Open Access Original Research Article

Analytical Approximate Solutions of Fractional Convection-Diffusion Equation by Means of Local Fractional Derivative Operators

Mehmet Merdan

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/25827

In this article, the local fractional decomposition method (LFDM) is applied to obtain approximate the analytical solution of nonlinear fractional convection-diffusion. Numerical solutions obtained by local fractional decomposition method are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. A new application of local fractional decomposition method (LFDM) was extended to reproduce the analytical solutions to this equation in the form of a series. It is shown that the solutions obtained by the LFDM are reliable, simple and that LFDM is an effective method for strongly nonlinear partial equations.

Open Access Original Research Article

Curvature-based Penalty for Anatomical and Functional MR Human Spine Image Registration

Sahar Sabaghian, Mohsen Soryani, Mohammad Ali Oghabian, Amir Hossein Batoli

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/25075

This paper describes an application of image registration. The method is based on an efficient implementation of the curvature registration. This non-rigid registration allows us to find best geometric correspondence between two images. The goal is to register anatomical and functional spine images of the same patient to localize functionality in anatomical images. Most of previous experiments have been tested on brain images and it is the first time that the variational method has been used to register spine images. Registration results are compared with those of MIRT toolbox using two kinds of similarity measures; mutual information (MI) and correlation ratio (CR). MIRT is a Matlab software package for 2D and 3D non-rigid image registration. The model of transformation is parametric and based on B-spline method.  Superior results have been achieved compared to the results of MIRT.

Open Access Original Research Article

Sematic Web Mining Using Fuzzy C-means Algorithm

Wria Mohammed Salih Mohammed, Mohamad Mehdi Saraee

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/BJMCS/2016/25471

Semantic web mining (SWM) is the incorporation of two astonishing development research areas; semantic web and data mining. Semantic web can promote the performances and productivities of web mining. Also, data mining approaches can be applied on the semantic web data because the semantic web data is prosperous sources of knowledge to feed the data mining techniques.

In this research a SWM system is designed and implemented using fuzzy C-means (FCM) algorithm. This is performed by developing an application that is created using several techniques. The system makes up of creating the semantic web dataset, dataset query (SPARQL) and converting the semantic web dataset into traditional dataset. After that, data mining is implemented encompassing data pre-processing, fuzzy C-means algorithm and finally exploring the results. 

SWM using FCM has been practiced by producing an application, which involves various techniques such as DotNetRDF, C# programming language, SPARQL for query language. The final results that obtained from the achieved system are more accurate and knowledgeable because of the combination between semantic web and Fuzzy C-means.

Open Access Original Research Article

The Cauchy Problem for the Camassa-Holm Equation with Quartic Nonlinearity in Besov Spaces

Shan Zheng

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/BJMCS/2016/25518

In this paper, we study the Camassa-Holm equation with quartic nonlinearity. We prove that the Cauchy problem for this equation is locally well-posed in the critical Besov space Capture13.JPG or in Capture10.JPG with 1 ≤ p, r ≤ +∞, s > max{1+1/p, 3/2}. We also prove that if a weaker Capture14.JPG-topology is used, then the solution map becomes H¨older continuous. Furthermore, if the space variable x is taken to be periodic, we show that the solution map defined by the associated periodic boundary
problem is not uniformly continuous in  Capture15.JPG with 1 ≤ r ≤ +∞, s > 3/2 or r = 1, s = 3/2 .

Open Access Original Research Article

Demand Responsive Transportation Service Problem with Time Windows

Charles Sebil, Veronica Owusu, Samuel Asante Gyamerah

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2016/24872

Most countries have high unemployment levels of which Ghana is not an exception (www.ask.com). Most of these unemployed people, especially women engage themselves in wholesale and retail trading of fruits and vegetables. In Ghana, locally produced fruits are of high demand (www.myjoyonline.com/bussiness/2014/january-3rd), but its non-availability results in people patronizing imported fruits. Watermelon business in Bantama market, Kumasi-Ghana, was chosen as a case study. The study focused on an entrepreneur handling the purchasing and transportation of the fruits from source to the market instead of wholesalers. A mathematical model was used to estimate the number of vehicles needed to serve the requests of the wholesalers thereby minimizing cost of transportation with no option of non-availability in the market. In pursuit of the objectives, primary data was collected from the general public and wholesalers. The result showed that three (3) vehicles can be used to serve the twenty (20) wholesalers at Bantama market in Kumasi.

Open Access Original Research Article

Periodic Solutions of a Modified Duffing Equation Subjected to a Bi-Harmonic Parametric and External Excitations

A. M. Elnaggar, A. F. El-Bassiouny, K. M. Khalil, A. M. Omran

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/25684

In this paper, we investigated the periodic solutions of type superharmonic and subsuperharmonic of modified Duffing equation subjected to a bi-harmonic parametric and external excitations. The method of multiple scales is used to construct a first order uniform expansion of approximate solutions. Two first-order nonlinear ordinary differential equations(Modulation Equation) are derived from the evolution of the amplitude and the phase. Steady state solutions and their stability are given for selected values of the system parameters. The consequences of these (quadratic and cubic) nonlinearities on these the vibrations are particularly examined. With this research, it has been confirmed that the qualitative effects of these nonlinearities are different. Regions of the hard (soft) nonlinearity of the system exist for the case of subsuperharmonic oscillation. Numerical solutions are presented in a group of figures which demonstrate the actions of the steady-state reaction plenitude as the purpose of the detuning parameter.

Open Access Original Research Article

Action of a Polynomial Matrix on a Vector of Power Series

Ramamonjy Andriamifidisoa

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2016/25791

The adjoint of the right multiplication of a row vector by a fixed polynomial matrix gives a left operation of the polynomial matrix on column vectors of power series. This explain the polynomial matrix and vector of powers series “multiplication”, used to define discrete linear dynamical systems, according to Willems and Oberst theory.