iosr-Jm   Volume-10 ~ Issue-5 ~ Sep-Oct 2014

Abstract: This paper studies existence and uniqueness of solutions for system of fractional differential equations involving Caputo derivative with anti periodic boundary conditions of order  (0,3) . We obtain the result by using Banach fixed point theorem.
Keywords: Caputo fractional derivative, fractional differential equations, anti-periodic boundary conditions, Banach fixed point theorem.

[1]. M. Benchohra, S. Hamani, S. K. Ntouyas, Boundary value problems for differential equations with fractional order and nonlocal
conditions, Nonlinear Anal., 71:2391–2396 (2009).
[2]. K. S. Miller, P. N., B. Ross, An introduction to the fractional calculus and fractional differential equations, Willey, New York (1993).
[3]. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Amsterdam (2006).
[4]. I. Podlubny, Srinivasan, fractional differential equations, Academic Press, New York (1999).
[5]. R. Agarwal, M. Benchohra, S. Hamani, Boundary value problems for fractional differential equations, Georgian mathematuical
Journal, 16(3):401–411 (2009).
[6]. B. Ahmad, V. Otero Espiner, Existence of solutions for fractional inclusions with anti periodic boundary conditions, Bound. Value
Probl., 11:Art ID 625347 (2009).

Abstract: For two given graphs G and H, the Ramsey number R(G,H) is the positive integer N such that for every graph F of order N, either F contains G as a subgraph. The Ramsey number R(FƖ , K4 ) where FƖ is the graph of every triangle. The aim of this paper is to prove that R(FƖ , Kn) = 2Ɩ(n-1) + 1 for n=4 & Ɩ = 3 and R(FƖ , Kn) = 2Ɩ(n-1) + 1 for Ɩ ≥ n ≥ 5.

Keywords: Fan, Graph, Ramsey number, Tree, Wheel.

[1] S.A. Burr, Ramsey numbers involving graphs with long suspended paths, Journal of London Mathematical Society 24 (1981), 405–413.

[2] S.K. Gupta, L. Gupta and A. Sudan, On Ramsey numbers for fan-fan graphs, Journal of Combinatorics, Information & System Sciences 22 (1997), 85–93.

[3] Surahmat, E.T. Baskoro and H.J. Broersma, The Ramsey numbers of fans versus K4, Bulletin of the Institute of Combinatorics and its Applications 43 (2005), 96–102

[4] S.P. Radziszowski, Small Ramsey numbers, The Electronic Journal of Combinatorics, (2011), DS1.13.

[5] Yanbo Zhang, Yaojun Chen, The Ramsey numbers of fans versus a complete graph of order five , Electronic journal of graph theory and Applications 2 (1) (2014), 66–69..

Abstract: Thermo-mechanical analysis of functionally graded hollow sphere subjected to time dependant mechanical and thermal boundary conditions is carried out analytically in this study. The material properties are assumed to vary non-linearly in the radial direction, and the Poisson's ratio is assumed constant. For thermal boundary conditions, temperature is prescribed on both surfaces whereas for mechanical boundary conditions tractions are prescribed on the boundaries. Obtaining the distribution of the temperature, the dynamical structural problem is solved and closed form solution is obtained for stress components.

Keywords: Thermoelasticity; FGM; hollow sphere; Hankel transform; thermal shock; wave propagation

[1] Yamanouchi, M., Koizumi, M., Shiota, I. Proceedings of the First International Symposium on Functionally Gradient Materials,
Japan, 1990, 273–281.
[2] Koizumu, M. The concept of FGM, ceramic transactions. Funct. Grad. Mater. 34, 1993, 3–10.
[3] Johnson, W., Mellor, P.B. Engineering Plasticity (Ellis Harwood Ltd, Chichester, 1983)
[4] Zimmerman, R.W., Lutz, M.P. Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder.J.
Therm. Stress 22, 1999 177–188.
[5] Jabbari, M., Sohrabpour, S., Eslami, M.R. Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially
symmetric loads. Int. J. Press. Vessel. Pipi. 79, 2002, 493–497

Abstract: In this paper, we have considered an allelopathic model of two species and discussed the dynamics of the model when the effect of interaction on prey is based on the rate of consumption of the prey by the predator and the rate of release of toxicant by the predator. The interaction of the predator and prey results on the growth of predator after a time interval (τ). It is shown that the time delay can cause a switch from stable state to unstable state and there by Hopf-bifurcation occurs.
Key words: Hopf –bifurcation, Prey-Predator, Stability, Time-delay, Toxicant

[1]. A. J. Lotka , Elements of Physical biology, Williams and Wilkins, Baltimore, 1925.
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337)(1979).
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337)(1979).
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1998).

Abstract: Atmospheric internal waves can be represented by a nonlinear system of partial differential equation (PDE) under shallow-fluid assumption. In this paper, we exploited the homotopy analysis method (HAM) and variational iteration method (VIM) to obtain an approximate analytical solutions of the system. The results of both methods are then compared with numerical method. It is shown that both HAM and VIM are efficient in approximating the numerical solutions.

Keywords: Atmospheric internal waves, homotopy analysis method, nonlinear PDE system, variational iteration method.

[1] J.W. Rottman, D. Brottman and S.D. Eckermann, A forecast model for atmospheric internal waves produced by a mountain. 16th Australian Fluid Mechanics Confrence Crown Plaza, Goal Coast, AU, 2007.
[2] R.S. Lindzen, Internal gravity waves in atmospheres with realistic dissipation and temperature Part I. mathematical development and propagation of waves into the thermosphere, Geophysical Fluid Dynamics, 1, 1970, 303-355.
[3] B.P. Cassady, Numerical simulations of atmospheric internal waves with time-dependent critical levels and turning points, Department of Mechanical Engineering, thesis, Brigham Young University, Hawaii, USA, 2010.
[4] T.T. Warner, Numerical weather and climate prediction, (New York, USA: Cambridge University Press, 2011) 12-14.
[5] D.L. Williamson, J.B. Drake, J.J. Hack, R. Jacob R, and P.N.Awartrauber, A standard test for numerical approximation shallow-water equations in spherical geometry, Journal of Computation Physic, 102, 1992, 211-224.

Abstract: In this paper,we investigate the non-static massive string magnetized barotropic perfect
fluid cosmological models in Rosen's [Gen.Rel.Grav.Vol.4 (1973) 435] bimetric theory of gravitation.
Using the relation isotropic pressure 'p' directly proportional to energy density 'ρ' ( i.e p = Є1 ρ ,
where -1 ≤ Є1 ≤ 1) , dust filled geometric string model and stiff fluid filled model of the universe are
obtained. Some physical and geometrical behavior of the exhibited models are also discussed.
PACS: 04.50. +h
Keywords: Bimetric theory, magnetic field, cosmic string, perfect fluid.

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Abstract: In this paper, an application of A domain Decomposition method (ADM) is applied for finding the approximate solution of nonlinear partial differential equation. The results reveal that the A domain Decomposition method is very effective, simple and very close to the exact solution.

Keywords: - A domain Decomposition method, nonlinear partial differential equation.

[1] Jerri, Introduction To Integral Equations With Applications, (Marcel Dekker, Inc, New York and Basel,1985) .
[2] Raftari," Application of He's homotopy perturbation method and variational iteration method for nonlinear partial integro-differential equations", World Applied Sciences Journal, 7, 4, (2009), 399-404.
[3] Raftari," Numerical solutions of the linear volterra integro-differential equations: homotopy perturbation method and finite Difference method", World Applied Sciences Journal, 9, (2010), 7-12.
[4] A., Coddinggton, An introduction To Ordinary Differential Equations With Applications, (Prentics-Hall,INC.,1961) .
[5] Brauer and J. A Nohel, Ordinary Differential Equations,( a First Course, 2nd edition, W. A. Benjamin

Abstract: The Wiener index is the one of the oldest and most commonlyused topological indices in the
quantitative structure-property relationships. It is defined by the sum of the distances between all (ordered)
pairs of vertices of G. In this paper, we use MATLAB program for finding the Wiener index of the vertex
weighted, edge weighted directed and undirected graphs
Keywords: Distance Sum, MATLAB, Sparse Matrix, Wiener Index

[1] Amos Gilat, "MATLAB An Introduction with Applications", John Wiley & Sons, Inc. U.K, 2004.
[2] Bla` Zmazek and JanezZerovnik ,Computing the Weighted Wiener and Szeged Number on Weighted Cactus Graphs in Linear Time, Croaticachemicaacta, CAACAA 76 (2) 137-143(2003) ISSN-0011-1643
[3] Igor Pesek, MajaRotovnik, DamirVukiˇcevi´candJanez ˇZerovnik, Wiener Number of Directed Graphs and Its Relation to the Oriented Network Design Problem, MATCH Commun. Math. Comput. Chem. 64 (2010) 727-742,ISSN 0340 – 6253
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[5] Mohar.B, and Pisanski.T, How to compute the Wiener index of a graph, Journal of mathematical Chemistry, 2 (1988) 267-277.
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Abstract: In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

Keyword: Adomian decomposition method; boundary-value problems; integro-differential equation

[1]. G. Adomian, Solving Frontier Problems of Physics: The Decompositions Method, Kluwer, Boston,(1994).
[2]. W. Chen and Z. Lu, An algorithm for Adomian decomposition method. Appl Math Comput, 159 (2004) 221–235.
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Abstract: We consider here the gravitational collapse of a inhomogeneous dust cloud described by Tolman-bondi models. We find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of initial density distribution. Collapse ends into a black hole if the dimensionless quantity 𝜓 is greater than −22.18033 and ends into a naked singularity if 𝜓 ≤ −22.18033. We find the occurrence of naked singularity in higher dimensional case. We proposed the concept of 'trapped range' of initial data in the different higher dimensional space-times. We show that 'trapped range' of initial data increases with the increase in dimensions of the space-times.

Keywords: Dust collapse, naked singularity, dust collapse, cosmic censorship.

[1]. J. R. Oppenheimer and H. Snyder, On continued gravitational contraction, Phys. Rev. D 56, 0455 (1939).
[2]. R. C. Tolman, Effect of inhomogeneity on cosmological models, Proc. Natl. Acad. Sci. USA 20, 169 (1934).
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Abstract: We study the concept of strong equality of majority domination parameters. Let 1 P and 2 P be
properties of vertex subsets of a graph, and assume that every subset of V (G ) with property 2 P also has
property 1 P . Let 1 (G ) and 2 (G ) , respectively, denote the minimum cardinalities of sets with properties 1 P
and 2 P , respectively. Then 1 2  (G )  (G ) . If 1 2  (G )   (G ) and every 1 (G ) -set is also a 2 (G ) -set
, then we say 1 (G ) strongly equals 2 (G ) , written 1 2  (G )   (G ) . We provide a constructive
characterization of the trees T suchthat ( ) ( ) M M  T  i T , where ( ) M  T and ( ) Mi T are majority domination
and independent majority domination numbers, respectively.
Keywords: Domination number, Majority domination number,Independent majority domination number,
Strong equality. 2010 Mathematics Subject Classification: 05C69

[1]. J. JoselineManora, B. John, Independent Majority Dominating set of a Graph, International Journal of Applied Computational Science and Mathematics -Accepted.
[2]. J. JoselineManora, B. John, Majority Independence Number of a Graph, International Journal of Mathematical Research, Vol-6, No.1 (2014), 65-74.
[3]. J. JoselineManora, V. Swaminathan, Majority dominating sets in graphs, Jamal Academic Research Journal, Vol-3, No.2 (2006), 75-82.
[4]. J. JoselineManora, V. Swaminathan, Results on Majority dominating set, Science Magna, North West University, X'tion, P.R. china, Vol.7, No.3 (2011), 53-58.
[5]. T. W. Haynes, M. A. Henning, P. J. Slater, Strong equality of domination parameters in trees, Discrete Mathematics 260 (2003) 77-87.
[6]. T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.