iosr-Jm   Volume-10 ~ Issue-4 ~ July-August 2014

Abstract: The research paper aims to determine the divisibility's of a fixed set of common primes namely 7,11,13,17,23,29,31,43,47,43,89& 97 via the compartment method. The method initially during its foundation was extended to 7 but was later successfully extended to the remaining selected numbers. Number Trials (divisibility checker) provide an impetus to check the validation of the compartment method. In spite of the intricacies entailed by the proposed method it successfully aids in determining the divisibilities of other numbers (composites also) as well. An extension to the Number Generator Method has been made to encryption & code generation employing the usage of the former & Euler's Totient function on a primary level.

Keywords: Divisibility, Compartment method, Primes, Number Generator method,Euler-Totient,Greatest Integer Function

[1]. Self Realization of Divisibility Methods.
[2]. Verification & Testing of Divisibility Methods
[3]. Divisibility Theory in Integers (Elementary Number Theory by David M. Burton 2nd Edition)
[4]. Cryptography using RSA technique(Rivest,Shamir,Adleman(1978))
[5]. Euler Totient Theorem(Elementary Number Theory by David M. Burton 2nd Edition)
[6]. Number Theoretic Functions(Elementary Number Theory by David M. Burton 2nd Edition)
[7]. Afrah M Ibraheem,Ahlam J, Lazem(2014) 'Acts freely on Prime & semi-primer near Rings' IOSR Journals ,Vol-10,Issue 3,pp 45-48

Abstract: In this paper, we formulate the mathematical model for the epidemiology of fowl pox infection transmission that incorporates discrete delay. The model results in a discrete delay system of ordinary differential equations with delay parameter 𝜏≥0. Analysing the system using theorems from differential and integral calculus, we discovered that the number of infectives after a very long time from the day of inception of the epidemic is constant. 12𝛿−𝛼 𝑁 + 𝜇14𝛿 − 12𝛼 . The disease free equilibrium and the endemic equilibrium of the system were both established. Using the computable criteria for stability of discrete delay system, unlike ordinary differential equations models, we obtained exponential polynomial equations. Analysing the system using lemmas and theorems from [1], [7],[4] , it was established that both the disease free equilibrium endemic equilibrium points of the system (2.1) – (2.3) are stable in the absence of delay and unstable with increasing delay if 𝛽< 𝜇(𝜇−𝜆)𝛼−𝛿 , that is, the rate at which the birds are recruited into the system must be greater than the rate at which birds die and the rate at which infection transmission is taking place.

Keywords: epidemiology, discrete delay, fowl pox, delay parameter, stability.

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[4]. Hong-shan Ren and Hong-yan, (2002) Explicit Asymptotic Stability Criteria for Neutral Differential Equations with Two Delays ,
Journal of Applied Mathematics e-Notes, 2(2002), 1-9

[5]. Ruan Shigui and Wei Junjie(2001), On the zeros of a third degree Exponential polynomial with application to a delay model for the control of testerone secretion. IMA Journal of mathematics Applied to Medicine and Biology, 18 , page 41 - 52

Abstract: This study concerns with the concepts of join distributive, distributive elements of join semi lattice, modular and super modular semi lattice. We define a join distributive element in super modular semi lattice and obtained every join distributive element of super modular semi lattice is distributive. Also it is proved that every directed below modular semi lattice is a super modular semi lattice. It is defined a super modular pair elements in join semi lattice and proved that, in a super modular semi lattice S, if an element a is join distributive, the pair of elements (a, b) is super modular pair elements of S for b ∈ S.

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Abstract: Limitations record on a variable which have continuous variable changes make the 'time' attached to the data is discrete. That underlies development of continuous time model. Compared to discrete time model, the continuous time model has advantages that can make prediction at different lag. In addition, it still can perform continuous time model parameter estimation, although the objects observations do not always have the same time interval (irregular time). Thus, the purpose of this study is to examine the consistency of continuous time model coefficient parameter with structural equation model (SEM) approach in irregular time data. The method used is the Exact Discrete Model (EDM) with SEM approach. EDM is a model that connects the parameter to value which is underlying parameter of the continuous time model with non-linear relationships. The result analysis of the research indicated that the coefficients of continuous time model parameter are still consistent until 20% of irregular time with 5% consistency limits.

Keywords: Irregular Time, Continuous Time Model, EDM, Consistency of Parameter Coefficient

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Abstract: The success rate of any firm in the industry depends greatly on its sales output. This is achievable only when certain strategies are employed to overcome competition pressures from allied firms. We utilize the tools of Markov decision process in designing our model that improves on the quality of advertisement, research and manpower development to yield an optimal choice leading to profit maximization and cost effectiveness. Finally, we solve our model equations by the value iteration method
Keywords: markov decision process, value iteration method, optimal choice policy,

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Abstract: Sequences are indispensible to the pure and applied mathematicians, and thus, by extension, to all field of sciences. The idea o f difference sequence spaces was introduced in 1981, which has been generalized. The space of almost convergence sequences introduced in 1948 was generalized in 1978. Almost convergence difference sequence spaces have undergone series of gradual generalization. The purpose of this paper is to introduce the concept of m v  almost strongly summable difference sequence spaces with respect to a sequence of moduli on a seminorm q and to examine some properties of the three introduced sequence spaces which generalize many existing results, Various topological properties of these spaces with some of their inclusion relations, were studied including their solidity, symmetricity, sequence algebra, convergence free and so on. In this work, concerted effort has been made to generalize some existing sequence spaces by extending their definitions to a wider space in which the existing ones are contained.
Key Words: Difference Sequence Spaces, Strongly Almost summable sequences, Modulus Function

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Math Anal Appl, 292 (2): 423–432.

Abstract: In this paper it is shown that all standard partial orderings are preserved for con-s-k-EP matrices.
Keywords: Con-s-k-EP Matrix, Partial Ordering.

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Alg. Appl. 82 (1986), 145-161.
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Engineering Applications , Vol. 5, No.1, 2011, 353 – 364.

Abstract: Weconsiders a nearly hyperbolic Kenmotsu manifold admitting a semi-symmetric semi-metric connection and study semi-invariant submanifolds of a nearly hyperbolic Kenmotsu manifold with semi-symmetric semi-metric connection. We also find the integrability conditions of some distributions on nearly hyperbolic Kenmotsu manifold and study parallel distributions (horizontal & vertical distributions) on nearly hyperbolic Kenmotsu manifold.

Key Words : and Phrases:Semi-invariant submanifolds, Nearly hyperbolic Kenmotsu manifold, Parallel distribution, Integrability condition & Semi-symmetric semi-metric connection. 2000 AMS Mathematics Subject Classification:53D05, 53D25, 53D12.

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[2]. Ahmad, M., Semi-invariant submanifolds of nearly Kenmotsu manifold with semi-symmetric semi-metric connection, MathematickiVesnik, 62 (2010), 189-198.
[3]. Ahmad, M.and Ali, K., CR-submanifolds of a nearly hyperbolic Kenmotsu manifold with quarter symmetric non-metric connection, J. Math. Comput. Sci. 3 (2013), No. 3, 905-917.
[4]. ---------------,Semi-invariant submanifolds of a nearly hyperbolic Kenmotsu manifold with semi-symmetric non-metric connection, IJERA, Vol. 7, No. 4 (2013), 107-119.
[5]. Ahmad, M. and Jun, J. B., On certain class of Riemannian manifold with a semi-symmetric semi-metric connection, Tensor N. S. 72 (2010), 143-151.

Abstract: This paper was statistical experimental design to analyze and compare the effect of various inorganic manures on the growth of varieties of maize (Zea mays) in agricultural sector and their significances. Randomised complete block design was employed in analysis of data obtained from secondary source. From the employed analysis of variance test to examine the significance of the effect of inorganic fertilizers on different varieties of maize, the following facts were deduced: the null hypothesis of factor A, which is inorganic fertilizer for the height of the plant, the number of leaves per plant were accepted at 0.05 level of significance. Similarly, the null hypothesis for factor B which is varieties of maize for the number of leaves and height per plant were accepted at 0.05 level of significance. It shows that there is s significant difference in growth of maize when various inorganic fertilizers were applied. Finally, any of the inorganic manures must always be use in order to increase the growth and yield of maize.

Keywords: Randomized complete block design, Inorganic, Fertilizer.

[1]. Cochran W.G and Cox G (1957). Experimental Design, Macmillian Co; NY, USA (2nd edition)
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Abstract: In this paper, the authors introduce a new class of functions called contra gp*-continuous function in
topological spaces. Some characterizations and several properties concerning contra gp*-continuous functions
are obtained. Mathematics Subject Classification: 54 C 05, 54 C 08, 54 C10.
Keywords: gp*- open set, gp*-continuity, contra gp*-continuity

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Abstract: In this paper, we establish exact solutions for some nonlinear partial differential equations. The hyperbolic-sine method [16] is used to construct periodic and solitary wave solutions for some soliton equations and systems such as the generalized Klien-Gordon, the general improved Kadomtsev-Petviashvili (KP), and the Zakharov-Kuznetsov (ZK) with power law nonlinearity equations, the generalized coupled Drinfeld –sokolov –wilso, and the generalized coupled Hirota-Satsuma Kdv systems.
Keywords: Nonlinear PDEs and systems, Exact Solutions, Nonlinear Waves and The hyperbolic-sine function method.

[1]. M.T. Alquran, Solitons And Periodic Solutions To Nonlinear Partial Differential Equations By The Sine-Cosine Method, Appl.
Math. Inf. Sci. 6, No. 1, pp. 85-88, 2012.
[2]. S. A. Mohammad-Abadi, Analytic Solutions Of The Kadomtsev-Petviashvili Equation With Power Law Nonlinearity Using The
Sine-Cosine Method, American Journal of Computational and Applied Mathematics, Vol. 1,No. 2, pp. 63-66, 2011.
[3]. A. J. M. Jawad, The Sine-Cosine Function Method For The Exact Solutions Of Nonlinear Partial Differential Equations, IJRRAS,
Vol. 13, No. 1, 2012.
[4]. M. Hosseini, H. Abdollahzadeh, M.Abdollahzadeh, Exact Travelling Solutions For The Sixth-Order Boussinesq Equation, The
Journal of Mathematics and Computer Science Vol. 2, No.2, pp. 376-387, 2011.
[5]. S. Arbabi, M. Najafi, M. Najafi, New Periodic And Soliton Solutions Of (2 + 1)-Dimensional Soliton Equation, Journal of
Advanced Computer Science and Technology, Vol.1, No. 4, pp. 232-239, 2012.

Abstract: In this paper, the homotopy perturbation method (HPM) and variational iteration method (VIM) are applied to approximate solutions for nonlinear fractional integro-differential equations with boundary conditions. A comparison between these methods takes place. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed methods.

Keywords: Boundary value problems, Caputo fractional derivative, Fractional integro-differential equations, Homotopy perturbation method and Variational iteration method.

[1] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006
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[5] K. Diethelm and A.D. Freed, "On the solution of nonlinear fractional order differential equations used in the modeling of viscoelasticity," in Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, F. Keil, W. Mackens, H. Voss, and J. Werther, Eds., pp. 217--224, Springer, Heidelberg, Germany, 1999

Abstract: Let G= ( V , E ) be a simple connected graph. A set S V is a total dominating set of G if every vertex is adjacent to an element of S. Let Dt(Cn2,i) be the family of all total dominating sets of the graph Cn2, n ≥ 6 with cardinality i, and let dt (Cn2,i) = │Dt (Cn2 , i) │. In this paper we construct dt(Cn2,i),and obtain the polynomial Dt(cn2, x) = Σn dt (Cn2,i)xi i= 𝛾t(Cn2) which we call total domination polynomial of Cn2, n ≥6 and obtain some properties of this polynomial.

Keywords: square of cycle, total domination set, total domination polynomial

[1]. T.W. Haynes, S.T. Hedetniemi, and P.J.Slater, Fundamentals of Domination in Graphs, vol 208 of Manographs and textbooks in Pure and Applied Mathematics, Marcel Dekker, New York,NY,USA,1998.

[2]. S.Alikhani and Y.H. Peng Dominating sets and Domination polynomials of paths,International journal of Mathematics and Mathematical sciences,volume 2009.

[3]. S.Alikhani and Y.H. Peng Dominating sets and Domination polynomials of cycles, Global journal of pure and Applied Mathematics, vol. 4 No 2,2009.

[4]. S.Alikhani and Y.H. Peng, Dominating sets and Domination polynomials of certain graphs, II, OpusculaMathematica.Vol.30No.i.2010

[5]. C.Sekar and T.Premala, Total dominating sets and total domination polynomials of square of paths, IOSR Journal of Mathematics,volume 10,Issue 2 (Mar- Apr, 2014), pp52-58.