New Generating Sets of the First Order Lane-Emden Differential Equations in *N*-Dimensional Radially Symmetric Polytropes

Affiliation(s)

Department of Astronomy, Faculty of Science, King Abdul-Aziz University, Jeddah, Saudi Arabia.

Department of Astronomy, National Research Institute of Astronomy and Geophysics, Cairo, Egypt.

Department of Astronomy, Faculty of Science, King Abdul-Aziz University, Jeddah, Saudi Arabia.

Department of Astronomy, National Research Institute of Astronomy and Geophysics, Cairo, Egypt.

ABSTRACT

In the present paper, two new generating sets, of homology invariant functions will be established. Moreover, by the aid of two independent homology invariant functions of each set we established the transformed first order Lane-Emden equation. The first equation for polytropic index *n* ≠–1, ±∞ depends on five free parameters, while the other equation is for, *n ＝ *±∞ and depends on three free parameters.

Cite this paper

M. Sharaf and A. Saad, "New Generating Sets of the First Order Lane-Emden Differential Equations in*N*-Dimensional Radially Symmetric Polytropes," *Applied Mathematics*, Vol. 4 No. 4, 2013, pp. 659-662. doi: 10.4236/am.2013.44090.

M. Sharaf and A. Saad, "New Generating Sets of the First Order Lane-Emden Differential Equations in

References

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[1] S. Eilenberg and J. C. Moore, “Foundations of Relative Homological Algebra,” Memoris of the American Mathematical Society, No. 55, 1965.

[2] P. Hilton, “A Brief, Subjective History of Homology and Homotopy Theory in This Century,” Mathematical Association of America, Vol. 60, No. 5, 1988, pp. 282-291.

[3] A. Hatcher, “Algebraic Topology,” Cambridge University Press, Cambridge, 2002.

[4] T. Kaczynski, K. Mischaikow and M. Mrozek, “Compu tational Homology,” Springer, Kraków, 2004.

[5] D. H. Menzel, P. L. Bhatnagar and H. K. Sen, “Stellar Interiors,” John Wily & Sons Inc., New York, 1963.

[6] G. P. Horedt, “Polytropes: Applications in Astrophysics and Related Fields,” Kluwer Academic Publishers, Berlin, 2004.

[7] S. Chandrasekhar, “An Introduction to the Study of Stellar Structure,” Dover Publications, Inc., New York, 1957.