iosr-Jm   Volume-12 ~ Issue-1 ~ Jan-Feb 2016

Abstract:Williem H. Haemers (2011) reported that the adjacency matrix of a graph can be interpreted as the generator matrix of a binary code [1]. This paper aims at Establishing yet another interplay between the already existing Application of the known (132) –Avoiding class of AUNU Numbers in Eulerian Graphs [2], in coding theory (generation of cyclic codes) with length n  5 and dimension k  4 [3], and the construction of a general linear code of sizeM  8 with n  5 and k  3 .This is achievable first, by considering the three
adjacency matrices constructed using the subsets 1 2 3 5 , (132) A C C and C of    as in [2]. Next , we choose arbitrarily a row each from the three adjacency matrices and form a new matrix say G.

[1] Willem H. Haemers(2011) Matrices for graphs, Designs and Codes, (NATO Science for Peace and security, series 29 Information
Security), Coding theory and Related Combinatorics, IOS press, 2011.
[2] Ibrahim M, Ibrahim A.A, Yakubu M.A.(2012) Algebraic theoretic properties of the (132)-Avoiding class of Aunu patterns
application in Eulerian graphs, Journal of Science and Technology Research, 2012.
[3] Chun P.B, Ibrahim A.A, Nimyel T.N, Choji N.M (Accepted; yet to be published) Algebraic theoretic properties of the (132) 
avoiding class of AUNU permutation patterns: Application in cyclic codes generation and analysis. American Journal of
engineering research..

Abstract: In this paper, we introduce a new algorithm for the public key transferring which is based upon functional analysis and metric spaces with basic properties of circles. Furthermore, we introduce an algorithm to make the changes in keys without meeting. The algorithms presented in this paper promises a high level of security as it uses metric distances, in spite of the large prime numbers used in the present algorithms. The security analysis of the new scheme is also discussed.

[1]. A. J. Menezes, P. C. van Oorschot, S. A. Vanstone "Handbook of Applied Cryptography", CRC Press ISBN: 0-8493-8523-7, 1996, 816 pages.
[2]. S. Punnusamy, "Foundations of Functional Analysis", CRC Press, 2002,457 pages. http://www-history.mcs.st-and.ac.uk/~john/MT4522/Lectures/L5.html. https://en.wikipedia.org/wiki/Ball_(mathematics). [3]. R. D. Sharma, "Mathematics Class- IX," Dhanpat Rai Publications. [4]. C. I. Delman, G. C. Galperin, "A Tale of Three Circles," Mathematics Magazine, Santa Clara University, Vol. 76, no. 1, 2003.

Abstract: The discretized approach for the space variable will be used in this paper to transform nonlinear parabolic partial differential equation into system of ordinary differential equations, then using the backstepping transformation approach to stabilize and solve the obtained system of nonlinear ordinary differential equations, based on evaluating the Lyapunov function of the system which stabilize the original nonlinear partial differential equation.

Keyword: Backsteppingmethod, Parabolicpartial differential equation, Stabilization of boundary control problems, Lyapunov function.

[1]. Balogh A. and Krstic M., (2002), "Infinite Dimensional Backstepping Style Feedback Transformations for a Heat Equation with an Arbitrary Level of Instability", European Journal of control, vol. 8, pp.165-175.
[2]. Burden R. L. and Faires J. D., (2010), "Numerical Analysis", 9th Edition, Cengage Learning, Canada.
[3]. Byrnes, C. I. and Isidori A., (1989), "New Results and Examples in Nonlinear Feedback Stabilization", Systems and Control Letters SCL-12, pp.437–442.
[4]. Fossen T. I., (2011), "Handbook of Marine Craft Hydrodynamics and Motion Control", First Edition. John Wiley & Sons Ltd.
[5]. Isidori A., (1989), "Nonlinear Control Systems", Springer-Verlag. Berlin.
[6]. Koditschek D. E., (1987), "Adaptive Techniques for Mechanical Systems", In: Proceedings of the 5th Yale Workshop on Adaptive Systems, New Haven, CT, pp. 259–265.

Abstract: One of the most recent generalizations of concept of classical convergence of sequences ("a new type of convergence") is statistical convergence defined by Fast. Recently, it became the centre of attraction for many researchers. The objective of this review is to discuss fundamental concepts and results in statistical convergence along with various generalizations which have been subsequently formulated. And finally expose the statistics in statistical convergence.

Keywords: Statistical convergence, convergence in statistics and sequences. Mathematics subject classification: Primary 40F05, 40J05, 40G05.

1]. Abdullah M. A. (2010). On statistical convergence of double sequences in random 2-normed spaces. Journal of Inequalities and Special Functions, 1(2), 17-22.
[2]. Akcoglu, M. A. & Del Junco, A. (1975) convergence of averages of point transformations. Proc. American Mathematics. Soc. 49:265-266.
[3]. Ackcoglu, M. A. Sucheston, L. (1975) weak convergence of positive contractions implies strong convergence of averages, probability theory and related fields, 32:139-145.
[4]. Assani, I. (2005). Pointwise convergence of non conventional averages, college mathematics 102, 245-262
[5]. Bala, I. (2011). On Weak Statistical Convergence of Sequence of Functionals. International Journal of Pure and Applied Mathematics. 70 (5): 647-653
[6]. Bardaro, C. et al., (2015) Korovkin-Type Theorems for Modular Ψ-𝐴-Statistical Convergence. Journal of Function Spaces, Article ID 160401.
[7]. Belen, C. & Yildirim, M. (2015). Generalized statistical convergence and some sequence spaces in 2-normed spaces. Hacettepe Journal of Mathematics and Statistics Volume 44 (3), 513 – 519

Abstract: In this paper, we study a nonlinear boundary value problem (bvp) which generalizes capillarity problem. An existence and uniqueness result is obtained using the knowledge of range for nonlinear operator. Ours extends the result in [12]..

[1]. B.D.Calvert and C.P Gupta "Nonlinear elliptic boundary value problems in Lp-spaces and sums of ranges of accretive operators," Nonlinear Analysis, vol.2, no. 1, pp1-26,1978.
[2]. L. Wei and Z. He;"The applications of sums of ranges of accretive operators to nonlinear equations involving the p-laplacian operator," Nonlinear Analysis: Theory, Methods and Applications, vol.24, no.2, pp 185-193, 1995.
[3]. L. Wei; "Existence of solutions of nonlinear elliptic boundary value problems," Mathematics in Practice and Theory, vol. 31, no.3 pp 360-364, 2001 (chinese)
[4]. L. Wei and Z. Hen; "The Applications of Theories of accretive operators to non-linear elliptic boundary value problems in Lp spaces" Nonlinear Analysis:Theory, Methods and Applcations, vol.46, no. 2, pp 199-211, 2001.
[5]. L. Wei and H.Y.Zhou ; "Existence of solutions of a family of non-linear boundary value problems in L2-spaces", Applied Mathematics: a journal of Chinese unversities, vol.20, no. 2, pp 175-182, 2005.

Abstract:This paper will focus mainly on the relation with commutative ring 𝑅 related on primal ideals. It will represent an efficient decomposition of an ideal 𝐴 of a commutative ring 𝑅 of primal ideals. Here primal
decomposition is denoted as =∩𝑝 ∈𝑋𝐴 𝐴(𝑃) , where 𝐴(𝑃) is the isolated components of 𝐴. To prove 𝑃 ∈ 𝑆𝑝𝑒𝑐 𝑅
that an ideal 𝐴  P is an intersection of 𝑃 - primal ideals iff the elements of the primal ideal to primal
decomposition that is denoted as 𝐴.
Keywords: Primal Ideal, Decomposition of an ideal, Associated Prime, Set -Theoretic Union, Krull-dimension.

[1]. Laszlo Fuchs, William Heinz and Bruce O lberding ,Commutative Ideal Theory without Finiteness Conditions: Primal Ideals, Transactions of the American Mathematical Society, Vol.357,No.7(July.2005) pp:2771-2776.
[2]. W .Krull,Idealtheorie, Ergebnisse d. Math.(Springer-Verlag,Berlin,1935),MR37:5197(2nd edition)
[3]. J. Iroz and D.Rush, Associated Prime Ideals in Non-Noetherian Rings, Can.J.Math.36(1984),344-360 MR85j:13002.
[4]. L.Fuchs , On Primal ideals, Proc Amer.Math.Soc.1(1950),1-6 MR11:310d.
[5]. R. Berger ,Various notations of associated prime Ideals , Annal. Univer. Saraviensis 5(1994), 245-271. MR95g:13001.

Abstract: Inthis paperweconsider the Dunkl-StruveLaplace operatorΔk,αonRd+1,wedefinetheDunkl-Bessel-StruveintertwiningoperatorXk,αwhichhturn outtobetransmutationoperator between Δk,αandtheLaplacian Δd+1,nextweconstructtXk,αthe dual ofthe Dunkl-Bessel-Struve intertwining operator. Weexploit theseoperatorstodevelopanewharmonic analysis corresponding toΔk,α.

[1] Hatem MejjaoliandKhalifaTrimèche, HypoellipticityandHypoanalyticityoftheDunklLaplacianoperator,Integral Transformsand Special FunctionsVol.15,No.6,December 2004,pp.523-548.

[2] L. Kamoun, S.Negzaoui, SonineTransform Associated to Bessel-Struve Operator, arXiv:1011.5394v1.

[3] L.KamounandM.Sifi,Bessel-Struve IntertwiningOperatorand Generalized Taylor Serieson theRealLine,Integral TransformsandSpecialFunctions,Vol.16,January2005,39-55.

Abstract: In this article we study a more general queuing network model of computing systems with non - exponential service times product form solution is obtained for this system and numerical examples are provided to illustrate the more general network of servers in system computer with optimal memory management.

Keywords: Network of queues, memory management, non-exponential service, product form solutions.

[1]. Beutler, F.J., and Melamed, B., (1978)"'Decomposition of Customers streams of Feedback Network of Queues in Equillibrium"',Operartions Research, 26:6, pp. 1059-72.
[2]. Burke, P.J.,"'Output of a Queuing Systems"',Operartions Research, Volume 4, pp. 699-704.
[3]. Burke, P.J.,"'Proof of a Conjecative on the Inter arrival Time Distribution in a M/M/1 Queue with Feedback"',IEEE Trans on Communications, Volume 24, pp. 175-78.
[4]. Buzen, J.P.,(1978)"'A Queuing Network Model of MVS"',ACM Computing Surveys
[5]. Chandy, K.M.,Howard,J.P., and Towsley,D.F.,"'Product From and Local Balance in Queuing Networks,"'JACM, 24:2,pp250-263
[6]. Chandy, K.M.and Sauer,C.H.,"'Approximate Methods for Analyzing Queuing Network Models of Computer System,"'ACM Computing Surveys, 10,pp.281-317.

Abstract:Following the introduction of the concept of statistical monotonicity and upper (or lower) peak point of real valued single sequences by Kaya et al in 2013, we shall in this paper investigate properties of statistically convergent double sequences, introduce definitions of statistical monotonicity and lower (upper) peak points of real valued double sequences. And establish the relationships between the statistical convergence of double sequences and these notions. Finally, we generalised statistical monotonicity using an 𝑅𝐻−regular doubly infinite matrix transformation.

Keywords: Statistical convergence of double sequences, lower to upper peak point and statistical monotone. Mathematics subject classification: Primary 40F05, 40J05, 40G05..

[1]. Armitage D.H. and Maddox, I.J. (1989). A new type of Ces𝑎 ro mean, Analysis, 9(1-2), 195-206.
[2]. Birch, B.J. (1967). Multiplicative functions with non-decraasing normal order, Journal of London Mathematical Socociety, 42, 149-151.
[3]. Buck, R.C. (1953). Generalized asymptotic density, American Journal of Mathematics, 75, 335-346.
[4]. Brono, A. M. & Siddiqui, Z. U. (2013). Generalized statistical convergence for double sequences. IOSR Journal of Mathematics, 6(2), 1-4.
[5]. Fridy, J.A. (1978). Submatrices of summability matrices, International Journal of Mathematical Sciences, 1(4), 519-524.
[6]. Fridy, J.A. (1985). On statistical convergence, Analysis, 5, 301-313.

Abstract:This paper deals with the theoretical investigation of thermal instability of a thin layer of electrically non-conducting, incompressible, rotating micropolar fluid saturating a porous medium in the presence of horizontal magnetic heated from below. A dispersion relation is obtained for a flat fluid layer contained between two free boundaries using a linear stability analysis theory and normal mode analysis method. The influence of various parameters like medium permeability, rotation, coupling parameter, micropolar coefficient , magnetic field and micropolar heat conduction parameter has been analyzed on the onset of stationary convection and results are depicted graphically.

[1]. A.C. Eringen, "Theory of thermo-microfluids", J. Math. Anal. Appl., vol. 38, pp. 480, (1972).
[2]. A.C. Eringen, Int. J. Eng. Sci. 2, 189, (1964).
[3]. R.C. Sharma and P. Kumar, "Effect of rotation on thermal convection in micropolar fluids", Int. J. Engg. Sci., vol. 32(3), pp.
545-551, (1994).
[4]. R.C. Sharma and P. Kumar, "Effect of rotation on thermal convection in micropolar fluids in porous medium", Int. J. Pure
Appl. Math. 29, 95 (1998).
[5]. R.C. Sharma and P. Kumar, "On micropolar fluids heated from below in hydromagnetics", J. Non-Equilibrium
Thermodynamics, vol. 20, pp. 150-159, (1995).

Abstract: The steady, two dimensional, laminar flow of a power - law fluid over a permeable a stretching sheet in the presence of viscous dissipation and convective boundary condition. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, bvp4c MATLAB solver has been used for solving it. Numerical results are obtained for the skin-friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for different values of the governing parameters, namely suction parameter, power-law index parameter, Eckert number, convective parameter, Prandtl number.

Keywords: power-law fluid, viscous dissipation, stretching sheet, suction, convective boundary condition.

[1]. Acrivos, A., Shah, M. J., and Petersen, E. E., (1960), Momentum and heat transfer in laminar Boundary-Layer flows of non-
Newtonian fluids past external surfaces, AIChE Journal, vol.6, pp. 312–317.
[2]. Andersson, H.I., and Irgens, F., (1990), Film flow of power-law fluids, In Encyclopedia of Fluid Mechanics, edited by Cheremisin
off, N.P. Houston: Gulf Publishing. pp.617-648.
[3]. Anuar Ishak, (2012), Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction, Haliza Rosali,
Anuar Ishak, Ioan Pop, International Communications in Heat and Mass Transfer, Vol.39, pp.826-829.
[4]. Aziz A, Ali Y, Aziz T, Siddique J.I., (2015), Heat Transfer Analysis for Stationary Boundary Layer Slip Flow of a Power-Law
Fluid in a Darcy Porous Medium with Plate Suction/Injection, PLoS ONE 10(9): e0138855. doi:10.1371/journal.pone.0138855.Eng
J., http://dx.doi.org/10.1016/j.asej.2015.08.012.

Abstract:The Ternary Quadratic Diophantine Equation given by 𝑥2 + 𝑥𝑦 + 𝑦𝟐 = 12𝑧2 is analyzed for
its patterns of non-zero distinct integral solutions. A few interesting relations between the solutions and special
polygonal numbers are exhibited.
Keyword- Quadratic equation with three unknowns, Integral Solutions.

[1]. L.E.Dickson, History of Theory of Numbers Vol.II, Chelsea Company, New York (1952)
[2]. L.J.Mordell, Diophantine equations, Academic press, London (1969)
[3]. Carmichael, R.D. The Theory of numbers and Diophantine Analysis, Dover Publications, New- York(1959).
[4]. Andre Weil, Number Theory: An approach through history: from hammurapi to legendre / Andre weil: Boston 1983.
[5]. Nigel P. Smart, The algorithmic Resolutions of Diophantine equations, Cambridge university press, 1999.
[6]. Smith D.E History of mathematics vol.I and II, Dover publications, New York 1953.

Abstract:The ternary quadratic homogeneous equations representing homogeneous cone given byz ² = 15x²+y² is analyzed for its non-zero distinct integer points on it. Five different patterns of integer points satisfying the cone under consideration are obtained. A few interesting relations between the solutions and special number patterns namely Polygonal number, Pyramidal number, Octahedral number, Pronic number, Stella Octangular number and Oblong number are presented. Also knowing an integer solution satisfying the given cone, three triples of integers generated from the given solution are exhibited.

Keywords: Ternary homogeneous quadratic, integral solutions.

[1]. L.E. Dickson, History of Theory of numbers, Vol.2, Chelsea Publishing Company, New York, 1952.
[2]. L.J. Mordell, Diophantine Equations, Academic press, London, 1969.
[3]. Andre Weil, Number Theory: An approach through history: from hammurapi to legendre / Andre weil: Boston (Birkahasuser
boston, 1983.
[4]. Nigel P. Smart, The algorithmic Resolutions of Diophantine equations, Cambridge university press, 1999.
[5]. Smith D.E History of mathematics vol.I and II, Dover publications, New York 1953.
[6]. M.A. Gopalan, Note on the Diophantine equation 𝑥2 + 𝑎𝑥𝑦 + 𝑏𝑦2 = 𝑧2 Acta Ciencia Indica, Vol.XXVIM, No: 2, 2000, 105-106.
[7]. M.A. Gopalan, Note on the Diophantine equation 𝑥2 + 𝑥𝑦 + 𝑦2 = 3𝑧2 Acta Ciencia Indica, Vol.XXVIM, No: 3, 2000, 265-266.
[8]. M.A. Gopalan,R.Ganaathy and R.Srikanth on the Diophantine equation 𝑧2 = 𝐴𝑥2 + 𝐵𝑦2 , Pure and Applied Mathematika Sciences
Vol.LII,No: 1-2, 2000, 15-17.

Abstract: In this paper, we present an analysis for an M/D/1 queueing system with balking. It is assumed that arriving customers may balk with a probability according to an exponential distribution. We develop the equations of the steady state probabilities and solution of the steady-state probabilities. The steady-state solution of the models is derived. Some useful measures of performance are derived. Some queueing models are obtained as particular cases of the model are discussed.

Keywords: Balking; Reneging; Steady-state Solution.

[1]. Ancker Jr., C. J. and Gafarian, A. V., Some Queuing Problems with Balking and Reneging. I, Operations Research, vol. 11, no. 1, pp. 88-100, 1963.
[2]. Ancker Jr., C. and Gafarian, A. Queueing with impatient customers who leave at random. Journal of Industry Engineering, XIII, 84–90, 1962.
[3]. A. Shawky. The machine interference model: M/M/C/K/N with balking, reneging and spares. Opsearch, 37, 25–35, 2000.
[4]. Ayyapan, G., Muthu Ganapathi Subramanian, A. and Sekar, G., M/M/1 Retrial Queueing System with Loss and Feedback under Non-pre-emptive Priority Service by Matrix Geometric Method, Applied Mathematical Sciences, vol. 4, no. 48, pp. 2379-2389, 2010.
[5]. Al-Seedy, R.O., El-sherbiny, A.A., El-Shehawy, S.A, and Ammar, S.I., Transient Solution of the M/M/c queue with balking and reneging, Computer and Mathematics with Applications, vol. 57, no. 8, pp. 1280-1285, 2009.

Abstract:The consideration of nanofluids has been paid a good attention on the free convection; the analysis focusing nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very much helpful in heat and mass transfer enhancement. In this paper, the influence of magnetohydrodynamic, thermal radiation, Newtonian heating and chemical reaction on heat and mass transfer over a horizontal linearly stretching sheet embedded in a porous medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure together with shooting method and graphical results for the resulting parameters are displayed and discussed. The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood number are shown in a tabulated form.

Keywords: MHD, nanoparticle, Newtonian heating, porous medium, viscous dissipation, Williamson fluid model.

[1] Buongiorno, J., (2006), Convective transport in nanofluids, Journal of heat transfer, Vol. 128, No.3, pp.240-250.

[2] Choi SUS, Zhang, ZG, Yu, W., Lockwood, F.E & Gruike, EA, (2001), Anomalously thermal conductivity enhancement in nano tube suspensions, Applied Physics Letters, Vol.79, No.14, pp.2252-2254.

[3] Choi, S. U. S., (1995) "Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non-Newtonian flows," ASME, FED-vol. 231/MD- vol. 66, pp. 99-105.

[4] Das M., Mahato, R., Nandkeolyar, R., (2015), Newtonian heating effect on unsteady hydromagnetic Casson fluid flow past a flat plate with heat and mass transfer, Alexandria Engineering Journal, Vol.54, pp.871–879.

[5] Gorla, R.S.R., and Sidawi, I., (1994), Free convection on a vertical stretching surface with suction and blowing, Appl Sci Res, Vol.52, pp.247-257.

[6] Hussanan, A. Khan, I. Shafie, S., (2013), An exact analysis of heat and mass transfer past a vertical plate with Newtonian heating, J. Appl. Math., Article ID: 434571.