iosr-Jm   Volume-12 ~ Issue-5 ~ Sep-Oct 2016

Abstract: In this paper, generalized Hat functions operational matricesare proposed and combined with the method of steps to solve linear and nonlinear delay differential equations of fractional order.We convert the delay differential equationsof fractional order to non-delay differential equationsof fractional orderon a given intervalby apply the method of steps, and then apply the operational matrices for generalized Hat function on the obtained non-delay differential equationsof fractional order to transform linear and nonlinear non-delay differential equationsof fractional order into a system of algebraic equations and then find the solution.Two illustrative examples will be presented to show the accuracy and efficiencyof the proposed method.

Keywords: Fractional calculus, Delay differential equations, Fractional delay differential equations, Hat functions, Method of Steps.

[1] Loverro, A., " Fractional Calculus: History, Definitions and Applications for the Engineer", Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA, May 8, 2004.
[2] KolowankarK. M. and Gangal, " Fractional Differentiability of no-where differentiable functions and dimensions ", CHAOS V.6, No.4, American Institute of Physics, 1996.
[3] Podlubny I . ," Fractional Differential Equations " , Mathematics in Science and Engineering V198, Academic Press, 1999.
[4] Wang Z., Huang X., Li N. and Song X., Chin. Phys. B, 5 050506(2012).
[5] KilbasA. A., Srivastava H. M. and Trujillo J. J. , Theory and Applications of Fractional Di fferential Equations. Elsevier, Amsterdam (2006)..

Abstract: In [5], we introduced the notion of S− valued graphs, where S is a semiring. The fastest growing area in graph theory is the study of domination. In this paper, we introduce the notion of Vertex domination on S− valued graphs and prove simple properties.

Keywords: Semirings, Graphs, S−valued graphs, Vertex Dominating set.

[1] Berge C Theory og Graphs and its Applications, Methuen, London, (1962 ).
[2] Jonathan Golan Semirings and Their Applications, Kluwer Academic Publishers, London.
[3] Jeyalakshmi.S, Rajkumar.M, and Chandramouleeswaran.M: Regularity on S− Graphs,(Submitted)
[4] Ore . U: Theory of Graphs, Amer. Math. Soc. Coll09. Publ. 38, (Amer.Math.Soc., Providence RI) 1962.
[5] Rajkumar.M., Jeyalakshmi.S and Chandramouleeswaran.M: Semiring-valued Graphs International Journal of Math. Sci. and Engg. Appls. , Vol. 9 (III), 2015, 141 152.

Abstract: Geodetic number of a graph is one of the widely studied graph theoretic parameters concerning geodesic convexity in graphs. In this paper, we introduce a variant of this parameter namely, doubly geodetic number of a graph. For a connected graph 𝐺, a set𝑆of vertices of 𝐺is called a doubly geodetic set of𝐺if each vertex in𝑉−𝑆lies on atleast two distinct geodesics of vertices in 𝑆.The doubly geodetic number𝑑 𝑔 𝐺 of 𝐺 is the minimum cardinality of a doubly geodetic set. Any doubly geodetic set of cardinality 𝑑 𝑔 𝐺 is called 𝑑 𝑔-set of 𝐺. In this paper, the doubly geodetic number of certain standard graphs is determined.

Keywords: Doubly geodetic number, doublygeodetic set, geodesic, geodetic number, geodetic set.

1]. Buckley F., Harary F., Distance in Graphs(Addison- Wesley, Redwood City, CA, 1990).
[2]. Harary F., Graph Theory (Reading, MA: Addison-Wesley,1969).
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[4]. Chartrand G., Harary F., and Zhang P., On the geodetic number of a graph,Networks, 39(1), 2002, 1-6.
[5]. Chartrand G., Palmer E. M., and Zhang P., The geodetic number of a graph: A survey, Congr.Numerantium, 156, 2002, 37-58.

Abstract: Jawarneh manifold along with semi-symmetric metric connectionhave been studied, and some of its geometric properties are derived, and some application in general relativity are mentioned.Also a new example of Jawarneh manifold is given.s is determined.

Keywords: Riemannian manifold, semi-symmetric metric connection,locally flat manifold, locally con-harmonically flatmanifold, conformally flatmanifold, Jawarneh manifold,general relativity.

[1] British Journal of Mathematics & Computer Science, 7(3): 191-196, 2015.
[2] K. Yano and M. Kon: Structures on Manifolds, World scientific 1989.
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Abstract: This paper aim to find a suitable model to predict the demand of medical oxygen. The study data contained a number of 120 observations of oxygen consumption( in m3 ) were taken from Soba University Hospital in Khartoum state, since January 2005 to December 2014. We have used Box-Jenkins, Auto Regressive Integrated Moving Average (ARIMA) methodology for building forecasting model. Results suggest that ARIMA(0,1,1) is the most suitable model to be used for predicting the demand of medical oxygen. For testing the forecasting accuracy Root Mean Square Error, Mean Absolute Error, and Mean Absolute Percentage Error are calculated..

Keywords: Modeling Medical Oxygen Demand , Box-Jenkins Methodology, ARIMA ,forecasting oxygen consumption

[1]. Akaike, H. (1973) "Information theory and an extension of the maximum likelihood principle". In B.N. Petrov and B.F. Csaki, eds,
Second International Symposium on Information Theory pp. 267–281, Akademiai Kiad ´ o, Budapest.
[2]. Adriana AnaMaria ALEXANDRU.2008. "MODELLING UNEMPLOYMENT RATE USING BOX-JENKINS PROCEDURE".journal of applied quantitative methods.vol3.p [156-166]..

[3]. American National Home Oxygen Patients Association (NHOPA) Reviewed and Revised 2013 (By: Dennis E. Doherty, MD, Physician Member of NHOPA Board of Directors ) Source URL :www.homeoxygen.com
[4]. Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis Forecasting and Control, 2nd ed., Holden-Day, San Francisco.
[5]. Box, G and Cox, R. (1964) "An analysis of transformations," Journal of the Royal Statistical Society, Series B 26, pp.211-252

Abstract: This paper uses the Generalized Autoregressive Conditional Heteroskedasticity models to estimate volatility (conditional variance) in the monthly returns of the principal stock exchange of Sudan. over the period from January 1999 to December 2013. The models include both symmetric and asymmetric models that capture the most common stylized facts about index returns such as volatility clustering and leverage effect. The empirical results show that the conditional variance process is highly persistents.........

[1] Ahmed Elsheikh M. Ahmed and Suliman Zakaria Suliman – December 2011 MODELING STOCK MARKET VOLATILITY USING GARCH MODELS EVIDENCE FROM SUDAN International Journal of Business and Social Science Vol. 2 No. 23 [Special Issue – December 2011]
[2] Alexander, C. (2001) Market Models: A Guide to Financial Data Analysis,
[3] Bera, A. K., and Higgins, M. L. (1993), "ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Vol. 7, No. 4, 307-366.
[4] Bollerslev, T. (1986), "Generalized Autorregressive Conditional Heteroskedasticity," Journal of Econometrics, 31, 307-327.
[5] Bollerslev, T., and Engle, R. F. (1993) Common persistence in conditional variances. Econometrica, 61, 167{186.

Abstract: we search for a new formula to increase the accuracy of the Alternative Direction Iteration method for solving Partial Differential Equation by using the forth order finite difference method in time and space which will be still consist and unconditional stable

Keywords: Accuracy of ADI method, Finite Difference Method, Partial differential Equation

[1] Douglas Jim & Peasman D.W., Numerical Solution for the Two Dimensional Heat Flow Problem, AM., Inst., Chemical Eng. Dept., J.1 505-512,1955.
[2] AL-Saif A.S.Jand AL-Kanani M.J, Alternating Direction Implicit Formulation of the Differential Quadrature Method for Solving the Unsteady State Two Dimensional Convection-Diffusion Equation,Gen. Math., Vol.7, No.1, pp.41-50, ISSN 2219-7184, November 2011
[3] Tristan S. Ursell,The Diffusion Equation A Multi-dimensional Tutorial, Department of Applied Physics, California Institute of Technology, Pasadena, , October 2007

Abstract: In this paper, we consider deterministic inventory model with power demand and constant deteriorating in considered. The time – varying holding cost is al linear function of time. Shortage are allowed and fully backlogged. The items (like food grains, fashion apparels and electronic equipments) have fixed shelf-life which decreases with time during the end of the season. Using the differential equations the instantaneous state of inventory is derived. With suitable cost considerations the total cost function is obtained. By minimizing the total cost function the optimal ordering policies are derived. A numerical illustration is presented to demonstrate the model and the sensitivity analysis of various parameters is carried out.

Keywords: Constant Deterioration; Power Demand; Inventory; Shortages; Time Dependent Holding Cost

[1] Bose, S. Goswami, A. and Chaudhuri, K.S. (1995) "An EOQ model for deteriorating items with linear time – dependent demand rate and shortages under inflation and time discounting‟, Journal of the Operations Research Society, Vol- 46, pp. 771-782.
[2] Chang, H. J. and Dye, C. Y. (1999) "An EOQ Model for Deteriorating Items with Time Varying Demand and Partial Backlogging‟, Journal of the Operational Research Society, Vol. 50, pp. 1176-1182.
[3] http://dx.doi.org/10.1057/palgrave.jors.2600801
[4] Chung, K. J. and Ting, P. S. "A Heuristic for Replenishment for Deteriorating Items with a Linear Trend in Demand," Journal of the Operational Research Society, Vol. 44, pp. 1235-1241.
[5] Datta, T.K. and Pal, A.K. (1988) "Order level inventory systems with power demand pattern for items with variable rate of deterioration‟, Indian Journal of Pure and Applied Mathematics, Vol.19 (1), pp. 1043-1053.

Abstract: An inventory model with 3-variable Weibull distribution demand rate and constant deterioration is developed. The holding cost is constant. Shortages are not allowed. The salient feature of this inventory model is for non-perishable products or deteriorating items. A numerical example has been illustrated using MATLAB to describe the model and the sensitivity analysis of various parameters is carried out.

Keywords: Constant deterioration; 3-variables Weibull demand; Inflation; Inventory; Constant holding cost

[1] Aggarwal, S. P. (1978). A note on an order-level inventory model for a system with constant rate of deterioration" Journal of the
Operational Research Society, Vol. 15, pp. 184–187.
[2] Balkhi,Z. T., and Benkherouf, L. (2004). "On an inventory model for deteriorating items with stock dependent and time-varying
demand rates "Computers & Operations Research, Vol. 31, pp. 223–240.
[3] Tripathy, C. K., and Mishra,U. (2010)."Ordering Policy for Weibull Deteriorating Items for Quadratic Demand with Permissible
Delay in Payments" Applied Mathematical Sciences, Vol.4, no.44, 2181-2191.
[4] Chakrabarty, T. B., Giri, C. et. al. (1998). "An EOQ model for items with weibull distribution deterioration, shortages and
trended demand: an extension of philip's model [J]," Computers & Operations Research, Vol. 25, No. 7–8, pp. 649–657.
[5] Covert, R.B., and Philip, G.S. (1973). "An EOQ model with Weibull distribution deterioration" AIIE Transactions, 5 (1973) 323-
326.

Abstract: The aim of this paper is to derive the new correlation about the first and second kind of chebyshev wavelets and proposed to new results on the derivative function on chebyshev wavelets. It is most helpful for the optimal control analysis.

Keywords: Chebyshev Wavelet, Derivative of Chebyshev Wavelet, First and Second Chebyshev Wavelet

[1] A. Alipanah and M. Dehghan, Numerical solution of the nonlinear Fredholm integral equations by positive definite functions,
Applied Mathematics and Computation, 190(2), 2007, 1754–1761
[2] E.Babolian and F.Fattah Zadeh, Numerical Solution of differential equation by using Chebyshev Wavelet Oprational Matrix of
Integration, Applied Mathematics and Computation, 188, 2007, 417-426
[3] K.T. Chi, A wavelet approach to fast approximation of steady-state waveforms of power electronics circuits, Int. J. Circ. Theor.
Appl. 31, 2003, 591–610
[4] M.R.Fatihi and M.Smavat., State Analysis and optimal control of Linear Time-Invariant Scaled Systems Using the Chebyshev
Wavelets, Contemporary Engineering Sciences, .20(5), 2012, 91-105,
[5] G.Hariharan and K.Kannan, Haar wavelet in estimating depth profile of soil temperature, Appl.Math.Comput., 21, 2009, 119-225

Abstract: In this paper we have introduced prime harmonious labeling of some new graphs. We prove that the graphs Fan fn, Star Sn, Comb graph Pn.Kn , Crown graph Cn . K1,n , Bistar Bn,n , Middle graph M(Pn) and paths are prime harmonious labeling.

Keywords: Prime labeling, Harmonious labeling, Prime harmonious labeling, Bistar Bn,n , Middle graph M(Pn).

[1]. E. L. Aldred and B. D. Mckay, Graceful and harmonious labeling of trees, personal communication.
[2]. Dushyant Tanna, " Harmonious Labeling Of Certain Graphs"(IJAERS) E-ISSN 2249-8974
[3]. Gallian , J.A.(2010).A dynamic survey of graph labeling, The Electronics Journal of Combinatorics, 17 (#DS6).
[4]. R. L. Graham and N.J.A. Sloane, on additive bases and harmonious graphs, SIAM, J. Alg. Disc. Meth. 1, (1980), 382 – 404.

Abstract: Throughout this paper, we consider finite, simple connected and undirected graph G (V,E) V denotes its vertex set while E its edge set. The number of vertices in G is denoted by P. Degree of a vertex v is denoted by d(v), the maximum degree of a graph G, denoted by Δ. A graph G is connected if any two vertices of G are connected by a path. A maximal connected subgraph of a graph G is called a component of G. The number of components of G is denoted by 𝜔(𝐺). The complement 𝐺 of G is the graph with vertex set V in which two vertices are adjacent if and only if they are not adjacent in 𝐺 . We denote a cycle on p vertices by Cp, a path on P vertices by Pp, complete graph on P vertices by Kp.

Keywords: domination number, Triple connected graph, global triple connected domination number

[1] John Adidharan Bondy , Murthy U.S.R .(2009): graph Theory
[2] Paulraj Joseph J.,Angel Jebitha M.K.,Chithra Devi P.and Sudhana G. (2011): Triple connected graphs , Accepted for publication
[3] Paulraj Joseph J and Arumugham. S. (1995): Domination in Graphs, International journal of Management systems,11:177-182.
[4] Sampathkumar , E;Waliker , HB(1979): The connected domination number of a graph,J.Math. Phys.Sci 13(6):607-613.
[5] Teresa W.Haynes, Stephen T. Hedetniemi and peter J. Slater (1998):Domination in graphs, Advanced Topics, Marcel Dekker, New York.

Abstract: Magnetohydrodynamics (MHD) boundary layer flow past a wedge through porous medium with the influence of thermal radiation, heat source, viscous dissipation and chemical reaction has been analyzed in the present study. The governing nonlinear boundary layer equations for momentum, thermal energy and concentration are transformed to a system of nonlinear ordinary coupled differential equations by using suitable similarity transformation..............

Keywords: Porous medium; MHD; wedge; radiation; viscous dissipation; chemical reaction

[1] Ahmad, R., and W.A. Khan (2015). Unsteady heat and mass transfer magnetohydrodynamic (MHD) nanofluid flow over a stretching sheet with heat source-sink using quasi linearization technique, Canadian J. of physics, 93(12), 1477-1485.
[2] Chamkha, A.J., S. Abbasbandy, A. M. Rashad, and K. Vajravelu (2012). Radiation effects on mixed convection over a wedge embedded in a porous medium filled with a nanofluid, Trans. Porous Med., 91, 261-279.
[3] Chamkha, A.J. (2000). Thermal radiation and buoyancy effects on hydromagnetic flow over an accelerating permeable surface with heat source or sink, Int. J. Heat Mass Transfer, 38, 1699-1712.
[4] Choi S.U.S. (1995). Enhancing thermal conductivity of fluids with nano particles, Devels Appls Non Newtonian Flows, 66, 99-105.
[5] Eshetu, H. and B. Shankar (2014). Heat and mass transfer through a porous media of MHD flow of nanofluids with thermal radiation, viscous dissipation and chemical reaction effects, American Chemical Science, Journal, 4(6), 824-846.

Abstract: This research work investigated the panel of seven African Countries from 1990 to 2015 with a view to determine the direction of causality between the financial development and economic growth in Africa. Dumitrescu-Hurlin Panel Causality test was implemented and the results across the countries under study revealed thatit is strongly evident to reject the null that market value does not homogeneously cause economic growth.This tends to imply that market value across the countries can be used to predict the economic growth in the long run. Similarly, there is strong evidence to reject the null that inflation does not homogenously cause economic growthwhich tends to imply that there is causality effect of inflation on the economic growth of these African countries.

[1] Adnan, N. (2011).Measurement of Financial Development: A Fresh Approach. 8th [2] International Conference on Islamic Economics and Finance. www.qfis.edu.qa/app/media/234. Retrieved on 19/05/13, Time: 2:15pm
[3] Adusei, M. (2013). Financial Development and Economic Growth: Evidence from Ghana.
[4] The International Journal of Business and Finance Research, Vol. 7, No. 5, p. 61-76.
[5] Allen, F. and Gale, D. (1999). Comparing Financial Systems. MA: MIT Press, Cambridge, London

Abstract: Quality of Experience (QoE) evaluation, compared with Quality of Service (QoS), can better reflect the quality of the network by considering the end-user's experience. Based on the number of users and the difference of user's behavior, the operators need to selectsome candidate test points which can perfectly represent all the users, and use the selected test points to simulate the user's behavior in the network. Due to users' different behavior, every candidate test point dominates different users' different behavior, which is described by corresponding dominated matrixes. In this article we present the multi-dominated QoE evaluation point selection problem and establish a.............

Keywords: QoE evaluation, multi-dominated point selection, 0-1 integer linear programming, the improved Ant Colony Optimization, heuristic information

[1] Q Dai, A Survey of Quality of Experience(Berlin:Springer Berlin Heidelberg, 2011,146-156).
[2] M Varela, L Skorin-Kapov, T Ebrahimi, Quality of Service Versus Quality of Experience(Springer International Publishing, 2014, 85-96).
[3] MR Garey, DS Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company. 1979.
[4] M Dorigo, GD Caro, The ant colony optimization meta-heuristic, New Ideas in Optimization, 28(3), 1999, 11--32.
[5] M Dorigo, M Birattari, T Stützle. Ant Colony Optimization: Artificial Ants as a Computational Intelligence Technique, IEEE COMPUT. INTELL. MAG, 2010, 28-39.

Abstract: The concept of connectivity plays a vital role in the theory and applications of graphs. In this paper,
the concept of fuzzy sets and soft sets are applied to study uncertainty and vagueness in graphs. The concept of
m-strong fuzzy soft arc and the complement of fuzzy soft graph are introduced. Connectivity in fuzzy soft graphs
in comparison with their complements is discussed through various examples.

Keywords: fuzzy graph, fuzzy soft graph, complement of fuzzy soft graph, connectivity in fuzzy soft graph, mstrong
fuzzy soft arc.

[1]. Dmitriy Molodtsov, Soft set theory first results, Computers & Mathematics with Applications, 37 (4), 1999, 19-31.
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[3]. 1975) 77-95.
[4]. Lotfi A Zadeh, Fuzzy sets, Information and control, 8(3),1965, 338-353.
[5]. P. K. Maji, Akhil Ranjan Roy, and Ranjit Biswas, An application of soft sets in a decision making problem, Computers &
Mathematics

Abstract: In this note we show that the quark coupling constant q=0.06583 yields the lattice of E6 which has been shown to map the Standard Model. Thus there is no appeal to QCD for binding the quarks. AMS Classification Code:14J247, 14K25, 14M25, 22E70, 81V05.

Keywords: Equiharmonics, Jacobi Theta Function, QCD, Coupling Constant, E6 lattice, Standard Model.

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