##### Supervised Linear Classification Performance Based on Marginal Probability for Two Groups

F. Z. Okwonu

Journal of Advances in Mathematics and Computer Science, Page 606-612
DOI: 10.9734/BJMCS/2015/13449

The conventional technique to determine classification performance for the linear classification techniques strictly depends on the mean probabilities of correct classification or misclassification. Based on the mean probabilities of correct classification, robustness can be determined. In this paper, a new analytic procedure based on the joint and marginal probabilities is applied to determine robustness and the number of sample observations correctly classified. The classification results computed using this approach is unbiased. This technique is applied to investigate the classification performance of the Fisher linear classification analysis and the robust Fisher’s technique based on the minimum covariance determinant. The performance analysis when compared to the conventional procedure revealed that this technique is very informative. Relying on the analysis and the data set used, the recognition rate of the conventional approach is more accurate than the robust Fisher’s technique.

##### On a Local Equality of Distributions and Relation of Jumps of Distributions with Fourier Series

Egzona Iseni, Shpetim Rexhepi, Halil Snopce

Journal of Advances in Mathematics and Computer Science, Page 553-561
DOI: 10.9734/BJMCS/2015/13876

Distribution theory has an important role in applied mathematics. Firstly, in the introduction part of this paper we will give some general notations, definitions and results in distribution theory, as analytic representation of distribution, distributional jump behavior, distributional symmetric jump behavior, tempered distributions, formulas for the jump of distributions in terms of Fourier series and global equality in distributional sense. Then in final part we will state two results, the first one has to do on local equality of two distributions and the second one states if a 2π− periodic distribution has jump behavior at point, then exists the relation of jumps of distributions with Fourier series in a subset of the upper half-plane.

##### Symbolic Computation of Adomian Polynomials Based on Rach’s Rule

M. Kaliyappan, S. Hariharan

Journal of Advances in Mathematics and Computer Science, Page 562-570
DOI: 10.9734/BJMCS/2015/14067

This paper presents a simple way of computing Adomian polynomials by applying the decomposition of positive integers as a subscript of the variable ‘u’ for nonlinear terms much similarly motivated by Abbaoui et al. through the use of MATLAB software. The proposed MATLAB program exploits symbolic programming for generating Adomian polynomials.

##### On the Solution of Bi-level Large Scale Quadratic Programming Problem with Stochastic Parameters in the Constraints

O. E. Emam, S. A. Kholeif, S. M. Azzam

Journal of Advances in Mathematics and Computer Science, Page 571-582
DOI: 10.9734/BJMCS/2015/14371

In this paper, the bi-level large scale quadratic programming problem with stochastic parameters in the constraints (SBLLSQPP) is solved. Randomness is assumed only on the right-hand side of the constraints and the random variables are assumed to be normally distributed. The main features of the proposed solution procedure are based on convert the probabilistic nature of this problem into an equivalent deterministic, Taylor transformation and decomposition algorithms. An illustrative numerical example is given to clarify the main results developed in the paper.

##### Finite Element Analysis of Bamboo Bicycle Frame

Ukoba Kingsley, Imoisili, Patrick Ehi, D. Adgidzi

Journal of Advances in Mathematics and Computer Science, Page 583-594
DOI: 10.9734/BJMCS/2015/13451

This work looked into the finite element analysis of Bamboo frame bicycle using commonly used Computer Aided Design softwares. A solid model of the frame was created and a finite element analysis (FEA) was conducted using the ASTM standard as a guide, with appropriate mechanical properties for various sections of the bike and the joining welds. A maximum weight of 120kg was used for the weight and seat analysis, from the analysis performed, the most fragile area was identified as being the tubes near the bottom bracket, extra carbon fiber wrapping during assembly is recommended during production for the frame. Due to the nature of Nigeria’s (developing country) road, we simulated a pothole situation using a horizontal force of 1000N to the front tire. The analysis showed that the highest stress would occur nearest to the point of impact with the pothole.

##### Traveling Wave Solutions of the Simplified MCH Equation via Exp (−Φ(ξ)) -expansion Method

Harun -Or- Roshid, Md. Nur Alam, M. Ali Akbar, Rafiqul Islam

Journal of Advances in Mathematics and Computer Science, Page 595-605
DOI: 10.9734/BJMCS/2015/10800

The exp(−Φ(ξ)) -expansion method is an efficient method for obtaining exact traveling wave solutions of nonlinear evolution equations. In this paper, the exp(−Φ(ξ)) -expansion method is applied to construct exact traveling wave solutions of the simplified MCH equation. The traveling wave solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. It is shown that the method is straightforward and effective mathematical tool for solving nonlinear evolution equations in mathematical physics and engineering.

##### Modified Matrix Modular Cryptosystems

S. K. Rososhek

Journal of Advances in Mathematics and Computer Science, Page 613-636
DOI: 10.9734/BJMCS/2015/14321

The Basic Matrix Modular Cryptosystem (BMMC) is a public-key cryptosystem, which uses some matrix modular exponentiations in the matrix ring over the residue ring modulo n. The aim of this article is to decrease the number of these exponentiations and consequently to accelerate the execution of encryption algorithm. There are two ways to reach this aim. First way is to determine the large abelian subgroup in general linear group over the large residue ring and to choose the session keys in this subgroup, what will be to give the encryption without exponentiations. Other way is to use random integral exponent of the given matrix in the public key as session key and this will be the only exponentiation in encryption algorithm. A discussion about the security of built modifications made in the article shows that the level of security is high enough for an appropriate choice of parameters of the cryptosystems, namely, the lower bound for the selection of secure modulus n is 40-bit integer. Both modified cryptosystems are faster than BMMC and balanced with respect to a pair of security – efficiency, and BMMC is much faster than RSA.

##### Numerical Approaches for Tenth and Twelfth Order Linear and Nonlinear Differential Equations

Md. Shafiqul Islam, Md. Bellal Hossain, Md. Azizur Rahman

Journal of Advances in Mathematics and Computer Science, Page 637-653
DOI: 10.9734/BJMCS/2015/13388

The aim of this paper is to solve the tenth and twelfth order linear and nonlinear boundary value problems numerically by the Galerkin weighted residual technique with two point boundary conditions. The well known Bernstein polynomials are exploited as basis functions in the technique and thus the basis functions are needed to modify into a new set of basis functions where the Dirichlet types of boundary conditions are satisfied. The method is developed as a rigorous matrix formulation. Numerical examples, available in the literature, are considered to implement the proposed technique. The comparison shows that the present method is more efficient and yields better results.

##### On the Dynamics of the Solutions of the Rational Recursive Sequences

M. A. El-Moneam

Journal of Advances in Mathematics and Computer Science, Page 654-665
DOI: 10.9734/BJMCS/2015/9657

In this article, we study the periodicity, the boundedness and the global stability of the positive
solutions of the following nonlinear difference equation where the coefficients while k; l and are positive integers. The initial
conditions are arbitrary positive real numbers such that k < l < :
Some numerical examples will be given to illustrate our results.