Open Access Original Research Article

On the Weyl Approach to Tensor Representations of Exceptional Lie Groups: The Case of G2 and F4

Luis J. Boya, R. Campoamor-Stursberg

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/10.9734/BJMCS/2015/10887

An attempt is made to approach the irreducible representations of the exceptional Lie groups G2 and F4 by symmetrization of some defining representations by means of Young tableaux, procedure that works rather well for most of the classical groups. For G2 the program is completely successful, while it is not quite so for F4. As the five exceptional Lie groups are related to octonions, we also comment on the “octonion” character of these two groups, in particular the relation of F4 to some other connected Spin groups.

Open Access Original Research Article

Chebychev Polynomial Solutions of Twelfth-order Boundary-value Problems

Mohamed El-Gamel

Journal of Advances in Mathematics and Computer Science, Page 13-23
DOI: 10.9734/BJMCS/2015/8874

In this paper, Chebychev method is applied to solve twelfth-order boundary-value problems. The numerical results obtained with minimum amount of computation are compared with differential transformation method to show the efficiency of the method. The results show that the Chebychev method is high accuracy, more convenient and efficient for solving twelfth-order boundary-value problems.

Open Access Original Research Article

Open Access Original Research Article

A GI (A, B/(A,Q)) /D/ 1/Qmax Queue Approach for the Estimation of the Proportion of a Deteriorated Length of a Road Network

P. M. Kgosi, R. Sivasamy

Journal of Advances in Mathematics and Computer Science, Page 30-40
DOI: 10.9734/BJMCS/2015/13589

This article proposes a simple methodology for the classification of road segments of a highway into a set S={0, 1, 2 , …, Qmax} of states. A GI(A, B/(A,Qmax)/D/1/Qmax queueing approach, estimates the length of a deteriorated/damaged portion of a road network which requires reconstruction for a better riding comfort which is measured in terms of multiples of the service period. One unit of service time is defined by a pavement management system (PMS) monitoring the queue aspects as an hour or a day needed to reconstruct a length of ‘D’ kilometers (km) of a damaged portion of a road segment; i.e. the service time here is deterministic. The entire coded length of the highway in terms of the maximum discrete service period is Qmax which means that the real length of the highway under study is (DQmax) km. Here, the inter-arrival time ‘A’ between consecutive batch arrival of damages and the size of a number ‘B’ of units of damaged portion arrived are measured as multiples of the single service time. Treating the sequence {tn; n [0,1,2,…}} of arrival epochs as renewal points of the queue occupancy process Q(t), the queueing number of damaged units of road length at time ‘t’, this queueing problem is investigated further using the embedded Markov Chain (MC) methods.

Open Access Original Research Article

A Class of Implicit Six Step Hybrid Backward Differentiation Formulas for the Solution of Second Order Differential Equations

Umaru Mohammed, Raphael Babatunde Adeniyi

Journal of Advances in Mathematics and Computer Science, Page 41-52
DOI: 10.9734/BJMCS/2015/14769

In this paper, we propose a class implicit six step Hybrid Backward Differentiation Formulas (HBDF) for the solution of second order Initial Value Problems (IVPs). The method is derived by the interpolation and collocation of the assumed approximate solution. The single continuous formulation derived is evaluated at grid point of X = Xn+k and its second derivative at X = Xn+j, j = 1,2,.....k - 1 and  X = Xn+μ respectively, where k is the step number of the methods. The interpolation and collocation procedures lead to a system of (k+1) equations, which are solved to determine the unknown coefficients. The resulting coefficients are used to construct the approximate continuous solution from which the Multiple Finite Difference Methods (MFDMs) are obtained and simultaneously applied to provide the direct solution to IVPs. Numerical examples are given to show the efficiency of the method.

Open Access Original Research Article

Fuzzy Rule Based Salt and Pepper Noise Removing in Gray Images

Nadeem Salamat, Malik Muhammad Saad Missen

Journal of Advances in Mathematics and Computer Science, Page 53-67
DOI: 10.9734/BJMCS/2015/14233

This paper presents the application of the diffusion equation for removing the salt & pepper noise in the field of image processing along with the fuzzy logic. The fuzzy logic differentiates the noisy pixels, especially the salt & pepper noise and the edges, then diffusion equation is applied to only noisy pixels and the diffusivity is proportional to the noise. The proposed method is applied to many test images. The simulated results demonstrate the effectiveness of the method based on statistical measures such as Mean Square Error (MSE) and Peak Signal Noise Ratio (PSNR) and Structure Similarity Index Measure (SSIM).

Open Access Original Research Article

The Use of Gradient Based Features for Woven Fabric Images Classification

Saad Al-Momen, Loay E. George, Raid K. Naji

Journal of Advances in Mathematics and Computer Science, Page 68-78
DOI: 10.9734/BJMCS/2015/14043

Texture classification is used in various pattern recognition applications that possess feature-liked appearance. One of the main texture types is the woven fabric texture. This paper aims to improve the classification accuracy of this type of texture based on extracting a directional based texture features. Three different types of features are proposed: (i) first order gradient feature vector, (ii) max-min gradient feature vector, and (iii) second order gradient feature vector. Each one of these feature vectors is studied individually, and then the possible combinations of them are studied also. This study applied on 22 classes of woven fabric with 225 images per class taken from the Brodatz album.
The experiments showed that the results are competitive to that gotten from the other popular methods in this field, such as GLCM, Gabor filters, wavelets and other transformation methods. The test results indicated that the attained average accuracy of classification is improved up to (99.909%) for the training set and (99.714%) for the testing set.