iosr-Jm   Volume-1 ~ Issue-1

ABSTRACT: The main aim of this paper is to obtain new triple integral relations that involve H -function and the multivariable H-function. The main results of our paper are unified in nature and capable of yielding several cases of interests (New and known).
Keywords: H -function, H-function, Multivariable H-function

[1] V.B.L. Chaurasia and Vishal Saxena, Certain Triple Integral Relations Involving Multivariable H-function : Scientia, Series A:
Mathematical Sciences 19 (2010), 69-75.
[2] A.A. Inayat-Hussain, New properties of hypergeometric series derivable from Feynman integrals, II : A generalization of the Hfunction.
J. Phys. A : Math. Gen. 20 (1987), 4109-4128.
[3] Y.L. Luke, The Special functions and their approximations, Academic Press, New York and London, I, (1969).
[4] A.M. Mathai and R.K. Saxena; The H-function with Applications, in Statistics and other Disciplines, Wiley Eastern Limited,
New Delhi (1978).
[5] H.M. Srivastava and R. Panda, Some bilateral generating functions for a class of generalized hypergeometric polynomials, J.
Reine Angew. Math., 283/284, (1976), 265-274.
[6] H.M. Srivastava and M.C. Daoust, Certain generalized Neumann expansions associatged with the Kampé de Fériet's function, Nederl. Akad. Wetensch. Proc. Ser. A 72, Indag. Math., 31 (1969), 449-457.
[7] H.M. Srivastava, K.C. Gupta and S.P. Goyal, The H-function of One and Two Variables with Applications. South Asian Publishers, New Delhi (1982).

Abstract: In this paper , we investigate the oscillation of second order nonlinear delay differential equations with impulses of the form
Key words :Oscillation; delay; second-order;impulses Mathematics Subject classification 34A37

[1] V.Lakshmikanthan,D.D.Bainov,P.Simeonov,Theory of Impulsive Differential equations,World Scientific,Singapore.
[2] Y.V.Rogovchenko,Oscillation theorem for second-order equations with damping,Nonliaear Anal. 41(2000)1005-1028.
[3] Xiaojing Yang, Oscillation criteria for nonlinear differential equations with damping,Applied Mathematics and Computation136(2003) 549-557.
[4] Y.Chen,W.Feng,oscillation theorem for second order non linear ODE equations with impulses,J.Math.Anal.Appl.210(1997)150-159.
[5] J.Luo,Z.Hou,Oscillation theorem for second order non linear ODE equation with impulses,J.Northeast Math.15 (1999)459-454.
[6] M.S.Peng,W.G.Ge,Oscillation criteria for second order nonlinear differential equations with impulses, Computers and Mathematics with Applications 39(2000)217-225.
[7] Wu Xiu-li , Chen Si –Yang ,Hong Ji ,Oscillation of a class of second order non linear ODE with impulses,Applied Mathematics and Computations 138 (2000)181-188.
[8] Xiaosong Tang,Asymptotic behaviour of solutions of second-order nonlinear delay differential equations with impulses,Journal of Computational and Applied Mathematics,233(2010)2105-2111

Abstract: In this paper, I show that exact value of pi (π) is . I found that π is an algebra . My findings are based on geometrical constructions, arithmetic calculation and algebraic formula & proofs.

[1] Basic algebra & geometry concepts .
[2] Histry of Pi(π) from internet .

ABSTRACT: coloring takes its name from the map coloring application, we assign labels to vertices. When the numerical value of the labels is unimportant, we call them colors to indicate that they may be elements of any set. In graph theory, a connected component of an undirected graph is a subgraph in which any two vertices are connected to each other by paths. The rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this paper we show that the rainbow connection number of an interval graph, which are of the form the rainbow connection number is less than or equal to the diameter of the graph G plus one.
Keywords – diameter, eccentricity, interval graph, rainbow connection number, rainbow path.

[1] Y. Caro, A. Lev, Y. Roditty, Z. Tuza, and R. Yuster, On rainbow connection, Electr J Combin 15(R57) (2008), 1.
[2] G. Chartrand, G.L. Johns,K.A. McKeon, and P. Zhang, Rainbow connection in graphs, Math Bohemica 133(1) (2008), 5-98.
[3] P. Erdos, J. Pach, R. Pollack, and Z. Tuza, Radius, diameter and minimum degree, J Combin Theory, Ser B 47(1) (1989), 73-79.
[4] I. Schiermeyer, Rainbow connection in graphs with minimum degree three, in : Combinatorial Algorithms, Lecture Notes in Computer Science 5874 (J. Fiala, J. Kratochvl, and M. Miller, Eds.), Springer Berlin/ Heidelberg, 2009, pp. 432-437.
[5] S. Chakraborty, E. Fischer, A. Matsliah, and R. Yuster, Hardness and algorithms for rainbow connection, J Combin Optimiz (2009), 1-18.

Abstract: This note presents the discussion regarding the flow of a dusty viscous fluid through hexagonal duct, i.e. , the cross-section of the long rectilinear duct is a regular hexagon. Developed integral transform and trilinear co-ordinates have been employed to solve the problem. The pressure gradient has been taken any function of time. A few particular cases, i.e. , flow under an impulsive pressure gradient and flow under constant pressure gradient have also been discussed.

[1] Fan, C. (1965) : ZAMP, 16: 351-360.
[2] Michael, D. N. and Norey, P. N. (1965) (1968) : Q.J.M.A.M., 21, 375-389.
[3] Michael, D.N. (1965) : Proc. Camb. Pill. Soc. 61, 569-71.
[4] Rao , P.S.S. (1969) : Def. Sc. Journal, 19, 135-138.
[5] Saffman , P.G. 1962) : Journal Fluid Mech, 13, 123-26.
[6] Sen , B. (1968) : Bull. Cal. Math. Soc. Vol. 60, No. 1, 2, 25-30.

Abstract: Recently Deo N.et.al. (Appl. Maths. Compt., 201(2008), 604-612.) introduced a new Bernstein type special operators. Motivated by Deo N.et.al., in this paper we introduce generalization of positive linear operators (1.5) and (1.6) which is the particular case of positive linear operators (1.7) and (1.8). We shall study some approximation results on it.

[1] Deo N. , Noor M.A. and Siddiqui M.A. "On approximation by class of new Bernstein type operators", Appl. Math. Comput., 201 (2008), 604-612.
[2] Kasana H.S. , Prasad G., Agrawal P.N. and Sahai A. "Modified Szậsz operators" Proceeding of International Conference on Mathematical Analysis and its Applications Pergamon Press, 1985, 29-41.
[3] Papanicolau C.G. "Some Bernstein type operators" Amer. Math. Month, 82 (1975) ,674-677.
[4] Singh S.P., "Some problems on approximation of functions by positive linear operators" Ph.D. Thesis, Roorkee University (1982).

Abstract : In this paper the two non-identical operative parallel cold standby systems has been analyzed by using regenerative point technique.The concept of inspection policy has been introduced for failed automatic unit for detecting the kind of failures (major or minor) after which it get repaired by some repair mechanism.But the manual one is free from inspection.The model has been design for the system to calculate the various important measures of reliability i.e MTSF, steady state availability, busy period of repairman and inspector, profit function using discrete distribution and regenerative point techniques. Profit function and MTSF are also analyzed graphically.
Keywords - Geometric distribution, Regenerating point technique, MTSF, Availability, Busy period and Profit function.

[1] Agarwal S.C, Sahani M, Bansal S (2010) "Reliability characteristic of cold-standby redundant syatem", May 2010 3(2), IJRRAS.
[2] Haggag M.Y (2009) "Cost Analysis of a System Involving Common Cause Failures and Preventive Maintenance", J.Math & Stat., 5(4):305-310, 2009, ISSN 1549-3644.
[3] Haggag. M.Y. (2009), "Cost analysis of two-dissimilar unit cold standby system with three states and preventive maintenance using linear first order differential equations" J.Math & Stat., 5(4):395-400, 2009, ISSN 1549-3644.
[4] Bhardwaj N (2009) "Analysis of two unit redundant system with imperfect switching and connection time", International transactions in mathematical sciences and Computer,July-Dec. 2009,Vol. 2, No. 2, pp. 195-202.
[5] Bhardwaj N, Kumar A, Kumar S (2008) "Stochastic analysis of a single unit redundant system with two kinds of failure and repairs", Reflections des. ERA-JMS, Vol. 3 Issue 2 (2008), 115-134
[6] Gupta R, Varshney G (2007) "A two identical unit parallel syatem with Geometric failure and repair time distributions", J. of comb. Info. & System Sciences, Vol. 32, No.1-4, pp 127-136 (2007)
[7] Said K.M.EL, Salah M, Sherbeny EL (2005) "Profit analysis fof a two unit cold standby system with preventive maintenance and random change in Units", 1(1):71-77, 2005, ISSN 1549-3644 (2005).

Abstract : The problem of MHD visco-elastic fluid flow over a non-isothermal stretching surface with variable thermal conductivity is analysed. Two different types of heating process are considered namely, (i) A surface with prescribed wall temperature (PST) ii) A surface with prescribed wall heat flux (PHF). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted in to ordinary differential equations by means of similarity transformation. The resulting momentum equations is solved exactly and the solution of energy equation by considering thermal conductivity as function of temperature is solved numerically by shooting technique with fourth order Runge kutta method. The effects of different physical parameters like visco-elasticity, Magnetic parameter, space and temperature dependent heat generation /absorption, Prandtl number etc on temperature profile are thoroughly discussed
Keywords - visco-elasticity, Magnetic parameter, thermal conductivity, space and temperature dependent heat generation /absorption

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[5]. B.K.Dutta, P.Roy, A.S.Gupta: Temperature field in flow over a stretching sheet with uniform heat flux, Int.comm.Heat Mass Transfer 12(1985)89-94