Open Access Original Research Article

A Novel Method for Compact Listing of All Particular Solutions of a System of Boolean Equations

Ali Muhammad Ali Rushdi, Waleed Ahmad

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/BJMCS/2017/33884

Any system of ‘big’ Boolean equations can be reduced to a single Boolean equation {g(Z) = 1} . We propose a novel method for producing a general parametric solution for such a Boolean equation without attempting to minimize the number of parameters used, but instead using independent parameters belonging to the two-valued Boolean algebra B2 for each asserted atom that appears in the discriminants of the functiong(Z). We sacrifice minimality of parameters and algebraic expressions for ease, compactness and efficiency in listing all particular solutions. These solutions are given by additive formulas expressing a weighted sum of the asserted atoms of g(Z), with the weight of every atom (called its contribution) having a number of alternative possible values equal to the number of appearances of the atom in the discriminants of g(Z) . This allows listing a huge number of particular solutions within a very small space and the possibility of constructing solutions of desirable features. The new method is demonstrated via three examples over the ‘big’ Boolean algebras,B4,B16, and B256, respectively. The examples demonstrate a variety of pertinent issues such as complementation, algebra collapse, incremental solution, and handling of equations separately or jointly.

Open Access Original Research Article

DT- optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design

D. M. Mwan, M. K. Kosgei, S. K. Rambaei

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2017/34288

Experimenters have come to a realization that a design can perform very well in terms of a particular statistical characteristic and still perform poorly in terms of a rival characteristic. Due to this studies have narrowed down to the area of optimality criteria. Some of these criteria include the alphabetic optimality criteria and compound optimality criteria. Compound optimality criteria are those that combine two or more alphabetic optimality criteria in one particular design. In this paper two alphabetic optimality D- and T- criteria are combined to obtain DT- compound optimality criteria for the existing second order rotatable designs using Balanced Incomplete Block Designs. The purpose of this paper is to bring a balance between to statistical properties; parameter estimation and model discrimination. This will aid those researchers who are interested in more than two desired traits in one design. In this analysis, we note that the more homogenous the design is the more optimal it becomes.

Open Access Original Research Article

Mixed Convection and Radiative Heat Transfer of MHD Casson Fluid Flow by a Permeable Stretching Sheet with Variable Thermal Conductivity and Lying in Porous Medium

Hassan Waqas, Sajjad Hussain, Rabia Naseem, Amna Mariam, Shamila Khalid

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/BJMCS/2017/33762

This work investigates the mixed convection radiative heat transfer of electrically conducting Casson fluids. The fluid flows past a permeable stretching sheet lying in the porous medium. The heat transfer involves variable thermal conductivity and convective boundary conditions. The formulation of the problem is primarily in the form of the non-linear partial differential equations. These governing equations are transformed to their ordinary differential form by employing similarity transformation. The resulting equations are then solved numerically by classical Rung-Kutta method. Computations have been made for some representative values of the pertinent parameters to elaborate the physical behavior of flow and thermal characteristics.

Open Access Original Research Article

Evaluation of Calinski-Harabasz Criterion as Fitness Measure for Genetic Algorithm Based Segmentation of Cervical Cell Nuclei

Caglar Cengizler, M. Kerem Un

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2017/33729

In this paper, the classification capability of Calinski-Harabasz criterion as an internal cluster validation measure has been evaluated for clustering-based region discrimination on cervical cells. In this approach, subregions in the sample image are initially randomly constructed to be the individuals of the population. At each generation, individuals are evaluated according to their Accordingly a novel genetic structure for meta heuristic area isolation is proposed. Evaluation of proposed combination of genetic algorithm and Calinski-Harabasz measure is achieved by experiments, conducted on real cervical cell samples. We have used two separate cluster validity measures to evaluate the performance of the clustering approach. Jaccard index and F-score are utilized for objective comparison. Results shows that, Calinski-Harabasz criteria may have a better performance with proposed novel genetic structure and presented mechanism may have great potential on discrimination of specific regions.

Open Access Original Research Article

Comparison of State-Estimation Algorithms for a Noise-Injected Lithium-ion Battery System

Hasan A. Bjaili, Ali M. Rushdi, Muhammad Moinuddin

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2017/34222

This paper deals with one of the most prominent problems in industrial prognostics, namely the estimation of the Remaining Useful Life (RUL) of the most popular industrial battery, viz., the lithium-ion battery. The paper presents a state-space model of the battery, and then estimates the dynamic behavior of seven of its process variables and two of its sensor variables. The estimation is achieved via two well known estimators, the Unscented Kalman Filter (UKF) and the Particle Filter (PF) when noise of various levels and types is injected. Numerical and chart comparisons of these two computing estimators are reported and discussed.