iosr-Jm   Volume-11 ~ Issue-1 ~ Jan-Feb 2015

Abstract: Today is a world of uncertainty with its associated problems, which can be well handled by soft set theory. In this paper, we extend sanchez`s approach for medical diagnosis using the representation of an interval valued fuzzy soft matrices. we introduce the definition of union and intersection of Interval valued fuzzy soft matrices with examples.Finally, we extend our approach in application of these matrices in medical Diagnosis.

Keywords: Soft set, fuzzy soft set, Interval valued fuzzy soft matrix, Union and intersection of Interval valued fuzzy soft matrix, Interval valued fuzzy soft matrix medical diagnosis.

[1]. Chetia, B., and Das, P.K. (2010). An Application of Interval valued fuzzy soft set in medical diagnosis, Int.J. contempt.math., science, vol. 5, 38, 1887-1894.
[2]. De, S. K., Biswas, R., and Roy, A.R. (2001), An Application Intuitionistic fuzzy set medical diagnosis, Fuzzy sets and systems, 117, 209-213.
[3]. Meenakshi, A.R., and Kaliraja, M. (2010) . Regular Interval valued fuzzy matrices, Advances in Fuzzy Mathematics, Vol.5 (1), 7-15.
[4]. Meenakshi, A.R., and Kaliraja, M. Regular Interval valued fuzzy relational equations, Int.J.comp.cognition (accepted).
[5]. Sanchez, E. (1976). \ Resolution of composite Fuzzy Relational equations, Information and control, 30, 38 -48.

Abstract: In the Present paper effect of angle of incidence on Damping derivative of a delta wing with Curved leading edges for attached shock case in Supersonic Flow has been studied. A Strip theory is used in which strips at different span wise location are independent of each other. This combines with similitude to give a piston theory which gives closed form solutions for damping derivatives at low to high supersonic Mach numbers. From the results it is seen that with the increase in the Mach number, there is a progressive decrease in the magnitude of damping derivatives for all the Mach numbers of the present studies; however, the decrease in the magnitude is variable at different inertia level.

[1]. Pike. J, "The Pressure On Flat And Anhydral Delta Wings With Attached Shock Waves", The Aeronautical Quarterly, November 1972, XXIII, Part 4, Pp. 253-262.
[2]. Hui, W.H., "Stability Of Oscillating Wedges And Caret Wings In Hypersonic And Supersonic Flows", AIAA Journal, Vol. 7, Aug. 1969, Pp.1524-1530.
[3]. Carrier, G.F. 1949, "The Oscillating Wedge In Supersonic Stream", Journal Of Aeronautical Sciences, Vol. 16, No. 3, Pp. 150-152, March.
[4]. Hui, W. H., "Supersonic/Hypersonic Flow Past On Oscillating Flat Plate At High Angles Of Attack", ZAMP, Vol. 29, 1978, Pp. 414-427.
[5]. Hui, W. H., "Supersonic And Hypersonic Flow With Attached Shock Waves Over Delta Wings", Proc Of Royal Society, London, 1971, A. 325, Pp. 251-268.
[6]. Orlik-Ruckemann, K. J., "Dynamic Stability Testing Of Aircraft Needs Versus Capabilities", Progress In The Aerospace Sciences, Academic Press, N.Y., 1975, 16, Pp. 431-447.
[7]. Hui, W. H. And Hemdan, H. T., "Unsteady Hypersonic Flow Over Delta Wings With Detached Shock Waves", AIAA Journal, April 1976, 14, Pp. 505-511.

Abstract: Probabilistic operator theory is the branch of probabilistic analysis which is concerned with the study of operator-valued random variables and their properties. The development of a theory of random operators is of interest in its own right as a probabilistic generalization of (deterministic) operator theory and just as operator theory is of fundamental importance in the study of operator equations, the development of probabilistic operator theory is required for the study of various classes of random equations.

[1]. O. Hanŝ, Reduzierende zufällige Transformationen, Czechoslovak Math. J. 7 (82) (1957), 154-158. MR 19, 777.
[2]. R. Kannan and H. Salehi, Measurability du point fixe d'une transformation aleatoire separable, C. R. Acad. Sci. Paris Ser A-B 281 (1975), A663-A664.
[3]. Mukherjea, Random transformations on Banach spaces, Ph. D. Dissertation, Wayne State Univ., Michigan, 1966.
[4]. L. S. Prakasa Rao, Stochastic integral equations of mixed type. II, J. Mathematical and Physical Sci. 7 (1973), 245-260. MR 50 # 14933.

Abstract: The characterization of g-inverses, minimum norm g-inverses and least square g-inverses of bimatrices are derived as a generalization of the generalized inverses of matrices.

Keywords: g-inverse, minimum norm g-inverse, least square g-inverse. AMS Classification: 15A09, 15A15, 15A57.

[1]. Ben Isreal.A and Greville.T.N.E, Generalized Inverse: Theory and Applications, Wiley-Interscience, New York, 1994.
[2]. Campbell.S.L and Meyer.C.D, Generalized Inverses of Linear Transformations,Society for Industrial and Applied
Mathematics,Philadelphia, 2009.
[3]. Haruo Yanai, Kei Takeuchi, Yashio Takane, Projection Matrices, Geneneralized Inverse Matrices, and Singular Value
Decomposition, Springer, New York, 2011.
[4]. Penrose.R, A generalized Inverse for Matrices, Proc. Cambridge Phil. Soc., Vol.51, 1955, (PP 406-413).
[5]. Radhakrishna Rao.C, Calculus of Generalized Inverses of Matrices Part-I: General Theory, Sankhya, Series A, Vol.29, No. 3,
September 1967, (PP 317-342).

Abstract: In this paper, we applied the method double Elzaki transform to solve wave equation in one dimensional and the results are compared with the resultsof double Laplace transform.
Keyword: Double Elzaki troundaryansform, Double Laplace transform, Inverse Double Elzaki transform, Convolution.

[1]. Abaker. A. Hassaballa, yagoub. A. Salih, Elzaki, Elzaki transform solution for Klein Gordon equation of one dimensional,
ICASTOR journal of mathematical Sciences,( 2014).
[2]. Abdul MajidWazwaz, Partial Differential Equations and Solitary Waves Theory, Higher Education Press Beijing and Springer -
Verlag Berlin Heidelberg (2009).
[3]. ArtionKashuri., Akli Fundo., RozanaLiko, Onduble new integral transform and double Laplace transform, European Scientific
journal, 2013.
[4]. Hassan Eltayeb., AdemKilicman, On double Sumudu transform anddouble Laplace transform, Malaysian journal of Mathematical
Sciences, 2010.
[5]. Hassan Eltayeb., AdemKilicman, A note on solution of wave, Laplace andheat equations with convolution terms by using a double
Laplace transform, Elsevier, 2007.
[6]. Hassan Eltayeb., AdemKilicman, A note on double Laplace transform, and Telegraphic equation, Hindawi Publishing Corporation,
2013.

Abstract: In this paper, a modified numerical algorithm for solving the fractional diffusion equation is proposed. Based on Tau idea where the shifted Legendre polynomials in time and the shifted Chebyshev polynomials in space are utilized respectively. The problem is reduced to the solution of a system of linear algebraic equations. From the computational point of view, the solution obtained by this approach is tested and the efficiency of the proposed method is confirmed.
Keywords: Tau method, Shifted Chebyshev polynomial, Shifted Legendre polynomial, Fractional diffusion equation.

[1]. Podlubany I., '' Fractional Differential Equations '', New York, 1999.
[2]. Su L., Wang W., Xu Q., '' Finite Difference Methods for Fractional Dispersion Equations '', Appl. Math. Comput. 216 (2010) 3329-3334.
[3]. Oldham K.B., Spanier J., '' The Fractional Calculus '', Academic Press, New York, 1974.
[4]. Gejji V.D., Jafari H., '' Solving A Multi-Order Fractional Differential Equation '', Appl. Math. Comput. 189 (2007) 541-548.
[5]. Odibat Z., Momani S., '' Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order '', Int. J. Nonlinear Sci. Numer. Simut. 7 (2006) 27-35.
[6]. Inc M., '' The Approximate and Exact Solutions of The Space- and Time-Fractional Burger's Equations with Initial Conditions by Variational Iteration Method '', J. Math. Anal. Appl. 345 (2008) 476-484.

Abstract: In this paper, a new approach for identifying fuzzy critical path is presented, based on converting the fuzzy network project into deterministic network project, by transforming the parameters set of the fuzzy activities into the time probability density function PDF of each fuzzy time activity. A case study is considered as a numerical tested problem to demonstrate our approach.

Keywords: Project network, Fuzzy Network, Defuzzification Techniques.

[1]. Alauldin N. A. and Saad M. S. 2014; "Scheduling Algorithm of fuzzy critical paths in project network". Jr. of Eng. & Technology, Iraq. To be appeared.
[2]. Prade H., 1979; Using fuzzy set theory in a scheduling problem: a case study, Fuzzy Sets and Systems, 2, 153-165.
[3]. Chanas S. and Kamburowski J., 1981; The use of fuzzy variables in PERT, Fuzzy Sets and Systems, 5, 11-19.
[4]. Dubios D. and Prade H., 1979; Decision-making under fuzziness, Advances in Fuzzy Set Theory and Applications, North-Holland, Amsterdam, 279-302.
[5]. Hapke M. and Slowinski R., 1993; A DSS for resource-constrained project scheduling under uncertainty, Journal of Decision Systems, 2, 111-128.
[6]. Kaufmann A. and Gupta M.M., 1988; Fuzzy Mathematical Models in Engineering and Management Science, North-Holland, Amsterdam, 1988..

Abstract: The object of this paper is to present several classes of linear and bilateral generating relations by employing operational techniques, which reduces as a special case of (known or new) bilateral generating relations.At last some of generating functions associated with stirling number of second kind are also discussed. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C45.

Keywords: Generating relations, Differential operator, Rodrigue formula, Stirling number.

[1] H.M. Srivastava and J.P. Singhal , A class of polynomials defined by generalized Rodrigue's formula , Ann. Mat. Pura Appl. Ser. ,Ser. IV 90 (1971), 75-85 .
[2] H.M. Srivastava, Some families of series transformations related to Euler-Knopp transformation, Internat. J. Nonlinear Sci. Numer. Simulation,2 (2001), 83-88.
[3] K.Y. Chen, C.J. Chyan, and H.M. Srivastava, Some polynomials associated with a certain family of differential operator, Journal of Mathematical Analysis and Applications,268 (2002), 344-377.
[4] A.K. Shukla and J.C. Prajapati, A general class of polynomials associated with generalized Mittag- Leffler function , Integral Transform and Special Function, Vol.19, No.1 (2008), 23-34.
[5] A.K. Shukla, and J.C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl.,336 (2007), 797-811.
[6] M. Singh, M.A. Khan, and A.H. Khan, On some properties of generalized Bessel-Maitland function, International Journal of Mathematics Trends and Technology, Volume 14, Number 1, Oct 2014.

Abstract: We consider a nearly hyperbolic cosymplectic manifold and we study some properties of CR-submanifolds of a nearly cosymplectic manifold with a semi-symmetric semi-metric connection. We also obtain some results on 𝜉−horizontal and 𝜉 −vertical CR- submanifolds of a nearly cosymplectic manifold with a semi-symmetric semi-metric connection and study parallel distributions on nearly hyperbolic cosymplectic manifold with a semi-symmetric semi-metric connection.

Keywords: CR-submanifolds, Nearly hyperbolic cosymplectic manifold, totally geodesic, Parallel distribution and Semi-symmetric semi-metric connection. 2000 AMS Subject Classification : 53D05, 53D25, 53D12

[1] A. Bejancu, CR- submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. 69, (1978), 135-142.

[2] A. Bejancu, CR- submanifolds of a Kaehler manifold II, Trans. Amer. Math. Soc., 250, (1979), 333-345.

[3] C.J. Hsu, On CR-submanifolds of Sasakian manifolds I, Math. Research Centre Reports, Symposium Summer ,(1983), 117-140.

[4] C. Ozgur, M. Ahmad and A. Haseeb, CR-submanifolds of LP-Sasakian manifolds with semi-symmetric metric connection, Hacettepe J. Math. And Stat., vol. 39 (4), (2010), 489-496.

[5] Lovejoy S.K. Das and M. Ahmad, CR-submanifolds of LP-Sasakian manifolds with quarter symmetric non-metric connection, Math. Sci. Res. J. 13 (7), (2009), 161-169.

[6] M. Ahmad and Kasif Ali, CR-submanifold of a nearly hyperbolic cosymplectic manifold, IOSR Journal of Mathematics (IOSR-JM) Vol 6, Issue 3 (May. - Jun. 2013), PP 74-77.

Abstract: Maths is older than oldest of civilization on this planet and at the same time it is as new as any. Mind and matter is proportional to spirituality and Science. To balance these two, mathematics play a very important role. Since deals with "why" and technology is related with "how" where as 'why' and how can't move without " what"..

Keywords: vaidik, infinity, zero, spirituality, vaidik

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[2]. Rigveda, Edited by Vauguseleo Sharma and Krishna Bhatta, Gore: Nirnaya sagar Press, Bombay, 1910
[3]. Brahonagupta, Brāhmasphuta siddhānta, Edited (with commentary) by Sudhakar' Driverti e vasana, New Delhi, 1966.
[4]. Bet Bertrand Rusell : The Principal of Mathematics,
[5]. A:l. Basham : The wonder that was India.