Open Access Original Research Article

Iterative Approximation of Solutions of Hammerstein Integral Equations with Maximal Monotone Operators in Banach Spaces

M. O. Uba, M. A. Onyido, P. U. Nwokoro

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/28691

Let X be a uniformly convex and uniformly smooth real Banach space with dual space X*. Let F : X → X* and K : X* → X be bounded maximal monotone mappings. Suppose the Hammerstein equation KFu = 0 has a solution. An iteration sequence is constructed and proved to converge strongly to a solution of this equation.

Open Access Original Research Article

Defect Prediction Framework Using Adaptive Neuro-Fuzzy Inference System (ANFIS) for Software Enhancement Projects

Vipul Vashisht, Manohar Lal, G. S. Sureshchandar

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/29644

Software Defect Prediction is the process of forecasting the defect count during various phases of software development life cycle. Defect prediction is vital to successful software project execution since the output is used to proactively plan defect prevention activities. During initial phases of software development life cycle, prediction is quite challenging due to the presence of uncertainty in input parameters, which constitute major component of estimated effort. Multiple attempts have been made by researchers in past to design an appropriate defect prediction model but so far none has found widespread adoption in software industry. In this communication, Adaptive Neuro-fuzzy Inference system (ANFIS) approach has been proposed for designing a defect prediction model. In order to achieve complexity reduction and to increase model adoption, an easy-to-use graphical user interface is designed. The proposed ANFIS based model makes use of organization’s historical projects’ data for building the model. The model provides a defect range (minimum, maximum) as a prediction output. The effectiveness and superiority of proposed ANFIS model is demonstrated through analysis of results achieved.

Open Access Original Research Article

Two Hidden Layer Multiconnected Boltzmann Machine for Controlling Moving Objects

T. D. Todorov, G. S. Tsanev

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/28955

There are various areas of industry where the remote control of machines significantly increases productivity. In terms of household this is extremely important for elderly and disabled people. Voice instructions are the most natural way of communication between employees from different hierarchical structures. The development of contemporary hardware allowing such relationships to build span between man and machine. Contact with the managed object of spoken language makes control very efficiently. Moving objects can be successfully controlled by voice commands having in mind that the voice control assures hands free and fast communication between human and controlled object. The present paper deals with the remote control of moving objects. Voice control is used for managing robots, drones, wheelchairs etc. A new stochastic classifier has been obtained for this purpose. A successful classification by a new two hidden layer Boltzmann machine has been realized. The process of deep machine learning has been studied with respect to the mean field approximation problem. An improved fixed-point iteration algorithm is used to accelerate the rate of convergence. An algorithm for training the classifier has been written explicitly in pseudocode. Real life tests are discussed.

Open Access Original Research Article

Some New Three Step Iterative Methods for Solving Nonlinear Equation Using Steffensen’s and Halley Method

Najmuddin Ahmad, Vimal Pratap Singh

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2016/29322

In this paper, we introduce the comparative study of new three step iterative methods for finding the zeros of the nonlinear equation f(x) = 0. The new method based on the Steffensen’s method and Halley method with using predictor – corrector technique. It is established that the new method (NTSM-1) has convergence order sixth and second new method (NTSM-2) has convergence order seventh. Numerical tests show that the new methods is comparable with the well known existing methods and gives better results.

Open Access Original Research Article

QE-Bayesian and E-Bayesian Estimation of the Frechet Model

Hesham M. Reyad, Adil M. Younis, Soha O. Ahmed

Journal of Advances in Mathematics and Computer Science, Page 1-29
DOI: 10.9734/BJMCS/2016/29231

This paper proposes a new technique namely QE-Bayesian estimation, which is a new modification to the E-Bayesian method of estimation. The suggested approach based on replacing the quasi-likelihood function instead of the likelihood function in the E-Bayesian technique. This study is concerned with evaluating the performance of the QE-Bayesian method versus the original E-Bayesian approach in estimating the scale parameter of the Frechet distribution. The QE-Bayes and E-Bayes estimates are obtained under symmetric loss function [squared error loss (SELF)] and three different asymmetric loss functions [entropy loss function (ELF), weighted balanced loss function (WBLF) and minimum expected loss function (MELF)]. The properties of the QE-Bayesian and E-Bayesian estimates are also studied. Comparisons among all estimators are performed in terms of absolute bias(ABias) and mean square error (MSE) via Monte Carlo simulation. Numerical results show that the QE-Bayes estimates are more efficient as compared with the E-Bayes estimates. 

Open Access Original Research Article

Open Access Original Research Article

Bayesian and Classical Approaches Applied on Saving Habits of Employees Data: A Comparative Study

Genanew Timerga, Nigatu Degu

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/23206

480 employees questionnaire were collected on saving habit at Debre Birhan town during February, 2010 to October, 2011. Descriptive statistics, Binary logistic regression and Bayesian statistical methods were used. Average private worker, low government worker were associated with a significantly lower likelihood of saving regularly versus not saving. Binary logistic regression indicates that age, education, dependent family members, transport, job satisfaction, expenditures and inflation significantly affect saving habits of employees. (Coeff-0.569, OR 0.566, P=0.000, CI 0.468, 0.685) the odds of saving decreases by 43.4% for one unit increase in dependent family members. The regression coefficient for the consumption growth rate on the one-period lagged consumption growth rate is expected to be positive. Capacity of employees’ utilized, formal method of saving institutes is higher than informal saving institutes. Our measures that are expected to capture various precautionary saving habits, that is, number of earners in a family and job security of the head of household, are not perfect in capturing uncertainty about future income.