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

Abstract: We are know that the properties of square and rectangle .In this paper we are discuss about relation between square and rectangle with the proof .In our real life and educational life, the geometrical figure like rectangle ,square,… etc. have so much importance that we cannot avoid them . We are trying to give a new concept to the world .I am sure that this concept will be helpful in agricultural, engineering, mathematical branches etc. Inside this research, square and rectangle relation is explained with the help of formula. Square-rectangle relation is explained in two parts i.e. Area relation and perimeter relation, rectangle can be narrowed in Segment & the rectangle can be of zero area also.

Keywords: Area, Perimeter, Relation , Seg-rectangle, B- Sidemeasurement

[1]. Surrounding agricultural life.
[2]. Answers.yahoo.com - relationship between a square and a rectangle ( www.answers.yahoo.com )
[3]. Wikipedia , Google and other search engines. ( www.wikipedia.org )

Abstract: Our work is finding continuous function y on (a, ) which is the unique solution for they()(x)=λ
f(y(x)),x(a, ), 0<≤1 with y(-1)(a) = , where is constant and λ is a real number using the picard
approximation method theorem.
Keywords: Fractional differential equation, picard approximation method

[1]. S. Abbas and M. Benchohra; Partial Hyperbolic Differential Equations with FinitedelyInvolving the CaputoFractional Derivative, commun.Math.Anal.7 (2009).
[2]. S. Abbas and M. Benchohra; DarbouxProblem for Perturbed Partial Differential Equations of Fractional Order with Finite Delay, Nonlinear Anal.Hybrid Syst. 3 (2009).
[3]. S. Abbas and M. Benchohra; Upper and Lower Solutions Method for Impulsive Hyperbolic Differential Equations with Fractional Order,Non Linear Anal. Hybrid Syst. 4 (2010).
[4]. R. P Agrawal, M. Benchohra and S. Hamani; A Survey Existence Result for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions, Acta. Appl. Math. 109 (3) (2010).
[5]. A. A. Kilbas,Hari. M. Srivastava and Trujillo;Theory and Applications of Fractional Differential Equations, Elsevier Science B. V., Amsterdam, (2006).

Abstract: The aim of this paper is to introduce a new type of functions called the α REGULAR ω continuous maps , αrω–irresolute maps, strongly αrω–continuous maps , perfectly αrω–continuous maps and study some of these properties.

Keywords: αrω–open sets, αrω–closed sets, αrω–continuous maps, αrω-irresolute maps, strongly αrω-continuous maps, perfectly αrω–continuous.

[2]. Y. Gnanambal, On generalized pre regular closed sets in topological spaces, Indian J. Pure. Appl. Math., 28(3)(1997), 351-360.
[3]. S. S. Benchalli, P. G. Patil and T. D. Rayanagaudar, ωα-Closed sets is Topological Spaces, The Global. J. Appl. Math. and Math. Sci,. 2, 2009, 53-63.
[4]. R.S Wali and Prabhavati S Mandalgeri, On α regular ω-closed sets inTopological spaces, Int. J. of Math Archive 5(10), 2014, 68-76.
[5]. N .Levine, Semi-open sets and semi-continuity in topological spaces,70(1963), 36- 41.
[6]. A.S.Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On pre-continuous and weak pre continuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
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[8]. M. E. Abd El-Monsef, S.N. El-Deeb and R.A.Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12(1983), 77-90.

Abstract: In this paper, we introduce a new class of maps called τ**- generalized semi continuous maps in topological spaces and study some of its properties and relationship with some existing mappings. Key Words: scl*, τ** -topology, τ**-gs-open set, τ**-gs-closed set, τ**- gs-continuous maps.

[1]. M.E. Abd El-Monsef, S.N.El.DEEb and R.A.Mahmoud, β-open sets and and β-continuous mappings, Bull. Fac. Sci. Assiut Univ.12(1)(1983),77-90.
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[4]. S. Easwaran and A Pushpalatha, τ* - generalized continuous maps in topological spaces, International J. of Math Sci & Engg. Appls.(IJMSEA) ISSN 0973-9424 Vol.3, No.IV,(2009),pp.67-76.

Abstract: A deterministic model for the transmission dynamics of avian influenza is formulated. The model is extended from the model proposed by Okosun and Yusuf (2007) by incorporating the culling of infected birds and isolation of infected humans with avian influenza. This study allows for recovery of infected humans. The model showed that the biological feasible region is positively – invariant and attracting. The behaviour of the solutions is illustrated by simulation with different parameter values.

Key words:Avian Influenza, Mathematical Model, Positive-Invariant Region, Proportions, Simulation

[1]. Alexander, D. J. (2000), A review of influenza in different bird species. Vet Microbiol. 72 pp3 – 13
[2]. Arora, D. R. and Arora, B. (2008), Text book of Microbiology(3rd Edition) CBS Publishers & Distributors, New Delhi.
[3]. Birkhoff, G. and Rota, G. (1982).Ordinary Differential Equations.(3rd Ed). John Wiley and Sons, New York.
[4]. Butler, D. (2006), Disease surveillance needs a revolution. Nature, 440(7080) pp 6 – 7.
[5]. Collizza, V., Barrat, A., Barthemy, M., Velleron, A. J. and Vespignani, A.(2007), Modeling the worldwide spread of pandemic influenza: Baseline case and containment interventions. Plos Medicine, 4(1) e13

Abstract: Pricing option is a challenging task in finance. Numbers of parametric and nonparametric methods have been developed for pricing an option. Both methods have their own pros and cons. In this paper fair price of an option is predicted using ɛ-insensitive support vector regression and smooth ɛ-insensitive support vector regression. The methods are applied on five different money market conditions i.e. deep-in-the-money, in-the-money, at-the-money, out-of-money and deep-out-of-money. The experiments are performed on S&P CNX Nifty index option data set. The experimental study reflects that both methods performed fairly well in comparison to Black and Scholes model.

Keywords: Black Scholes model, Moneyness, Option pricing, ɛ- Insensitive Support Vector Regression, Smooth ɛ- Insensitive Support Vector Regression.

[1]. J. C. Hull, Options, futures, and other derivatives (Prentice-Hall, 1997).
[2]. Heston, A closed form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, 6(2), 1993, 327-343.
[3]. Hutchinson, A nonparametric approach to pricing and hedging derivative securities via learning networks, Journal of Finance, 49(3), 1998,851-889 .
[4]. M. Liu, Option pricing with neural networks, in Progress in Neural Information Processing, S. I. Amari, L. Xu, L. W. Chan, I. King, and K. S. Leung, Eds. New York: Springer-Verlag, 2, 1996, 760–765.
[5]. Yao. J., Li. Y., and Tan. C. L., Option price forecasting using neural networks, Omega, 28(4), 2000, 455-466.
[6]. Andreou, Panayiotis C., Chris Charalambous, and Spiros H. Martzoukos, Pricing and trading European options by combining artificial neural networks and parametric models with implied parameters, European Journal of Operational Research, Elsevier, vol. 185(3), 2008, 1415-1433.

Abstract:The object of the present paper is to characterize generalized complex space forms satisfying certain curvature conditions on conhormonic curvature tensor and concrcular curvature tensor. In this paper we study conhormonic semisymetric curvature, conhormonic flat, concircular flat. Also we studied copmlex space form satisfying 𝑁.𝑆=0, 𝐶. 𝑆=0.

Key Words: Generalized complex space forms, Conhormonic semisymetric, Conhormonic flat, Concircular flat. Ams Subject Classification (2010): 53C15, 53C20, 53C21, 53C25, 53D10, 53C55;

[1]. P. Alegre, D.E Blair and A. Carriazo, Generalized Sasakian -space forms, Isrel. J. Math., 141(2004), 151-183.
[2]. D.E. Blair, Contact of a Riemannian geometry, Lecture notes in Math. 509 Springer verlag, Verlin,(1976).
[3]. U.C. De and Avijit Sarkar, On the projective curvature tensor of generalized -Sasakian-space forms, Questions Mathematicae, 33(2010), 245-252.
[4]. U.C. De and G.C. Ghosh, On generalized Quasi-Einstein manifolds, Kyungpoole Math.J.44(2004), 607-615.
[5]. U. K. Kim, conformally flat generalized Saskian-space form and locally symmetri generalized Sasakian space forms, Notedi Mathematica,
[6]. 26(2006), 55-67.
[7]. Mehmet atceken, On generalized Saskian space forms satisfying certain conditions on the concircular curvature tensor, Bulletin of Mathemaical analysis and applications, volume 6 Issue1(2014), pages 1-8.

Abstract:The study of optimization is getting broader with every passing day. Optimization is basically the art of getting the best results under a given set of circumstances. A very simple but important class of optimization problems is the unconstrained problems. Several techniques have been developed to handle unconstrained problems, one of which is the conjugate gradient method (CGM), which is iterative in nature. In this work, we applied the nonlinear CGM to solve unconstrained problems using inexact line search techniques. We employed the well-known Armijo line search criterion and its modified form.
Keywords: Line search, conjugate gradient method, unconstrained problems, step length.

[1]. Andrei, N. (2004). Unconstrained optimization test functions. Unpublished manuscript; Research Institute for Informatics. Bucharest 1, Romania.
[2]. Bamiigbola, O.M., Ali, M. And Nwaeze, E. (2010). An efficient and convergent method for unconstrained nonlinear optimization. Proceedings of International Congress of Matthematicians. Hyderabad, India.
[3]. Dai, Y and Yuan, Y. (2000). A nonlinear conjugate gradient with a strong global convergence properties: SIAM Journal on Optimization. Vol. 10, pp. 177-182.
[4]. Fletcher, R. and Reeves, C.M. (1964). Function minimization by conjugate gradients. Computer Journal. Vol 7, No. 2.
[5]. Fletcher, R. (1997). Practical method of optimization. Second ed. John Wiley, New York.

Abstract:In this paper, Manpower and Machine System breaks down when both of them are in failed state and if one is alone in failed state, the failed one is hired till the other one also fails.Man power system breaks down due to attrition and machine breaks down due to shocks.The entire system has life time which is the maximum of the individuals. During the operation time, the system produces products for sale. When the system fails, the recruitments, the repairs and sales are attended. We study two models In Model-I, the vacancies caused by departure of employees are filled up one by one and in Model-II,when the operation time is more than a threshold time, the recruitment are done all together and when the operation time is less than the threshold time, the recruitments are done one by one. Joint Laplace transform of the pdf of the operation time, the repair time of the machine, therecruitment time and sales time has been found. Their expectations and covariance are presented with numerical illustration .

Keywords: Manpower Machine system, attrition, shocks, Joint Laplace transform

[1]. Barthlomew.D.J,Statistical technique for manpower planning,John Wiley,Chichester(1979)
[2]. Esary.J.D, A.W. Marshall, F. Proschan, Shock models and wear processes, Ann. Probability, 1, No. 4 (1973), 627-649
[3]. Grinold.R.C,Marshall.K.T, Manpower Planning models,North Holl,Newyork (1977)
[4]. Hari Kumar.K, P.Sekar and R.Ramanarayanan, Stochastic Analysis of Manpower levels affecting business with varying
Recruitment rate, International Journal of Applied Mathematics, Vol.8,2014 no.29, 1421-1428.