##### Estimation of Binomial Distribution in the Light of Future Data

Kunio Takezawa

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2015/19191

A predictive estimator for estimating the parameter of binomial distribution is suggested. This estimator aims to maximize the expectation of expected log-likelihood. The results given by this estimator are superior to those given by the maximum likelihood estimator in terms of the predictions when a little prior knowledge about the parameter is available.

##### Solving Interval Linear Equations with Modified Interval Arithmetic

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2015/18825

Gaussian elimination method is one of the widely used methods for solving linear equations. An interval version of Gaussian elimination method has been used by simply replacing each real arithmetic step by the corresponding interval arithmetic step. Two interval arithmetics technique has been considered for modified interval arithmetics as well as several existing interval arithmetics. In this paper, modified interval arithmetic has been introduced based on two interval arithmetics technique. If we solve interval linear system of equations by existing interval arithmetic method the replacing solution in interval system of equations, the interval width is more than the interval width of right hand side intervals. On the other hand, applying modified interval arithmetic the interval width is less than interval width than previously obtained by existing interval arithmetic. Moreover, the closeness of interval width in system of equations to the right hand side is important so modified interval arithmetic is more effective and efficient for solving interval linear system of equations.

##### Determining the Effects of Cross-over Point on the Running Time of Strassen Matrix Multiplication Algorithm

S. C. Agu, T. A. Atabong

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2015/18772

This paper studies Strassen’s algorithms for fast multiplication of two finite dimensional matrices. However, one pertinent issue that has deterred Strassen’s scheme from been considered for practical usage is determining the cross-over point. In this light, large matrices with different sizes were randomly generated on which Strassen and conventional matrix multiplication algorithms were implemented in MATLAB R2008b. Two MATLAB built-in functions nextpow2 and pow2 were used for implementing padding techniques to ensure that the matrices are to the power of two. Three different experiments were carried out using five, four and three levels of recursion (divide and conquer algorithm) respectively to determine the suitable cut-off point  which were used to evaluate the optimal running time for Strassen’s algorithm. For each experiment, eight finite dimensional square matrices of real numbers were generated and iteratively multiplied. The experiment reveals that the cut-off point with five level of recursion optimized the Strassens time.

##### Design, Optimization and Fabrication of a Climbing Six Articulated-Wheeled Robot Using Artificial Evolution and 3D Printing

S. H. Lim, J. Teo

Journal of Advances in Mathematics and Computer Science, Page 1-21
DOI: 10.9734/BJMCS/2015/18555

Over the last decade, various mobile robots have been developed and widely used in myriad sectors. However, the vast majority of mobile robots are manually designed where the designers must have the preliminary knowledge of the interaction between the robots with the environment. Additionally, the high complexity involved in the design of the kinematics and controllers of a mobile robot has always been the biggest challenge for the researchers and practitioners alike. Thus, the task of designing a robot can be considered very demanding and extremely challenging. In this research, an artificial evolution approach utilizing Single-Objective Evolutionary Algorithm (SOEA) and Multi-Objective Evolutionary Algorithm (MOEA) respectively are investigated in the automatic design and optimization of the morphology of a Six Articulated-Wheeled Robot (SAWR) with climbing ability. Results show that SOEA is able to produce optimized SAWR with climbing ability while MOEA is able to produce a set of Pareto optimal solutions which provide users with a choice of solutions for trade-off between the objectives of morphology size and climbing performance. The Pareto optimal set of solutions are the smallest SAWR with least climbing ability to biggest SAWR with the best climbing motion. The research continues by transferring the evolved solutions from simulation to the real world using 3D printing. The body, legs and wheels of the evolved robots are printed by a 3D printer and assembled with sensors, servos and motors for real world testing. Results show that the fabricated real world SAWRs are able to perform the climbing motion with the average accuracy of 85.8% in comparing to the performance in simulation.

##### Topological Conditions for Automated Diagnostic Software to Estimate the Diagnosability of Digital Devices at the Structural Level

Rami Matarneh

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2015/18255

Diagnosability is the property of a partially observable system with a given set of possible faults; these faults can be detected with certainty with a finite observation. Usually, the definition and the verification methods of diagnosability ignore the nature of controllable and uncontrollable events of the system. This paper shows the influence of controllability of system’s events on the definition and the verification, also shows that the classical diagnosability is a special case where we consider the whole system as controllable. The definition of diagnosability had been generalized using model structure on topological spaces by mean of strategies. Alternating-time Temporal Logic and Model Checking are used to check diagnosability of uncontrollable events to build a whole framework which is suitable for both isolated and interacting systems.

##### Fourier Coefficients of a Class of Eta Quotients of Weight 12

Barış Kendirli

Journal of Advances in Mathematics and Computer Science, Page 1-34
DOI: 10.9734/BJMCS/2015/18442

Recently, Williams  and then Yao, Xia and Jin  discovered explicit formulas for the coefficients of the Fourier series expansions of a class of eta quotients. Williams expressed all coefficients of 126 eta quotients in terms of σ(n) σ(n/2), σ(n/3)  and σ(n/6) and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of σ3(n), σ3(n/2), σ3(n/3) and σ3 (n/6). Here, we will express the odd Fourier coefficients of 334 eta quotients in terms of σ11 (2n-1) and σ11 ((2n-1)/3)), i.e., the Fourier coefficients of the difference, f(q)-f(-q), of 334 eta quotients and we will
express the even Fourier coefficients of 198 eta quotients i.e., the Fourier coefficients of the sum, f(q)+f(-q), of 198 eta quotients in terms of σ11(n), σ11(n/2), σ11(n/3), σ11(n/4), σ11(n/6) and σ11(n/12)

##### A Fourth-Order Nonlinear Conjugate Gradient Method in Large Scale Optimization

Nwaeze Emmanuel

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2015/18694

This paper is presenting a fourth-order nonlinear conjugate gradient method in large scale optimization. This method solves unconstrained optimization problems. It is based on a nonlinear polynomial approximation of the objective function. The idea is to approximate the minimizing function by Taylor series development using fourth-order terms. The algorithm is presented in steps and some properties of the gradients are proved, using classical results. Also, the convergence analysis has been proved under known assumptions. Some numerical results have been compared to existing data. The analysis of these results confirms that the new method is accurate, since the computed results are very close to the exact solutions.