International Journal of Modern Mathematical Sciences
ISSN: 2166-286X (online)Search Article(s) by:
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Current Issue: Vol. 11 No. 2or Keyword in Title:
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Table of Content for Vol. 11 No. 2, 2014

Design Feed Forward Neural Network to Solve Eigenvalue Problems with Dirishlit Boundary Conditions
Luma. N. M. Tawfiq & Othman. M. Salih
      
 PP. 58 - 68
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ABSTRACT: The aim of this paper is to design feed forward neural network for solving nonlinear second order, eigenvalue problem for ordinary differential equations. The network technique finds eigenvalue and the corresponding nonzero eigenvector which represent the solution of equation in a certain domain. The neural networks use the principle of back propagation with different training algorithms such as quasi-Newton, Levenberg-Marquardt, and Bayesian Regulation. Illustration example is presented to show speed, accuracy and effectiveness of using the networks techniques for solving this type of equations, and a comparison between the suggested networks technique and other methods.


On Generalization of Enestrӧm - Kakeya Theorem
M .A. Kawoosa
      
 PP. 69 - 74
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ABSTRACT: In this paper the concept from number theory has been used to obtain some more generalizations of Enestrӧm–Kakeya theorem by taking the case when the coefficients are monotonic ,alternately monotonic, in general when coefficients are monotonic after every r=1,2,3 and so on.


A Possible Development of Nonlinear Quantum Theory and Its Tests
Yi-Fang Chang
      
 PP. 75 - 93
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ABSTRACT: The nonlinear approach of quantum mechanics is continuously an important direction. In this paper, basic nonlinear operators are proposed and corresponding Heisenberg equation was obtained. Then the present applied superposition principle is developed to the general nonlinear form. The quantum commutation and anticommutation belong to F and . This theory may include the renormalization, which is the correction of Feynman rules of curved closed loops. We think the interaction equations must be nonlinear. Many theories, models and phenomena are all nonlinear, for instance, soliton, nonabelian gauge field, and the bag model, etc. The superluminal entangled state, which relates the nonlocal quantum teleportation and nonlinearity, should be a new fifth interaction. Moreover, the nonlinear effects exist possibly for various interactions, for single particle, for high energy, and for small space-time, etc. The relations among nonlinear theory and electroweak unified theory, and QCD, and CP nonconservation, etc., are expounded. Finally, some known and possible tests are discussed. The nonlinear theory relates the possible decrease of entropy in isolated system.


On Beta Skew-t Distribution in Modelling Stock Returns in Nigeria
Shittu O.I, Adepoju K.A and Adeniji O.E
      
 PP. 94 - 102
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ABSTRACT: Stock returns in Nigeria have been modeled using the ARCH and GARCH approach and non-linear models because of the non-Gaussian nature of stock data assuming serial correlation of residual error term. This paper focused on developing a three parameter beta skew-t and four parameter generalized beta skew–t distributions using the logit of beta and that of the generalized beta. The new models extends the two well-known distributions and investigates the moments, shape and measure of skewness with extra shape parameters. The parameters were estimated using the maximum likelihood technique. The performance of the two new distributions was compared among themselves and with the skew–t distribution using the likelihood function and Akaike Information Criterion (AIC) as model performance criteria. Ten years monthly stock returns data from the Nigeria Stock Exchange were used to validate the new models using R-Codes.


On The Efficiency of Modified Ratio Estimator Based on Linear Combination of Kurtosis, Median and Quartile Deviation
Olanrewaju I. Shittu and Kazeem A. Adepoju
      
 PP. 103 - 107
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ABSTRACT: This article focuses on developing a new modified ratio estimator of population mean of the study variable using the linear combination of known values of Median, Coefficient of Kurtosis and Quartile deviation of the auxiliary variable. Comparison of the Mean square error and bias of the proposed estimator will be made with that of Yan and Tian (2010), Subramani, et.al G. (2012), and Jeelani et. al (2013) estimators. We demonstrate numerically that the proposed estimator is more efficient than some of the existing modified ratio estimators.


Existence of Solutions of Nonlinear Fractional Integrodifferential Equation with Analytic Semigroup
Kamalendra Kumar, Rakesh Kumar
      
 PP. 108 - 117
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ABSTRACT: In this paper, we prove the existence and uniqueness of local mild and classical solutions of a class of nonlinear fractional integrodifferential equations in Banach space with analytic semigroup. Gelfand-Shilov principle and fractional powers of operators are used to establish the results.