IOSR-JAP   Volume-5 ~ Issue-6 ~ January 2014

Abstract: In this paper we have obtained axially symmetric Bianchi type-I cosmological models for perfect fluid distribution in the context of Lyra's manifold. Exact solutions of the field equations are obtained by assuming the expansion  in the model is proportional to the shear . This leads to the condition A  Bn where A and B are scale factors and n( 0) is a constant. Some kinematical and physical parameters of the model have been discussed. The solutions are compatible with recent observations.
Key words: Bianchi type models, Cosmology, Lyra geometry.

[1] H. Weyl, Sber. Preussische Akademie der Wissenschaften zu Berlin, 1918, 465.
[2] G. Lyra, Über eine Modification der Riemannschen Geometrie, Mathematische Zeitschrift 54, 1951, 52-64.
[3] D. K. Sen, A static cosmological model, Zeitschrift fur Physik C 149, 1957, 311-323. [4] D. K. Sen and K. A. Dunn, A scalar-tensor theory of gravitation in a modified Riemannian manifold, Journal of Mathematical Physics 12, 1971, 578-586.
[5] W. D. Halford, Cosmological theory based on Lyra's geometry, Australian Journal of Physics 23, 1970, 863-9.
[6] W. D. Halford, Scalar-tensor theory of gravitation in a Lyra manifold, Journal of Mathematical Physics 13, 1972, 1699-1703. [7] A. Pradhan, Cylindrically symmetric viscous fluid universe in Lyra geometry, Journal of Mathematical Physics 50, 2009, 022501-022513.
[8] S. Kumar and C. P. Singh, An exact Bianchi type-I cosmological models in Lyra's manifold, International Journal of Modern Physics A 23, 2008, 813-822.
[9] V. U. M. Rao, T. Vinutha and M. V. Santhi, Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on Lyra manifold, Astrophysics Space Science 314, 2008, 213-216.
[10] J. K. Singh, Exact solutions of some cosmological models in Lyra geometry, Astrophysics Space Science 314, 2008, 361- 365.

Abstract: In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein's field's equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.

[1] Misner. C.W, Thorne. S. K, & Wheeler. J. A: GRAVITATION, W. H Freeman & Co., 1973.
[2] Rindler. W: Relativity, Special, General and Cosmological, Oxford University Press Inc., New York, 2006.
[3] Hawking. S: On the Shoulders of Giants, The Great Works of Physics and Astronomy, Penguin Books, Great Britain, 2003, Pg. 1214 – 1216.
[4] Schultz. B: A First Course in General Relativity, Cambridge University Press, New York, United States of America, 2009.
[5] Larsen. S: "Lots of Calculation in General Relativity", 2013.

Abstract: The detection and measurement of radionuclides in feed coal, bottom ash and fly ash samples collected from Barapukuria 2×125 MW coal-fired thermal power plant in Dinajpur district of Bangladesh, have been performed by gamma ray spectrometry technique. The average activity concentrations of 226Ra, 232Th and 40K in feed coal, bottom ash and fly ash samples were 10.46±5.24, 23.50±10.88 and 232.23±131.94 Bqkg-1; 56.91±2.77, 69.22±4.26 and 189.79±64.65 Bqkg-1; and 70.91±2.90, 115.26±5.79 and 205.53±65.56 Bqkg-1; respectively. These measured values were compared with other literature values.

[1] Beck, H. L., Miller, K. M., 1980. Some radiological aspects of coal combustion. IEE Trans. Nucl. Sci.27, 689-694.
[2] International energy outlook (IEO). Report Number: DOE/EIA-0484 (2011), Release Date: September 19, 2011,available at (http://www.eia.gov/forecasts/ieo/index.cfm)
[3] A. K. Garg, R. P. Chauhan , EraGarg ,Shikha Garg, Measurement of alpha radioactive air pollutants in some coal fired industrial units of northern India, American International Journal of Research in Science, Technology, Engineering & Mathematics, ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629, Available online at http://www.iasir.net.
[4] Xinwei Lu, Xiaodan Jia and Fengling Wang, Natural radioactivity of coal and its by-products in the Baoji coal-fired power plant, China, CURRENT SCIENCE, 1508 VOL. 91, NO. 11, 10 DECEMBER 2006.
[5] Sahithi Avirneni, Dharmateja Bandlamudi, Environmental Impact of Thermal Power Plant in India and Its Mitigation Measure, International Journal of Modern Engineering Research (IJMER) Vol.3, Issue.2, March-April. 2013, pp-1026-1031, www. ijmer.com.