iosr-Jm   Volume-12 ~ Issue-2 ~ Mar-Apr 2016

Abstract:In this papera new type of neural networks for the derivation of fourth order Runge-Kutta Method which involves tedious computation of many unknowns and its details.Its analysis can hardly be found in many literatures due to the vital role played by the method in the field of computation and applied science.

Keywords: Fourth order Rungekutta Method, Neural Network, Derivation, Analysis.

[1]. M.K. Jain,S .R. K.Iyengar, R. K. JainNumerical Methods for Scientific and Engineering computing,(2007).
[2]. J.D.Lambert , NumericalMethods for Ordinary Differential Systems, the initial value problem, John Wiley & Sons Ltd. , (1991).
[3]. J.C. Butcher, Numerical methods for Ordinary Differential Equations, John Wiley & Sons Ltd., (2003)
[4]. John R. Dorman , Numerical Methods for differential Equations, a Computational Approach, CRC Press, Inc. , (1996).
[5]. J .D. Lambert, Computational Methods in Ordinary Differential Equations, John Wiley & Sons Ltd., (1973).

Abstract:In this paper, we present a reliable iterative method proposed by Daftardar-Gejji and Hossein Jafari namely (DJM) for solving linear and nonlinear two-point boundary value problems. In comparing this method with the other methods proved it is easy in accessing to approximate solution and fast convergent series with easily computable components. Numerical examples are given to demonstrate the efficiency of the proposed method. The calculations in these examples are solved using the software MATHEMATICA® 10.0.

Keywords:Iterative method, Two-point boundary value problem, Numerical solution.

[1] C.Chun, R. Sakthivel, Homotopy pertubation for solving two-point boundary value problem-comparison with other method, Computer physics communications,181 (2010) 1021-1024.
[2] E. Doedel, Finite defference methods for nonlinear two-point boundary-value problems, SIAM J. Numer. Anal. 16 (1979) 173-185.
[3] A. G. Deacon, S Osher, Finite –element method for a boundary-value problem of mixed type, SIAM J. Numer. Anal. 16 (1979) 756-778.
[4] S. M. Roberts, J. S. Shipman, Two Point Boundary Value Problems: Shooting Methods, American Elsevier, New York, 1972.
[5] T. Y. Na, Computatinnonal Methods in Engineering Boundary Value Problems, Academic, New York, 1979.

Abstract:Approximate solutions of stationary exterior fields of Einstein's equations are obtained by expanding the metric in powers of a certain parameter and solving explicitly the first few orders in terms of two harmonic functions. Earlier approximate solutions up to third order were found. In the present paper we obtain the new fourth and fifth order equations and find their approximate solutions for the particular choice of the harmonic functions. There is a physical interpretation of the approximate solutions at the end of the paper.
Key word:Einstein's Field Equations, Approximate Solutions, Asymptotically Flat Solutions.

[1]. Lewis, T., Proc. Roy. Soc. Lond., A136, 176 (1932)
[2]. Papapetrou, A., Ann. Physik, 12, 309 (1953)
[3]. Kerr, R.P., Phys. Rev. Lett., 11, 237 (1963)
[4]. Tomimatsu, A., and Sato, H., Progr. Theor. Phys., 50, 95 (1973)
[5]. Herlt, E., Gen. Rel. Grav., 9, 711 (1978)

Abstract:By improving the classical Lotka-Volterra model, a reasonable dynamic model is established for the unilateral fish which cannot survive independently. We combine the established model with the stability theory of differential equations to obtain the equilibrium point of the dynamic model about fish mutualism, and analyze the locally stability of the equilibrium point.By constructing Lyapunov function further, we try to analyze the global asymptotical stability of the equilibrium point, and give the corresponding explanations in the view of the evolution of the shoals of fish.

Keywords: Global asymptotical stability, dynamic model, the unilateral fish cannot survive independently

[1]. Gaoxiong Wang et al, Ordinary differential equations (Beijing China: Higher Education Press, 2006).
[2]. Zhenshan Lin, Population dynamics (Beijing China: Science Press, 2006).
[3]. Shuang Liu, Study on population dynamics model of biological system (Chongqing China, Chongqing University, MA, 2012).
[4]. Qiyuan Jiang, Jinxing Xie, ye Jun, Mathematical model (Beijing China: Higher Education Press, 2003).
[5]. Shengqiang Liu, Lansun Chen, Population biology model with stage structure (Beijing China: Science Press, 2010).
[6]. Fengde Chen, Xiangdong Xie, Study on dynamics of cooperative population model (Beijing China: Science Press, 2014).

Abstract:In this paper we discuss the concepts of inverse accurate domination and inverse accurate independent domination in fuzzy graph.We determine the inverse accurate domination number fa-1 (G) and the inverse accurate independent domination number 
fai-1 (G) for several classes of fuzzy graph and obtain bounds for the same.We also obtain Nordhaus-Gaddum type result for these parameters......

[1]. T.W.Haynes, S.T.Hedetniemi and P.J.slater.Fundamentals of domination in graphs,Marcel Dekker,Inc.,New York,1998.
[2]. V.R.kulli and S.C. sigarkanti. Inverse domination in graphs.Nat.Acad.sci.Lelt.,14,473-475.1991.
[3]. G.S.Domke, J.E.Dunbar and L.R. Markus, The inverse domination number of a graph, Ars.Com.,72(2004)149-160.
[4]. V.R.kulli and M.B. Kattimani , Accurate domination in graphs, In V.R.kulli, Ed., Advances in Domination Theory I, vishwa International publications, Gulbarga,India (2012) 1-8.
[5]. V.R.kulli and M.B.kattimani, The Accurate domination number of a graph,Technical Report 2000:01Dept.of.Math. Gulbarga University, Gulbarga.India (200).

Abstract: An attempt is made in this paper to define fuzzy accurate domination number, fuzzy accurate total domination number, fuzzy global accurate domination number and some exact value for fatd(G). Also relationship between fgad(G) and other known domination parameters are explored.

Keywords:Fuzzy accurate domination, Fuzzy accurate total domination, Fuzzy global accurate domination.

[1]. V.R.Kulli, Theory of domination in Graphs, Vishwa International Publications, Gulbarga, India(2010).
[2]. V.R.Kulli and M.B.Kattimani "The accurate domination number of a graphs, Technical Report 2000:01, Dept.of.Math. Gulbarga, India(2000).
[3]. E.Sampathkumar, The global domination number of a graph, J.Math.Phy.Sci.23(1989)377-385.
[4]. V.R.Kulli,, "Global accurate Total domination in graphs" Vishwa International Publications, Gulbarga,India(2012)138.
[5]. A.Nagoorgani and V.T.Chandrasekaran, Domination in Fuzzy Graph, Advances in Fuzzy sets and systems, 1(1) (2006), 17 -26.

Abstract: A labeling graph G which can be gracefully numbered is said to be graceful. A graph which admits a fuzzy graceful labeling is called a fuzzy graceful graph. In this paper we introduced fuzzy vertex gracefulness and discussed to wheel graphs and fan graphs.

Keywords: Graceful labeling, Fuzzy graceful labelling.

[1]. A. Nagoor Gani and J. Malarvizhi , "Isomorphism on fuzzy graphs‟ , World Academy of Science, Engineering and Technology , 2(4) (2008) 11-28.
[2]. A.Nagoor Gani and K. Radha, "On Regular Fuzzy Graphs‟, J.of Physical science, Vol No 12, 2008,33-40
[3]. A. Nagoor Gani and D. Rajalaxmi (a) Subahashini, "Properties of fuzzy labeling graph‟, Applied Mathematical Science, Vol . 6, no . 69-72, pp .3461-3466, 2012.
[4]. A. Nagoor Gani and V.T Chandrasekaran , "A First look at fuzzy graph theory‟, Allied publishers Pvt .Ltd 2010

Abstract:The aim of this paper is to prove some common fixed point theorems for fuzzy mapping involving non-expansive type condition. Our results extend and generalized several known results existing in the literature.
Keywords: Fixed point ,fuzzy mapping, and non expansive mapping.

[1]. BOSE, R. K. and SAHANI, D., Fuzzy mappings and fixed Systems point theorems, Fuzzy Sets and 21 (1987), 53-58.
[2]. CHANG, S. S. and HUANG, N. J., Fixed point theorems for generalized fuzzy mappings, Acta ofEngineering Math. No. 2 (1984), 135-137 (in Chinese).
[3]. CHANG, S. S., Fixed point theorems for fuzzy mappings, Kexue Tongbao 14 (1984), 833-836 (in Chinese).
[4]. CHANG, S. S., Fixed degree for fuzzy mappings and a generalization of Ky Fan's theorem,
[5]. Fuzzy Sets and Systems 24 (1987), 103-112..

Abstract:In this research, an attempt is made to derive a self starting block procedure for some K-step linear multi-step methods (for K=1, 2 and 3), using Chebyshev polynomial as the basis function. The continuous interpolant were derived and collocated at grid and off-grid points to give the discrete methods used in block and applied simultaneously for the solution of non stiff initial value problem. The regions of absolute stability of the methods are plotted and are shown to be A (α) stable. The methods for K=2 and K=3 were experimented on initial value problems and the results reveal that the newly constructed block methods have good error stability
and are efficient.

Keywords:Collocation methods, Initial Value Problems, Chebyshev Polynomials, Perturbation Function, Convergence and Stability.

[1]. Dahlquist G. and Jorck A. B.(1974), Numerical Methods. Englewood Cliffs, N. J; Prentice hall. Pp 221-224
[2]. Fox L and Parker I. B., (1972), Chebyshev Polynomials in Numerical Analysis. University Press, Belfast, Northern Ireland. Pp 3, 22-25.
[3]. Jain M. K. (1979), Numerical Solutions of Differential Equations. Wiley Eastern Limited. New Delhi. Pp 107-140
[4]. Lambert J. D. (1973), Computational Methods in ODEs. John Wiley and Sons, New York. Pp 13.
[5]. Williams P. W. (1972), Numerical Computation. Thomas Nelson and Sons Ltd, 36 Park Street, London WIY 4DE. Pp 93.

Abstract:Linear and non-linear analyses of thermal convection in a sparsely packed porous medium with the external constraint of rotation are studied. The condition for stationary and oscillatory modes in the case of linear theory is obtained using the normal mode analysis. The non-linear analysis is based on the truncated representation of Fourier series. The influence of various parameters on the onset of convection has been analyzed. Using the non-linear theory, the thermal Nusselt number is calculated for different values of Rayleigh number and other parameters arising in the problem. New results in the realm of nonlinear convection are also discussed. A discussion is also made of low-porosity medium results for constant viscosity liquids.

Keywords: Convection, porous medium, anisotropy, stability, heat transport.

[1]. Rudraiah, N. and Rohini, G. (1975). Cellular convection in a rotating fluid through porous medium, Vignana Bharathi, India, 4, 23.
[2]. Rudraiah, N. and Srimani, P. K. (1976). Thermal convection in a rotating fluid through a porous medium, Vignana Bharati, India, 2, 11.
[3]. Rudraiah, N. and Vortmeyer, D. (1978). Stability of finite amplitude and overstable convection of conducting fluid through fixed porous bed, Warme-and Stoffibertragung therme and Fluid Dynamics, 11, 241.
[4]. Patil, P. R. and Vaidyanathan, G. (1983). On setting up of convection currents in a rotating porous medium under the influence of variable viscosity, Int. J. Engg. Sci., 21, 123.
[5]. Palm, E and Tyvand, P. A. (1984). Thermal convection in a rotating porous layer, ZAMP, 35, 122.

Abstract: The objective of this paper is to apply Belallah's model in pricing of coffee futures. This caters to the need to price the coffee futures which will be traded at the Nairobi Securities Exchange (NSE) by the end of year 2017, according to a report given by the Capital Market Authority of Kenya in 2013. We apply Belallah's three-factor model. The factors we consider are: the rate of interest which is assumed to be mean reverting, the convenience yield which is an adjustment to the pricing formula to reflect constraint in a market......

[1]. A. R. Conn, N. G. (1988). Global covergence of a class of trust region algorithms for optimization with simple bounds, . SIAM J. Numer. Anal., 25(2): , 433-460.
[2]. Anderson, R. W. (1983). Hedger Diversity in Futures Markets. The Economic Journal , 370-389.
[3]. Bellalah M. (2001). A reexamination of Corporate Risks Under Incomplete Inforamtion . International Journal of Finance and Economics .
[4]. Bellalah, M. a. (1995). Option Valuation with Infromation Costs:Theory and Tests. Financial Review , 617-635.
[5]. Bellalah, M. (1999b). Les biais des modeles d'options revites. Revenue Franaise de Gestion, Juin , 94-100.

Abstract:The present work deals with proposed and analyzed an eco-epidemiological model consisting of prey-predator system with SVIS  type of disease in prey species only. The boundedness of the solution is discussed. The local and global stability of the system is carried out. The local bifurcation conditions near the predator free equilibrium point are established. Finally the numerical simulation is used to complete our global analysis of the system.

Keywords: prey-predator, SVIS disease, local and global stability, local bifurcation.

[1]. K. P. Hadeler and H. I. Freedman, "Predator-prey populations with parasitic infection," Journal of Mathematical Biology, vol. 27,
no. 6, pp. 609–631, 1989.
[2]. G.-P. Hu and X.-L. Li, "Stability and Hopf bifurcation for a delayed predator-prey model with disease in the prey" Chaos, Solitons
and Fractals, vol. 45, no. 3, pp. 229–237, 2012.
[3]. W. Bob, A.K. George, V Voornb, and D. Krishna, "Stabilization and complex dynamics in a predatorprey model with predator
suffering from an infectious disease," Ecological Complexity, vol. 8, no. 1, pp. 113–122, 2011.
[4]. X. Niu, T. Zhang, and Z. Teng, "The asymptotic behavior of a nonautonomous eco-epidemic model with disease in the prey"
Applied Mathematical Modelling, vol. 35, no. 1, pp. 457–470, 2011.
[5]. E. Venturino, "Epidemics in predator-prey models: disease in the predators," IMA Journal of Mathematics Applied in Medicine and
Biology, vol. 19, no. 3, pp. 185–205, 2002.

Abstract: The concept of statistical limit inferior and superior for single sequences was introduced by Fridy and Orhan (1997) where some inequalities and Knopp type core theorem were obtained. Cakan and Altay extended these results to double sequences, similar results were obtained........

Keywords: Double sequence, limit superior and inferior, core of double sequences. Mathematics subject classification: Primary 40F05, 40J05, 40G05.

[1]. Cakan, C. & Altay, B. (2006). Statistically boundedness and statistical core of double sequences. Journal of Mathematical Analysis and Application, 317(2), 690-697.
[2]. Demirci, K. (2001). I-limit superior and limit inferior. Math. Commun. (6), 165–172.
[3]. Fridy, J. A. & Orhan, C. (1997). Statistical limit superior and inferior, Pro. Amer. Math. Soc.125, 3625-3631.
[4]. Hamilton, H. J. (1936). Transformations of multiple sequences, Duke Math. J. 2, 29-60.
[5]. Hamilton, H. J. (1938). Chang of dimension in sequence transformations, Duke Math. J. 2, 341-342.

Abstract: A numerical analysis is carried out for an unsteady free convective, radiative, chemically reactive, radiation absorption, viscous, incompressible and electrically conducting fluid past an exponentially accelerated vertical porous plate in the presence of sink and Soret and Dofour effects. The set of non-dimensional governing equations along with boundary conditions are solved numerically. The effect of various physical parameters on flow quantities are studied with the help of graphs.......

Keywords:Numerical study; MHD; Radiation; radiation absorption; Chemical reaction; Thermal diffusion and Diffusion thermo effect

[1]. G. S. Seth and Md. S. Ansari, MHD natural convection flow past an impulsively movingvertical plate with ramped wall temperature in the presence of thermal diffusion with heatabsorption, Int. Jou. Appl. Mech. Eng., Vol. 15, pp. 199–215, 2010.
[2]. A.A. Afify, MHD free convective flow and mass transfer over a stretching sheet with chemical reaction, Heat Mass Transfer, Vol. 40, pp. 495-500, 2004.
[3]. S. S. Das, and M. Mitra, Unsteady mixed convective MHD flow and mass transfer past an accelerated infinite vertical plate with suction, Ind. J. Sci. Tech., Vol. 2 (5), pp.18 – 22, 2009.
[4]. Y. J. Kim, Unsteady MHD convective heat transfer past a semi – infinite vertical porous moving plate with variable suction, Int. J. Engg. Sci., Vol. 38, pp. 833 – 845, 2008.
[5]. O.D. Makinde and P. Y. Mhone, Heat transfer to MHD oscillatory flow in a channel filled with porous medium, Rom Journal of Physics, Vol. 50(10), pp.931-938, 2005.

Abstract:In This Paper Some Fundamental Theorems , Definitions In Riemannian Geometry Manifolds In The Space n R To Pervious Of Differentiable Manifolds Which Are Used In An Essential Way In Basic Concepts Of Applications Riemannian Geometry Examples Of The Problem Of Differentially Projection Mapping Parameterization System By Strutting Rank k.

Keywords:Basic Notions On Differential Geometry – Tangents Spaces And Vector Fields – Differential Geometry – Cotangent Space And Vector Bundles – Tensor Fields – Differentiable Manifolds Charts - Surface N-Dimensional.

[1]. Osman.Mohamed M,Basic Integration On Smooth Manifolds And Application Maps With Stokes Theorem ,Http//Www.Ijsrp.Org-
6-Januarly2016.
[2]. Osman.Mohamed M, Fundamental Metric Tensor Fields On Riemannian Geometry With Application To Tangent And Cotangent
,Http//Www.Ijsrp.Org- 6januarly2016.
[3]. Osman.Mohamed M, Operate Theory Riemannian Differentiable Manifolds ,Http//Www.Ijsrp.Org- 6januarly2016.
[4]. J.Glover,Z,Pop-Stojanovic, M.Rao, H.Sikic, R.Song And Z.Vondracek, Harmonic Functions Of Subordinate Killed Brownian
Motion,Journal Of Functional Analysis 215(2004)399-426.
[5]. M.Dimitri, P.Patrizia , Maximum Principles For Inhomogeneous Ellipti Inequalities On Complete Riemannian Manifolds , Univ.
Degli Studi Di Perugia,Via Vanvitelli 1,06129 Perugia,Italy E-Mails : Mugnai@Unipg,It , 24July2008.sss

Abstract: The Study Investigated The Relationship Between Perceived Leadership Style, Organizational Justice And Work Alienation. Two Hundred And Forty-One Staff Of The University Of Nigeria, Nsukka Southeastern Nigeria Participated In The Study. Their Ages Ranged From 25years To 58years, With A Mean Age Of 41.5 Years. Work Alienation Scale, Multi-Factor Leadership Questionnaire And Organizational Justice Scale Were Used For Data Collection. Results Of The Hierarchical Multiple Regression Analysis Revealed That Transformational Leadership Style Negatively Predicted Work Alienation And Contributed 2% Variance In Work Alienation......

Keywords: Perceived Leadership Style, Organizational Justice, Work Alienation And Nigerian University

[1]. Adams, J.S. (1965). Inequity In Social Exchange. In L. Berkowitz (Ed), Advances In Experimental Psychology, 2, 267-299. San Diego, CA: Academic Press.
[2]. Alder, G. S., & Ambrose, M. L. (2005). Towards Understanding Fairness Judgments Associated With Computer Performance Monitoring: An Integration Of The Feedback, Justice, And Monitoringresearch. Human Resource Management Review. 15, (1), 43-67.
[3]. Ambrose, M. L., Seabright, M. A., & Schminke, M. (2002). Sabotage In The Workplace: The Role Of Organizational Injustice. Organizational Behavior And Human Decision Processes, 89, 947-965.
[4]. Armstrong-Stassen, M. (2006). Determinants Of How Managers Cope With Organizational Downsizing. Applied Psychology: An International Review, 55(1), 1-26.
[5]. Avolio, B. J., & Bass, B. M. (1997). The Full Range Leadership Development Manual For The Multifactor Leadership Questionnaire. Redwood City: Mind Garden Inc.

Abstract: A Retrial Queueing System With Two Types Of Batch Arrivals Has Been Considered. The Arrivals Are Called Type I And Type II Customers. The Type I Customers Arrive In Batches Of Size 𝑘 With Probability 𝑐𝑘 And Type II Customers Arrive Singly According To Two Poisson Processes With Rates k k c kc   1 1 1   And 2  Respectively. In Addition, Let P Be The Probability Of Admission For Each Individual Type I Customer.......

Keywords: Batch Arrival, Joint-Distribution, Operating Characteristics, Queueing, Retrial.

[1]. G.I. Falin, And J. G. C. Templeton, Retrial Queues (Chapman And Hall, London, 1997).
[2]. J.R. Artalejo, Accessible Bibliography On Retrial Queues, Mathematical And Computer Modelling, 30, 1999, 1-6.
[3]. J.R. Artalejo, A Classical Bibliography Of Research On Retrial Queues: Progress In 1990 -1997, Top, 7, 1999, 187-211.
[4]. J..R. Artalejo, And G.I. Falin, Standard And Retrial Queueing Systems: A Comparative Analysis, Rev. Mat. Complut., 15, 2002, 101-129.
[5]. J.R. Artalejo, A.N. Dudin, And V.I. Klimenok, Stationery Analysis Of A Retrial Queue With Preemptive Repeated Attempts, Operations Research Letters, 28, 2001,173-190.

Abstract: In this paper the exact solution of linear Fredholm-Volterra integral equations of the second second kind is presented. Which is obtained by using modified decomposition method and examples are given to show the validity of the method presented.

Keywords: Exact, modified decomposition method, Fredholm-Volterra integral equations.

[1] Abdul-majid W., "Linear and nonlinear integral equations", Saint Xavier University, 2011.

[2] Rahman M., "Integral Equation and Their Applications", Dalhousie University, 2007.

Abstract: A locally consecutive edge-labeling of a graph G is defined as an assignment of distinct positive integers from the set {1, 2, q } to the edges of G where q is the number of edges of G integers so that all the edges incident at each vertex receive consecutive integers and is said to be locally semi consecutive edge labeling, so that at each vertex of G having degree at least two, at least two of the incident edges receive consecutive. In this paper, we prove that a connected........

Keywords: Locally consecutive, locally semi - consecutive, caterpillar, tree, star.

[1]. M. Apostal, Introduction to Analytic Number Theory, Narosa Publishing House, Second edition, 1991.
[2]. J. A. Bondy and U. S. R. Murty, Graph Theory with applications, Macmillan press, London (1976)
[3]. J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of combinatorics (2014).
[4]. F. Harary, Graph Theory Addison – Wesley, Reading Mars., (1968)
[5]. I. Niven and Herbert S. Zuckerman, An introduction to the theory of numbers, Wiley Eastern Limited, Third edition, 1991.

Abstract: In this paper we obtained closed form expressions for crack shape and stress-intensity factors for single crack. These are very important parameters for fracture designing of structures. The problem is first reduced to dual series equations . The dual series equations is reduced to Fredholm-integral equation of second kind and obtained by along with other known functions, in terms of geometrical parameters..

Keywords: crack axis , composite plate , Griffith-Crack, Strain , stress , laminated plate , plane band

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[2]. Chao YJ, Yang S, Sutton MA (1994) On the fracture of solids characterized by one or two parameters: theory and practice. J Mech Phys Solids 42:629–647
[3]. Clausmeyer H, Kussmaul K, Roos E (1991) Influence of stress state on the failure behaviors of cracked components made of steel. Applied Mech. Rev 44:77–92
[4]. Guo W (1995) Elastoplastic three dimensional crack border field- III: fracture parameters. Eng. Fract. Mech 51:51–71
[5]. Hohe J, Hebel J, Friedmann V, Siegele D (2007) Probabilis- tic failure assessment of ferritic steels using the master curve approach including constraint effects. Eng Fract. Mech 74:1274–1292.