iosr-Jm   Volume-13 ~ Issue-5 ~ Sep-Oct 2017

Abstract: Sum Combination of elements of an Artex Space over a bi-monoid and the sum span of a subset of a completely bounded Artex space over a bi-monoid induced to define the sum span of sum span of a subset of a completely bounded Artex space over a bi-monoid. It is proved that the sum span of sum span of a subset of a completely bounded Artex space over a bi-monoid is the sum span. Product Combination of elements of an Artex Space over a bi-monoid and the product span of a subset of a completely bounded Artex space over a bi-monoid induced to define the product span of product span of a subset of a completely bounded Artex space over a bi-monoid. It is proved that the product span of product span of a subset of a completely bounded Artex space over a bi-monoid is the product span............

Keywords: Bi-monoids, Artex Spaces over bi-monoids, Completely Bounded Artex Spaces over bi-monoids, Sum Combination, Sum span the sum span of sum span the product span of product span

[1]. K.Muthukumaran and M.Kamaraj, "ARTEX SPACES OVER BI-MONOIDS", "RESEARCH JOURNAL OF PURE ALGEBRA", 2(5), May 2012, Pages 135-140.
[2]. K.Muthukumaran and M.Kamaraj, "SUBARTEX SPACES OF AN ARTEX SPACE OVER A BI-MONOID" ,"MATHEMATICAL THEORY AND MODELING"(with IC Impact Factor 5.53), An USA Journal of "INTERNATIONAL INSTITUTE FOR SCIENCE, TECHNOLOGY AND EDUCATION", Vol.2, No.7, 2012, Pages 39 – 48.
[3]. K.Muthukumaran and M.Kamaraj, "BOUNDED ARTEX SPACES OVER BI-MONOIDS AND ARTEX SPACE HOMOMORPHISMS", "RESEARCH JOURNAL OF PURE ALGEBRA", 2(7), July 2012, Pages 206 – 216.
[4]. K.Muthukumaran and M.Kamaraj, "SOME SPECIAL ARTEX SPACES OVER BI-MONOIDS", "MATHEMATICAL THEORY AND MODELING"(with IC Impact Factor 5.53), An USA Journal of "INTERNATIONAL INSTITUTE FOR SCIENCE, TECHNOLOGY AND EDUCATION", Vol.2, No.7, 2012, Pages 62 – 73.
[5]. K.Muthukumaran and M.Kamaraj, "BOOLEAN ARTEX SPACES OVER BI-MONOIDS", MATHEMATICAL THEORY AND MODELING" (with IC Impact Factor 5.53), An USA Journal of "INTERNATIONAL INSTITUTE FOR SCIENCE, TECHNOLOGY AND EDUCATION", Vol.2, No.7, 2012, Pages 74 – 85

Abstract: One of the useful tools and often used in the environmental science eld is the predator-prey models,this is because they allow researchers to both observe the dynamics of animal populations and make predictions as how they will develop over time. In this paper, six projections of animal populations based on a simple predator-prey model were created and explore the trends visible.Starting with a set of initial conditions that produced di erent outcomes for the function of the population of rabbits and foxes over a period of 100years time span.Using Runge Kutta method,a MATLAB program was developed to produce the values for the population of rabbits and foxes over the time span of 100years.

Keywords: predator, prey, limits cycle.

[1] S.R Jang and J. Baglama(2002), A nutrient-prey-predator model with intratrophic preda-tion.Journal of Applied Mathematics and Computation.Vol 129,pp517{536.
[2] J.M Cushing and M.Saleem(1982), A predator-prey model with Age structure .Journal of Mathematics Biology,Vol14:pp 231{250.
[3] A.Edwin(2010), Modeling and Analysis of a two prey-one predator system with har-vesting,Holling type II and ratio-dependent responses. M.Sc.Thesis,Makerere Univer-sity,Kampala,Uganda.
[4] R.P Canale(1970) , An analysis of models Describing predator-prey Interaction., The Journal of Biotechnology and Bioengineering Vol VII, pp353{378.
[5] J. Cao,G.F. Fussman and J.O Ramsay(2007), Estimating a predator-prey Dynamical Model with the parameter Cascades method, The Journal of Biometrics Vol10, pp237{ 241..

Abstract: In this paper.........

Keywords: .........

[1]. K. C. Das, B. Zhou, N. Trinajstic, Bounds on Harary index, J. Math. Chem. 46(2009)1369-1376.
[2]. L. Feng, A. Llic, Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number, Appl. Math. Lett. 23 (2010) 943-948.
[3]. B. Zhou, Z. Du, N. Trinajstic, Harary index of landscape graphs, Int. J. Chem. Model. 1(2008)35-44.
[4]. B. Zhou, X. Cai, N. Trinajstic, On the Harary index, J. Math. Chem. 44(2008)611-618.
[5]. K. Xu, K.C. Das, On Harary index of graphs, Dis. Appl. Math. 159 (2011) 1631-1640..

Abstract: This paper discusses the pricing of employee stock options (ESO) using the Boyle and Kamrad- Ritchken trinomial models as a different alternative to the binomial model used by Hull and White. From the numerical results, it was found that Kamrad-Ritchken's trinomial model with 𝜆 = 1.11803 gave the best results in the ESO price estimation. Also obtained the relationship between ESO price with some specific parameter to the ESO's values i.e: exit rate and vesting period. The interesting thing happens to the multiplier of the implementation price (M) as a trigger to execute an option that is, there is an M value at which the OSK price will be maximum.

Keywords: Early Exercise, Employee Stock Options, Exit Rate,Hull-White Model, Vesting Period, Trinomial Model

[1] Boyle. P, A Lattice Framework for Option Pricing with Two States Variables, The Journal of Financial and Quantitative Analysis,23, 1986, 1-12.

[2] Cox. J, S. Ross, and Rubinstein. M, Option Pricing: A Simplified Approach, Journal of Financial Economics7, 1979, 229-264.

[3] Cvitanic. J, Wiener. Z, and Zapatero. F, Analytic Pricing of Employee Stock Options,Review of Financial Studies, 2006,1-

[4] Huddart. S, Employee Stock Options, Journal of Accounting and Economics18, 1994, 207-231.

[5] Hull. J, and A. White, How to Value Employee Stock Option, Financial Analysts Journal 60, 2004, 114-119.

Abstract: A graph G = (V, E) with p vertices and q edges is said to be a skolem mean graph if there exists a function f from the vertex set of G to {1, 2, . . . , p} such that the induced map.........

Keywords: Skolem mean graph, skolem mean labeling, star graphs

[1] V. Balaji, D. S. T. Ramesh and A. Subramanian, Skolem Mean Labeling, Bulletin of Pure and Applied Sciences, Vol. 26E No. 2
(2007), 245-248.
[2] V. Balaji, D. S. T. Ramesh and A. Subramanian, Some Results on Skolem Mean graphs, Bulletin of Pure and Applied Sciences,
Vol. 27E No. 1 (2008), 67-74.
[3] J. A Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 14 (2016),#DS6.
[4] F.Harary, Graph Theory, Addison- Wesley, Reading Mars,(1972).
[5] D.S.T.Ramesh, S.O.Sopna, I.Gnanaselvi and M.P.Syed Ali Nisaya Skolem Mean Labeling Of Four Star Graphs.

Abstract: We present a novel method to fit a possibility distribution on a continuous stream data system and hence fitting a restriction on the same by using mode of the data. This method is an extension of Zadeh's restriction centered theory of information. The proposed method is suitable to measure and analyse information in complex or hybrid systems, where data sufficiency is never fulfilled and approximate reasoning is required. This method mimics the perception calculation technique, which is deeply ingrained in human mind, by which it gathers and analyse information in natural language. A method to precisiate the restriction on the basis of difference between probability and possibility summation is also proposed.

Keywords: Possibility Distribution, possibilistic restriction, Semantic Information

[1]. D. Dubois and H. Prade. Fuzzy sets and statistical data. European Journal of Operational Research, 25:345–356, 1986.
[2]. D. Dubois and H. Prade. Fuzzy sets, probability and measurement. European Journal of Operational Research, 40:135–154, 1989.
[3]. D. Dubois and H. Prade. Fuzzy set and possibility theory - based methods in artificial intelligence. Artificial Intelligence, 148:1–9, 2003.
[4]. D. Dubois and H. Prade. Practical methods of constructing possibility distributions. International Journal of Intelligent Systems, 31:215–239, 2016.
[5]. D. Dubois, H. Prade, and R. Sabbadin. Decision theoretic foundation of qualitative possibility theory. European Journal of Operational Research, 128:459–478, 2001..

Abstract: A Radio labeling of a connected graph G is an injective map h: V(G) → {0, 1, 2, …, N} such that for every two distinct vertices x and y of G,.........

Keywords: Radio labeling, Distance, Eccentricity, Diameter, Hurdle graph, Rooted tree, Biregular rooted trees, Status, Median.

[1]. Daphne Der-Fen Liu, Radio number of Trees, Discrete Mathematics, Vol.308, no.7, PP 1153 - 1164, 2008.
[2]. D. Liu and X.Zhu, multilevel distance labelings for paths and cycles, SIAM Journal on discrete mathematics, Vol.19, no.3,
[3]. pp 281-293, 2005
[4]. Gary Chartrand and Ping Zhang, Discrete Mathematics and its Applications, Series Editor Kenneth H. Rosen
[5]. Gary Chartrand, David Erwin, Ping Zhang, Frank Harary, Radio labeling of graphs, Bull. Inst. Combin. Appl. 33 (2001) 77-85
[6]. Harary F, 1988, Graph Theory, Narosa publishing House Reading, New Delhi..

Abstract: In this paper, a block method was constructed for the direct solution of general second order initial value problems of the Volterra type integro-differential equations. The method was investigated for the basic properties and was found to be zero stable, consistent and convergent. The region of absolute stability showed that the method is A-stable. The method was tested on some existing standard problems, the results revealed that Trapezoidal rule performed significantly better than Simpson's 1/3 and Gaussian quadrature rules as revealed by the absolute error values shown in Tables 2 and 4 signifying that the choice of quadrature rule play an important role in the determination of the solution for VIDEs.

Keywords: Volterra, integro-differential equations, Continuous, Block method, Collocation, Interpolation, second order equations, Hermite, polynomials, Trapezoidal rule, Simpson's 1/3 rule, Gaussian's quadrature rule..

[1] Al-Timeme, Atifa (2003). Approximated Methods for First Order Volterra Integro-Differential Equations, M.Sc. Thesis, University Technology
[2] Areo, E. A., Ademiluyi, R. A. and Babatola, P. O. (2008). Accurate Collocation Multistep Method for integration of first order ordinary differential equations. Journal of Modern Mathematics and Statistics. 2(1): 1-6.
[3] Brunner, H. (1984). Implicit Runge-Kutta Methods of Optimal Order for Volterra Integro-Differential Equations, Mathematics of Computation 42: (165) 95-109
[4] Brunner, P. (1996). The collocation Methods for Ordinary Differential Equations; An Introduction, Cambridge University Press
[5] Brunner, P. (1996). The collocation Methods for Ordinary Differential Equations. An `Introduction.Cambridge University Press..

Abstract: The purpose of this research paper is to develop a mathematical model to predict population figures of Niger state for the period of 20 years using2006 census figures. The data used were collected from National Population commission and were analyzed by using MATLAB Software. The idea behind the projection is to get an estimated figure of the population of Niger state without waiting for census data. The exponential growth model, also known as Malthus Model used in this paper simply shows that for any number of year specified as the proposed year for the growth model, the corresponding value can be obtain which importantly predicts the estimated amount of population. The parameter used for the population, can be used for any given region, which helps to check unwanted population increase or decrease. It can also be exploited to access the success of the method implemented over time.

Keywords: Radio labeling, Distance, Eccentricity, Diameter, Hurdle graph, Rooted tree, Biregular rooted trees, Status, Median.

[1] Banks R. B. (1994).Growth and Diffusion Phenomena: Mathematical Frame- works and Applications, Springer, Berlin.
[2] Central Intelligence Agency.(2016). World Factbook and other sources, prepared by the United States of America.
[3] Glen Ledder, (2005). Differential Equations: A modeling Approach. McGraw-Hill Companies Inc. USA.
[4] Lees, C. M. & Wilcken, J. (2009). Sustaining the Ark: the challenges faced by zoos in maintaining viable populations. International Zoo Yearbook 43: 6–18
[5] Malthus T. R.(1798). An Essay on The Principle Of Population (1st edition, plus excerpts 1803 2nd edition), Introduction by Philip Appleman, and assorted commentary on Malthus edited by Appleman, Norton Critical Editions, ISBN 0-393-09202-X, 1798.

Abstract: Let K be a closed convex nonempty subset of a uniformly convex Banach space E and let {Ti}mi=1 be a finite family of self maps on K such that T1 is uniformly continuous asymptotically Nonexpansive ln the intermediate sense Maps. with F=mi=1F(Ti), an m-step iteration process was used and sufficient conditions for the strong convergence of the process to a common fixed point of the family are proved. MSC(2010):- 47H10, 47J25.

Keywords: uniformly continuous; asymptotically Nonexpansive ln the intermediate sense Maps; finite family, common fixed point; M-step iteration process; strong convergence..

[1] Ya. Alber, C. E. Chidume and H. Zegeye, Approximating fixed points of total asymptotically nonexpansive mappings.Fixed point theory and applications, 2006 (2006), article ID 10673.
[2] K. Goebel and Kirk, A fixed point theorem for asymptotically nonexpansive mappings Proc. Amer. Math. Soc. 35(1972),171-174.
[3] Zegeye, H. and Shahzad (2013), Approximation of the common fixed point of finite family of asymptotically nonexpansive mappings, Fixed point theory and applications. 11186/1687-1812.
[4] L.J. Ciric, J.S. Ume, Ishikawa Iterative process for strongly pseudo-contractive operators in arbitrary Banach spaces, Math. Commun.8(2003),43-48.
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Abstract: When a set of vector fields is in normal forms this helps to understand the behavior of general nonlinear systems. In this work we describe the normal form of formal power series vector fields on R2n whose linear terms are the nilpotent matrix made up of n 22 Jordan blocks. We use an algorithm based on the notion of transvectants from classical invariant theory in determining the normal form for the system with nilpotent linear part.

Keywords: transvectant, equivariants, box product, Stanley decomposition

[1] C. David, L. John, D. O'shea. Ideals, varieties and algorithm, New York, Springer, 1997.
[2] Cushman, J.R. Sanders, N. White, Normal form for the (2;n) nilpotent vector field using invariant theory, Physica D, 1988, 30:399 - 412
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[5] J. Murdock, On the structure of nilpotent normal form modules, J differ Equations, 2002, 180:198-237

Abstract: In this paper certain spaces of testing functions contained in spaces are introduced. The elements of the dual spaces are ultradistributions. The finite generalized Hankel-Clifford transform is a continuous linear operator in spaces of these type. The finite generalized Hankel-Clifford transformation is defined as a continuous linear mapping between the dual spaces. The developed theory is applied to find the general solutions for a Cauchy problem.

[1]. M. Gelfand, G. E. Shilov , Generalized Functions, Vol. 3, Academic press, 1967.
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Abstract: In this paper we prove some theorems on the existence and uniqueness of coupled fixed pints, which are improvements of the results of Shanjit et al.[5].

Keywords: Multiplicative metric space, multiplicative contraction, Coincidence point, Coincidentally Commuting mappings, Common fixed point.

[1] Agamieza E.Bashirov, E.M.Kurpinar and Ali.Ozyapici, Multiplicative calculus and its applications,
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metric spaces without compatibility, Fixed point theorey and Applications (2013), 325.
[5] L. Shanjit, Y. Rohen, T.C. Singh, P.P.Murthy, Coupled Fixed Point theorems in partialy ordered multiplicative metric space and its
applications, Int. Journal. of Pure and Applied Math. Vol. 108, No.1, (2016), 49-62.

Abstract: In this paper some products of k-Pell number and k-Pell-Lucas number are investigated .It also present generalized identities on the product of k-Pell and k-Pell-Lucas numbers to establish connection formulas between them with the help of Binet`s formula

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Sciences,7(98)(2013),4867-4873.
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Sciences,7(121)(2013),6031-6037..

Abstract: This paper analyses a dynamic system which is reviewed at equidistant points of time and at each review, the system is classified into possible number of states and subsequently a decision has to be made. The economic consequences of the decisions taken at the review times are reflected in costs. These properties of Markov decision process are employed to study the maintenance condition of deteriorating equipment. The result could be used to study the status of equipment used in various organizations to determine their efficiency and productivity.

Keywords: Markov decision process, decision epochs, maintenance, deterioration, transition probability, probability, transition reward

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cost of treatment of Leprosy disease.Leonardo journal of sciences 11,69-78.
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