iosr-Jm   Volume-10 ~ Issue-6 ~ Nov-Dec 2014

Abstract: The basic tool we use in our investigation is the nonlinear variation of constants formula for delay systems whilst we determine the controllability of nonlinear functional differential systems. This paper also touches on capture in nonlinear functional differential games of pursuit.

Keywords: Delay systems, controllability, variation of constants formula.

[1]. Hermes,H. and Lasalle,J.P., Functional Analysis and Time Optimal ControlAcademic Press, 1969.
[2]. Chukwu, E. N.,On null-controllability of nonlinear delay systems with restrained controls, J. Math. Anal. Appl. Vol.76, no. 1, July 1980
[3]. ---------------, Capture in linear functional differential games of pursuit, J. Math. Anal. Appl., Vol. 70, No. 2, 1979.
[4]. Shanholt, G. A., A nonlinear variation of constants formula for functional differential equations, Math. Systems theory, Vol. 6, No. 4, 1972-1973.
[5]. Chukwu, E. N., Null-controllability in function space of nonlinear retarded systems with limited control. Preprint.

Abstract: The aim of this paper is to study some properties of ideal Hausdorff space. We introduce some new concepts in ideal topological space such as convergence of sequences and the concepts of Hausdorff axiom in ideal topological space.

Keywords: Ideal topological space, Hausdorff space, continuous, open set

[1]. Banu Pazar Varol, Halis Aygun (2010).
[2]. Clay Shonkwilers, Topology Final, University of Pennsylvania.
[3]. Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71(1951), 152-182.
[4]. N.Levine, Generalized closed sets in Topology, Rend.Circ.Math.Palermo (2), (19) (1970), 89-96.
[5]. Willard General topology. Addison Wesley(1970).

Abstract: In this paper rotating flow of a third grade fluid past a porous plate with partial slip is studied .The nonlinear boundary value problem is solved using finite difference method. The variations of velocity components for various values of partial parameter 𝜆1are discussed the results are reported for conclusion.

Keyword: third grade fluid, partial slip parameter, finite difference method, non - Newtonian fluid.

[1]. Asghar.S, Mudassar Gulzar.M ,Hayat.T,Rotating flow of a third grade fluid by homotopy analysis method ,Appl.Math.and Comput.,165,213-221(2005).
[2]. Asgar .S, Mudassar Gulzar .M and Ayub.M, Effects of partial slip on flow of a third grade fluid,Acta Mech.Sinica.,22,195-198(2006).
[3]. Rao.I.J and Rajagopal.K.R, The effect of the slip boundary condition on the flow of fluids in a channel, Acta Mech.,135,113-126(1999).
[4]. Hayat.T, Nadeem.S, Asghar.S and Siddiqui.A.M, Fluctuating flow of a third grade fluid on a porous plate ,Int.J.Non –Linear Mech.,368,901-906 (2001).

Abstract: In the study of Diophantine equations elliptic curves play a vital role due to its application in proof of famous Fermat's Las t Theorem (FLT) and were further developed with its applications in factoring and primality. In this paper we define elliptic curve E(K) over the field K and describe the arithmetic on elliptic curve and give the group law with respect to the characteristic of K.. Due to its group structure and its analogue nature to multiplicative group of a finite field , elliptic curves find their way in enormous applications in cryptography. In this paper we also describe the group law for elliptic curve over a finite ring and propose a public key encryption with elliptic curve over the ring Zpq for p, q are primes.

Keywords: Elliptic Curve, Cryptosystem.

[1]. R. Balasubramanian "Elliptic Curves and Cryptography" proceedings of the advanced instructional workshop on Algebraic number
theory, HBA (2003)325-345
[2]. I.F.Blake, G. Seroussi and N. P. Smart "Elliptic Curves in Cryptography", volume 265 of London Mathematical Society Lecture
Note Series. Cambridge University Press, Cambridge, 2000.
[3]. J. Buchmann"Introduction to cryptography" , Springer-Verlag 2001
[4]. Jeffery Hoftstein, Jill Pipher, Joseph H. Silverman, " An Introduction to Mathematical Cryptography", Springer
[5]. D. Husemoller. Elliptic Curves, 2nd edition, volume 111 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2004.
With appendices by O. Forster, R. Lawrence, and S. Theisen.
[6]. Neal Koblitz " Algebraic Aspects of Cryptography", volume 3 of Algorithms and Computation in Mathematics. Springer-Verlag,
Berlin, 1998.

Abstract: In this paper, we present the Mathematical model of the effect of complacency in HIV/AIDS preventions. The model was formulated under six (6) assumptions which resulted in a system of first order differential equations. Using methods from dynamical systems theory for analysis, it was shown that the disease free state is stable, the condition for this to be possible is: 1<(μ+𝜆), that is, sum of the rate of progression to AIDS and rate of natural death is greater than 1(one). Also the endemic equilibrium state is asymptotically stable.At this point, the disease will not invade the community; otherwise the disease will invade the community. This means that there should be a bound on the rate of progression to AIDS; this is possible if the tempo of campaign against HIV/AIDS is not relaxed.

Keywords: HIV, AIDS, Mathematical model, equilibrium, asymptotically stable, Complacency

[1]. Baryarama, F. ,(2005) , Periodicity of the HIV/AIDS Epidemic in a Mathematical Model that Incorporate Complacency, American
Journal Infectious Diseases I (I) : 55 – 60 ,2005
[2]. Inyama, S. C. (2004) , Mathematical Model of Transmission Dynamics of HIV/AIDS in Nigeria, A Journal of AMSE on Modelling
, Measurement and Control, France ,Vol.25 N0.4 , 47 – 54
[3]. Leaman, J. and Bhupal, N. ,(2000) , New Figures Suggest Worsening Public Complacency of HIV Threat in
Britain,http://www.mori.com/polls/2000/nat.shml
[4]. Medlock, J. P (1999) , The Effect of Stochastic Migration on an SIR Model for the Transmission of HIV, M.c. Thesis submitted to
the Faculty of the Division of Graduate Studies, Georgia Institute of Technology.

Abstract: In the present paper fractional integral operators associated with I -function for real positive symmetric definite matrix have been discussed. These operators have a wide range of applications in the field of Mathematical Physics and Linear differential equations. A number of special cases of our operators have been mentioned.
Key words: Fractional Integral Operators, I -function, H -function, Matrix transform, Symmetric matrix
(2000 Mathematical Subject Classification: 33C99)

[1]. C. Fox ; A formal solution of certain dual integral equations, Trans. Amer. Math. Soc. 119, 389-395, 1965.
[2]. Garding ; The solution of Cauchy's problem for two totally hyperbolic linear differential equation by means of Reisz integrals, Ann.
Of Math. 48, 785-826, 1947.
[3]. A.M.Mathai ; Special function of matrix argument II, Proc. Nat. Acad. Sci. India 35, Sect. A, 367-393, 1995.
[4]. A.M. Mathai and R.K. Saxena ; Gneralized Hypergeometric Functions With Applications in Statistics and Physical Sciences,
Spring-verleg, Lecture NotesNo. 348, Heidelberg 1973.
[5]. A.M. Mathai and R.K. Saxena ; A generalized probability distribution, Univ. Nac. Tucuman Rev. Ser. A21, 193-202 1978.
[6]. M. Riesz ; L integrale de Riemann-Liouville et. le problem de Cauchy pour 'L' equations desondens, Societe Mathematique de
France, Conference de La Re'Union international des Mathematiciens tenue a Paris on Juillet, Paris 1949.

Abstract: A study of a modification of moment estimation of a two parameter gamma distribution has been carried out. The scale parameter has been estimated using the Modified Moment Estimates (MMEs) and their performance is compared to the Maximum Likelihood Estimates (MLEs). Modified Moment Estimates are easy to compute relative to Maximum Likelihood Estimates. To adjust their bias, the Jackknife technique has been used. The efficiency of these estimators is compared by calculating their respective variances. The R-has been used to carry out the Monte Carlo simulation of data. The results obtained show that the Modified Moment
Estimates perform as well as the Maximum Likelihood Estimates when bias as well as variation of data is taken into account.
Keywords: Gamma distribution, Modified Moment Estimates, Maximum Likelihood Estimates

[1]. Choi, S.C and Wette R., 1969. Maximum likelihood estimation of parameters of the Gamma Distribution and their bias.
Technometrics 11, 83-90
[2]. Fisher, R. A., 1922. On the mathematical foundations of theoretical statistics, Philosophical transactions of the Royal Society of
London A222, 309-368.
[3]. Greenwood, J.A and Durand, D., 1960. Aids for fighting the gamma distribution by maximum likelihood. Technometrics, 2, 55-65
[4]. Hogg, R.V and Craig, A.T., 1978 . Introduction to mathematics statistics.4th edition, NewYork, Macmillan.
[5]. Kendall, M and Stuart, A., 1977. The advanced theory of statistics. Charles Griffin and company limited.
[6]. Thorn, H.C., 1958. A note on the gamma distribution, Monthly Weather Review, 86, 117-122

Abstract: An intuitionistic fuzzy finite automaton with an unique membership transition on an input symbol IFA-UM is considered. IFA-UM homomorphism and strong homomorphism are defined. Admissible relation on the set of states of an IFA-UM is characterized. Each admissible relation on an IFA-UM𝒜, finds an IFA-UM 𝒜1 and there is a strong homomorphism from 𝒜 to 𝒜1.

Keywords: Intuitionistic fuzzy finite automaton IFA-UM, Intuitionistic fuzzy behavior, Homomorphism, Strong homomorphism and Admissible relation.

[1]. K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 20, no.1,(1986),87-96.
[2]. K.T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 33, no.1,(1989a),37-46.
[3]. K.T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst vol.61, no.2,(1994),137-142.
[4]. P.Burillo ,H.Bustince, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets Syst vol.79, (1996),403-405.
[5]. Y.B.Jun, Intuitionistic fuzzy finite state machines, J. Appl. Math. Comput. vol.17, no.1-2,(2005),109-120.
[6]. E.T. Lee, L.A. Zadeh, Note an fuzzy languages, Infom. Sci. vol. 1,(1969),421-434.
[7]. D.S. Malik and J.N. Mordeson, Fuzzy Automata and languages, theory and applications,{CRC}, 2002.

Abstract: We propose an extension to the classical transportation problem by considering multiple incommensurate inputs and outputs for each shipment link. The relative efficiency concept is defined for each shipment link. Two linear programming models are used to determine the optimal transportation plan with maximum efficiency. The applicability of the approach is discussed with a numerical example.

Keywords: Transportation problem (TP). Decision making units (DMUs). Data envelopment analysis (DEA). Relative efficiency.

[1]. Alireza Amirteimoori (2012):An extended transportation problem: a DEA -based approach.: Central European Journal of
Operations research 19:513-521.
[2]. Banker R.D., Charnes A., Cooper W.W.(1984):Some methods for estimating technical and scale inefficiencies in data envelopment
analysis. Management Sci.30(9):1078-1092.
[3]. Charnes A., Cooper W.W., Rhodes E.(1978):Measuring the efficiency of decision making units. European Journal of Operational
Research 2(6):429-444.
[4]. Charnes A.,Cooper W.W.(1962):Programming with linear fractional functions. Naval Research Logistic quarterly 9:181-186.
[5]. Chen L.H., Lu H.W(2007):An extended assignment problem considering multiple inputs and outputs. Applied Mathematical
modelling31:2239-2248.
[6]. Cooper W. W., Seriford L.M., Tone K(2007):Data envelopment analysis: a comprehensive text with models, applications,
references and DEA-solver software.2nd edn. Springer. Berlin.

Abstract: The purpose of this paper is to prove some new coupled fixed point theorems for contractive type mappings defined on dislocated metric spaces. Also, we give an example to support our main theorem and some corollaries of the main result.

Keywords: coupled fixed point, dislocated metric spaces, Contractive type mappings

[1]. C.T. Aage and J.N. Salunke, Some results of fixed point theorem in Dislocated quasi-metric -spaces. Bulletin of Marathwada Mathematical Society, 9(2008), 1-5.
[2]. C.T. Aage and J.N. Salunke. The results on fixed points in dislocated and dislocated quasi-metric space. Appl. Math. Sci. 2(59): 2941-2948, 2008.
[3]. T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered cone metric spaces and applications, Nonlinear Anal., 65 (2006), 825–832.
[4]. P. Hitzler. Generalized Metrics and Topology in Logic Programming semantics. Ph.d thesis, National University of Ireland, University College Cork, 2001.
[5]. P. Hitzler and A. K. Seda, "Dislocated topologies," Journal of Electrical Engineering, vol. 51, no. 12, pp. 3–7, 2000.
[6]. A. Isufati. Fixed point theorems in dislocated quasi-metric space. Appl. Math. Sci. 4(5): 217-223, 2010
[7]. K. Jha and D. Panthi. A common fixed point theorem in dislocated metric spaces. Applied Mathematical Sciences, 6(91):4497:4503, 2012.

Abstract: In the present work we study the combined influence of chemical reaction, Hall currents and radiation absorption on convective heat and mass transfer flow of a viscous electrically conducting fluid past a stretching sheet. The equations governing the flow of heat and mass transfer have been solved by Galerkin finite element analysis with three nodded line segments. The velocity, temperature and concentration have been analysed for different values of M, m, R, N, N1, Sc and Q1. The rate of heat and mass transfer on the plate has been evaluated numerically for different variations.

Keywords: Hall Current, Chemical Reaction, Radiation absorption, Stretching sheet, Heat and Mass transfer.

[1] Abo-Eldahab, E.M and Elbarbary, E.M.E : Hall current effect on magnetohydrodynamic free convection flow past a semi-infinite vertical plate with mass transfer. Int. J. Eng. Sci., Vol.39, pp. 1641-1652 (2001).
[2] Afify, A.A : MHD free-convective flow and mass transfer over a stretching sheet with chemical reaction. Int. J. Heat Mass transfer. Vol.40, pp.495-500 (2004).
[3] Ali, M.E : On thermal boundary layer on a power-law stretched surface with suction or injection. Int. J. Heat Fluid Flow, Vol.16, No.4,pp.280-290 (1995).
[4] Anderson, H.I, Hansen, O.R and Holmedal, B : Diffusion of a Chemically reactive species from a stretching sheet. Int. J. Heat & Mass Transfer, pp. 37-659 (1994).
[5] Anjalidevi, S.P. and Kandaswamy, R : Effects of chemical reaction heat and mass transfer on laminar flow along a semi infinite horizontal plate. Heat Mass Transfer, pp. 35-465 (1999).

Abstract: The aim of the paper is to examine the boundary value problems characterized by the well-known Falkner- Skan Equation.The Falkner -Skan Equation is governed by the third order non liner ordinary differential equation and then to solve numerically using the RungeKutta 4th order with shooting techniques .and solve the Falkner Skan Equation for different parameters 𝛽 and the numerical results are obtain by using Mat lab Software and compare the results of the literature [1],[2],[3].

Key words: Boundary layer, Blasius flow, Falkner Skan flow, RungeKutta method, Shooting Technique.

[1]. Incropera, F.P. and D.P. Dewitt, 2002. Fundamentals of Heat and Mass Transfer. Fifth Ed. John Wiley & Sons Inc., NY.
[2]. Rosales-Vera, M. and A. Valencia, 2010. Solutions of Falkner-Skan equation with heat transfer by Fourier series. International Communications in Heat and Mass Transfer, 37: 761-765.
[3]. Meksyn, D., 1961. New methods in laminar boundary-layer theory. Pergamon Press.
[4]. Asaithambi, N.S., 1997. A numerical method for the solution of the Falkner-Skan equation. Appl. Math. Comput., 81: 259-264.
[5]. Asaithambi, A., 1998. A finite-difference method for the solution of the Falkner-Skan equation. Appl. Math. Comput., 92: 135-141.
[6]. Shi-Jun Liao, 1999. A uniformly valid analytic solution of two-dimensional viscous flow over a semi –infinite flat plate. J. Fluid Mech., 385: 101-128.