (Cambridge : Cambridge University Press).
[6]. Mendeez, V. and Pavon, D.(1996): Gen. Rel. Grav., 28. 697; Birrell N. D and Davies, P.C.W 1978 Nature 272 35
[7]. Bekenstein, J.D.1973 Phys. Rev. D. 72333; Bertin, G., and Radicati, L.A 1976 Astrophys.206 825;.
[8]. Candelas P., and Seiama, D.W. 1977 Phys. Rev. Lett. 38 1372; Carr, B. 1977 Mon, Not. R. Astrom. Soc. 181 293; Carter B 1973 Black-Holes ed DeWitt and DeWitt (London: Gordon and Breach) Casimir HBG 1948 Proc. Kon. Ned. Akad. Wetens chap. 51 793.
[9]. Christensen, S.M. and Fulling, S.A. 1977 Phys. Rev. D15 2088;Einstein Albert (1987): Ideas and Opinions, Crown Publishers, New York, pp-348.
[10]. Halliwel, J.J. Hawking, S.W., (1985): The Origin of Structure in the Universe, Phys. Rev. D 31 1777. Hawking, S.W.(1985): The Arrow of Time in Cosmology Phys. Rev., D 32 2489. 1.

Abstract: The purpose of this paper is to prove some fixed point theorems in dp - complete topological spaces which generalize the results of Troy L Hicks and B.E.Rhoades[6 ].

Keywords : dp - complete topological spaces, d-complete topological spaces, orbitally lower semi continuous and orbitally continuous maps.

[1] J. Achari, Results on fixed point theorems, Maths. Vesnik 2 (15) (30) (1978), 219-221.
[2] Ciric, B. Ljubomir, A certain class of maps and fixed point theorems, Publ. L'Inst. Math. (Beograd) 20 (1976), 73-77.
[3] B. Fisher, Fixed point and constant mappings on metric spaces, Rend. Accad. Lincei 61(1976), 329 – 332.
[4] K.M. Ghosh, An extension of contractive mappings, JASSY 23(1977), 39-42.
[5] Troy. L. Hicks, Fixed point theorems for d-complete topological spaces I, Internet. J. Math & Math. Sci. 15 (1992), 435-440.
[6] Troy. L. Hicks and B.E. Rhoades, Fixed point theorems for d-complete topological spaces II, Math. Japonica 37, No. 5(1992), 847-
853.
[7] K. Iseki, An approach to fixed point theorems, Math. Seminar Notes, 3(1975), 193-202.
[8] S. Kasahara, On some generalizations of the Banach contraction theorem, Math. Seminar Notes, 3(1975), 161-169.
[9] S. Kasahara, Some fixed point and coincidence theorems in L-Spaces, Math. Seminar Notes, 3(1975), 181-187.
[10] M.S. Khan, Some fixed point theorems IV, Bull. Math. Roumanie 24 (1980), 43-47.

Abstract: The main aim of this research work is to construct a statistical model for the determination of gateway prices of yam in Abia State, which could also be used to predict reliable and dependable future price values of yam in Abia State and Nigeria in general. It intends to estimate and isolate trend and seasonal components of time series present in the data, using Least Squares Dummy Variable Analysis Approach. The results obtained showed that monthly dummy variables are all positively related to gateway price of yam, which implies that as the months go by, the gateway prices of yam in Abia State keep increasing in arithmetic progression. Again, the monthly dummy variables are highly statistically significant at 5% level of significance, meaning that the gateway prices are highly influenced by the months especially, the festive and farming seasons. The deseasonalized values obtained were used to forecast the gateway price value of yam in Abia State, Nigeria for 2011.

Key words: deseasonalization, gateway price, yam and Dummy Variable.

[1]. Ahmed, H. Y. and Sobhi, M. R. "A Comparative Study for Estimation Parameters in Panel Data Model". Journal of Econometrics, 2009, pp 1 – 15.
[2]. Alper, C. E. and S. B. Aruoba, "Deseasonalizing Macroeconomic Data: A Caveat to Applied Researchers in Turkey " Journal of Econometrics, 2001, pp 1- 17
[3]. Box, G.E.P. and G.M. Jenkins "Time series Analysis Forecasting and Control". San Francisco: Holden Day 1976.
[4]. Coursey, J. "Production of Improved Planting Materials- Propagated by Seed, Agriculture in the Tropical" Longman, 2001, p264.
[5]. Francis, X. D. "Elements of Forecasting" 2nd ed., South- Western Publishing 2001.
[6]. Food and Agriculture Organization "Production Year Book Rome", 2008, p 39.
[7]. Gujarati, D. N.(2006), "Essentials of Econometrics" 4th ed. McGraw – Hill, New York.
[8]. Gujarati, D. N. and Porter, D. C. (2009), "Basic Econometrics", 5th ed. McGraw – Hill, New York.
[9]. Hylleberg, S., R. Engle, C. Granger and B. Yoo, "Seasonal Integration and cointegration" Journal of Econometrics, 1990, vol.44, pp 215 – 238
[10]. Hylleberg, S. "Modeling Seasonality Advanced Texts in Econometrics", Oxford University Press, New York, 1992, pp 476.

Abstract: This paper examines the effect of net migration on prospective population growth in Dhaka City for the next several years. The paper deals with the urban challenges in Bangladesh focusing on rapid urban growth in the megacity of Dhaka. Here Population of Dhaka city has been predicted with the help of an ordinary differential equation model known as Malthusian Exponential population model which is parameterized by growth rate. In order to include the immigrant population, we make necessary modification of the model, which is again an exponential model where the growth rate 𝑅 is the sum of the actual growth rate 𝑎 and immigrant rate 𝑟 .We use fourth order Runge-Kutta scheme for the numerical solution of the autonomous and non-autonomous case where we incorporate the growth rate as a function of time. We perform error estimation of the numerical solution which justifies the correctness of the implementation by using computer programming. The procedure used in this study is by comparing two projected population scenarios one with constant growth rate and the other is time dependent growth rate based on the latest data collected through surveys of population censuses and relevant studies.

Keywords: Exponential model, growth rate method, migration, population prediction, urban structure.

[1] M. Braun, Differential Equation and their Application (4th ed. Narosha Publishing House, 1993).
[2] N. Hasan, Population Projection in Dhaka City Based on Malthusian Model, M.Sc. Thesis, Dept. of Mathematics, Jahangirnagar University, 2008.
[3] S.Hossain, Rapid Urban Growth and Poverty in Dhaka city, Bangladesh e-journal of sociology, 5(1), 2008, 57-80.
[4] B.B.S. (2007), Population Census – 2001(Community Series, Zilla: Dhaka), Bangladesh Bureau of Statistics, Planning Division, Ministry of Planning, Government of Bangladesh.
[5] C.M. Arun, Projections of Population, Enrolment and Teachers: Module on enrolment and population projections, Fellow, ORSM Unit, National Institute of Educational Planning and Administration, 17-B, January 18 2004.
[6] Walter, W., Ordinary Differential Equation (Springer., 305-309, 1998).
[7] Dhaka: Improving Living Conditions for the Urban Poor, Bangladesh Development Series, Paper No. 17, The World Bank Office, Dhaka, June 2007.
[8] N. Islam, Dhaka city: Some general Concerns, Centre for Urban Studies, Dhaka. 3(6), 1999, 71-82.
[9] M. A. Mabud, Bangladesh‟s Population Projection, 2001-2101, Organization for Population and Poverty Alleviation (OPPA), Dhaka, 2008
[10] S.A. Sinthia, Sustainable Urban Development of Slum Prone Area of Dhaka City, World Academy of Science, Engineering and Technology , 2013,75.