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.