iosr-Jm   Volume-9 ~ Issue-6

Abstract: An infinite slab subject to temperature variation is analyzed, the problem is formulated using conformal mapping and solved by mellin transform and method of residue. A closed form solution for the temperature distribution is obtained .A detailed verification of the solution is carried out and find to satisfying the Laplace equation.

[1] I.N Sneddon : The use of integral transforms, McGraw-Hill,new York,1972.
[2] G.N.Emenogu and J.N.Nnadi: Analysis of elastic wedge under out-of-plane stress volume 66,number 1, pp117-125(2012)
[3] Z. Szmydt and B.Ziemian, The Mellin transform and fuchsia type partial differential equations, mathematics and its applications (East Europe Series)56,kluwer Academic publishers Group, Dordrech,1992
[4] J.N.Nnadi: Anti plane shear analysis for a Non-homogeneous semi-infinite layer. Journal of the Nigerian Association of mathematical physis,volume7,p215(2003)

Abstract: An elastic homogeneous isotropic material with a right line inhomogeneity embedded in the material under Anti-shear is analyzed; the mathematical model of the problem is a boundary value problem formulated using the mellin transform and solved by the Wiener-Hoph Techniques. A closed form solution for displacement is obtained from which the stress intensity factor is calculated. The stress field were found to have square-root singularity at the inner tip. As a result of this, micro-cracking can initiate at the inner tip of the line inhomogeneity in the matrix depending on the applied loads. The outer tip showed no singularly.

[1] Z. M Xiao and H. Fan, Micro Crack initiation at tip of a rigid inhomogeneity. Journal of fracture Vol. 83: Pp 1-9, 1996
[2] J. Dundurs and X. Markenscoff: A Green's function formulation of anti-cracks and their interaction with load induced singularities. ASME journal of Applied Mechanics Vol. 56, Pp. 550-555, 1989
[3] H. Tada, P.C. Paris and G. R. Trwin. Stress intensity hand book. Del. Research corporation. Heller town pennsyvania 1993.
[4] P. C Paris and G. C. Sil, Stress analysis of cracks. Symposium on fracture Toughness, Testing and its application. ASTM Special Technical publication 381; Pp. 30-83; 1965
[5] M.G. Arfken: Mathematical methods for physicists Academic press Inc. New York. 1966.
[6] R. V. Churchill: Complex variables and applications 2nd edition, McGraw-Hill, New York 1960.

Abstract:Finite difference solution of partial differential equations must satisfy the requirement of convergence and stability if they are to be reasonably accurate. In this paper, we examined convergence and stability criterion of finite difference scheme for solving a partial differential equation. A case which is possible when the cumulative effect of all rounding errors is negligible. Consequently, we investigated the propagation of these errors as increases by applying the Fourier series method.

[1]. Smith, G.D; Numerical solution of Partial Differential Equations. Oxford University Press (1965), page 70
[2]. Greenspan. D and Casulli, V.; Numerical Analysis for applied mathematics, Science and Engineering, (1988) Oxford University Press.
[3]. James W. Brown, Ruel V. Churchill: Fourier series and Boundary Value problems. International Students Edition, McGraw-Hill Book company Inc. (1941).
[4] Murray R. Spiegel; Theory and problems of complex variables: Schaum's outline series, McGraw Hill Book company Singapore (1981).

Abstract: In the present paper, soft -open and soft -closed sets in soft topological spaces are defined over an initial universe with a set of parameters. A necessary and sufficient condition for a soft set to be soft -open set in soft topological space is stated and proved. A detailed study is carried out on properties of soft -interier and soft -closure of soft sets.

Keywords: Soft -open sets, soft -closed sets, soft -interior, soft -closure.

[1] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, Vol. 70 (1963), 36-41.
[2] J. Mahanta and P. K. Das, On soft topological space via semi-open and semi-closed soft sets, arXiv [math.GN.], Vol. 1(2012), 1-9.
[3] D. Molodtsov, Soft set theory-First results, Comput. Math.Appli., Vol. 37 (1999), 19-31.
[4] O. Njastad, On some classes of nearly open sets, Pacific Journal of Mathematics, Vol. 15, No. 3, (1965), 961-970.
[5] M. Shabir and M. Naz, On soft topological spaces, Comput. Math.Appli., Vol. 61 (2011), 1786-1799.
[6] I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, Vol. 3, No. 2 (2012), 171-185.