iosr-Jm   Volume-10 ~ Issue-5 ~ Sep-Oct 2014

Abstract: In the present paper, after defining an integrated contact metric structure manifold [3] I have
defined n M
and nearly n M
manifold. It has been shown that n M
is integrable. Several useful theorems on
these manifolds have also been derived.
Mathematics Subject Classification: 53
Keywords : and Phrases: C -manifold, integrated contact structure, integrated contact metric structure,
Riemannian metric, Riemannian connection.

[1] K. Matsumoto., On Lorentzian Paracontact manifolds, Bull. Yamogata Univ. Nat. Sci., 12 , 1989,151-156.
[2] S. D. Singh and D. Singh., Tensor of the type (0, 4) in an almost Norden contact metric manifold, Acta Cincia Indica, India, 18
M(1), 1997, 11-16.
[3] Shalini Singh, Holomorphic sectional curvature on an integrated contact metric structure manifold, Ultra scientist of physical
sciences, 21 (3)M, 2009, 655-658.
[4] T. Adati and K. Matsumoto, On almost paracontact Riemannian manifold, T.R.U. Maths.,13(2), 1977, 22-39.

Abstract: This paper presents numerical solutions of first order linear fuzzy differential equations using Leapfrog method. The obtained discrete solutions are compared with single-term Haar wavelet series (STHWS) method [1]. Error graphs and error calculation tables are presented to highlight the efficiency of the Leapfrog method. This method can be implemented in the digital computers and take any time of solutions.
Keywords: Fuzzy differential equations, Fuzzy initial value problems, Haar wavelet series, Leapfrog method, Single-term Haar wavelet series method.

[1] S.Sekar and S.Senthilkumar, Single-term Haar wavelet series for fuzzy differential equations, International Journal of Mathematics Trends and Technology, 4(9), 2013, 181 – 188

[2] S. Abbasbandy and T. Allahviranloo, Numerical solutions of fuzzy differential equations by Taylor method, Journal of Computational Methods in Applied Mathematics. 2, 2002, 113-124.

[3] S. S. L. Chang and L. A. Zadeh, On fuzzy mapping and control, IEEE Transactions on Systems, Man, and Cybernetics, 2, 1972, 30–34.

[4] D. Dubois and H. Prade, Towards fuzzy differential calculus.III. Differentiation, Fuzzy Sets and Systems, 8( 3), 1982, 225–233.

[5] M. L. Puri and D. A. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, 91(2), 1983, 552–558

Abstract: Dengue fever is an infectious disease in tropical regions, where its spread is transmitted by Aedesaegypti mosquito. Modeling the spread of dengue disease will facilitate in understanding the dynamics of the spread of disease in a population. There have been several mathematical models of the spread of dengue, in this paper will be modified a model that considering the incubation period. At its transmission in both humans and mosquitoes, viruses undergo an incubation period before the virus can move from mosquitoes to humans and vice versa humans to mosquitoes. In this paper will discuss the transmission of dengue in SIR model involving the incubation of virus in humans it called Intrinsic Incubation Period and model involving virus incubation period in humans and in mosquitoes. The virus incubation period in mosquitos it called Extrinsic Incubation Period. The fixed points were determined on this paper on both models, there were two fixed point namely free disease fixed point and endemic fixed point. Stability analysis performed on both models and numerical approach also performed. It was found that model with intrinsic incubation oscillates towards a stable value, and model with the effect of intrinsic and extrinsic incubation oscillates cyclically.

Keywords: dengue fever, incubation, mathematical model, SIR model, stability

[1] P Pongsumpun, Transmission Model For Dengue Disease With And Without The Effect Of Extrinsic Incubation Period, KMITL Sci. Tech. J. Vol. 6 No. 2, 2006.
[2] M Derouich, A Boutayeb, EH Twizell, A Model of Dengue Fever, BioMedical Engineering OnLine 4 (2003):1-10.

[3] Esteva L, Dynamics of Dengue Disease, Mexico :Cinvestav-Ipv ,1998.

[4] DJ Gubler, Dengue and Dengue Hemorhagic Fever, Clinical Microbiology Review 11 :450-496, 1998.

[5] P Van Den Driesscheand J Watmough, Chapter 6: Further Notes on the Basic Reproduction Number, In: Brauer, F, Van Den Driessche P, Wu J (Eds.), Mathematical Epidemiology, Vol. 1945. Lecture Notes in Mathematics, Springer 159–178, 2008.

Abstract: This paper provided the preliminary test single stage shrinkage estimator for estimating the parameters of simple linear regression model, when a prior estimate of these parameters are available. This prior estimate has been referred in statistical literatures as guess point about the parameters. The expressions for Bias, Mean Squared Error (MSE) and Relative Efficiency of the proposed estimators are obtained. Numerical results are provided when the proposed estimators are estimators of level of significance .Comparisons with the usual estimator (O.L.S.) and existing estimators were made to show the usefulness of the proposed estimators in the sense of Relative Efficiency and Mean Squared Error.
Keywords: Simple Linear Regression Model, Least Square Estimator, Single Stage Shrinkage Estimator, Bias Ratio,Mean Squared Error, Relative Efficiency.

[1] Z.A. Al-Hemyari, A. Khurshid, and A. N. Al-Joboori, On Thompson Type Estimators for the Mean of Normal Distribution , Revista Investigación Operacional , 30(2),2009, 109-116.
[2] A.N. Al-Joboori, Preliminary Test Single Stage Shrunken Estimator for the Parameters of Simple Linear Regression Model, Ibn Al-Haitham Journal for Pure and Applied Science,13(3), 2000, 65-73.
[3] A.N. Al-Joboori, On Shrunken Estimators for the Parameters of Simple Linear Regression Model, Ibn Al-Haitham Journal for Pure and Applied Science, 15(4A), 2002, 60-67.
[4] A.N. Al-Joboori, Pre-Test Single and Double Stage Shrunken Estimators for the Mean of Normal Distribution with Known Variance, Baghdad Journal for Science,7(4), 2010,1432-1441.
[5] A.N. Al-Joboori, On Significance Test Estimator for the Shape Parameter of Generalized Rayleigh Distribution, AL-Qadesyia Journal for Computer and Mathematics Sciences ,3(2),2011,390-399.