Open Access Original Research Article

Maze Construction by Using Characteristics of Eulerian Graphs

Tomio Kurokawa

Journal of Advances in Mathematics and Computer Science, Page 453-472
DOI: 10.9734/BJMCS/2015/18125

This paper describes the method to construct a maze for which the solution path goes along with the line of a closed one stroke drawn curve. If the crossing of the curve is considered a vertex and the curve between the two crossings (vertices) an edge, the closed curve becomes an Eulerian graph. Since maze does not allow the solution path to intersect itself, the proposed method constructs the path with no crossing; but it goes through every part of the original curve only once. In the process of the path construction, it makes use of the characteristics of Eulerian Graph. The theory was developed and a number of experiments were successfully conducted in some different situations.

Open Access Original Research Article

The Law of Large Numbers: A Multicriterial Analysis

Ana-Maria Rîtea

Journal of Advances in Mathematics and Computer Science, Page 473-482
DOI: 10.9734/BJMCS/2015/17980

The paper presents the law of large numbers followed by a multicriterial analysis of the six theorems that compose the weak form. This group of theorems work on issues of sequences limit laws of sums of random variables in the sense of convergence almost surely of such sequences.

Open Access Original Research Article

Open Access Original Research Article

The Action of a Left Amenable Semi-topological Semigroup on a Weakly Compact Subset of a Banach Space with Normal Structure

Foad Naderi

Journal of Advances in Mathematics and Computer Science, Page 492-497
DOI: 10.9734/BJMCS/2015/18317

Let S be left amenable semi-topological semigroup such that its weak almost periodic compactification Sw is a topological semigroup. We show that every separately continuous, non-expansive and equicontinuous action of S on a weakly compact convex subset of a Banach space with normal structure has a fixed point.

Open Access Original Research Article

Approximation of Higher-order Singular Initial and Boundary Value Problems by Iterative Decomposition and Bernstein Polynomial Methods

O. A. Taiwo, M. O. Hassan

Journal of Advances in Mathematics and Computer Science, Page 498-515
DOI: 10.9734/BJMCS/2015/17157

In very recent time, various works have focused on the analysis of Singular Boundary Value Problems, with many techniques developed or used to deal with major questions relating to Singular Initial and Boundary Value Problems and their solutions. The main questions relate to existence and uniqueness of solution, the numerical approximation of solutions and convergence of solutions.
In this work, we focus on the last two questions for some classes of Singular Initial and Boundary Value Problems. We developed two approximation methods namely Iterative Decomposition and Bernstein Polynomial Methods and applied them to tackle the last two questions raised in this work.
Some numerical examples of second, third and fourth orders problems are considered to illustrate the efficiency and accuracy of the methods.

Open Access Original Research Article

A Novel Comparison between the Performances of Several Invariant Moments for Printed Multi-Oriented, Multi-Scaled and Noisy Eastern Arabic Numerals Recognition

R. Salouan, S. Safi, B. Bouikhalene

Journal of Advances in Mathematics and Computer Science, Page 516-536
DOI: 10.9734/BJMCS/2015/17566

In this paper, we present a novel comparison between the robustness against noise of Hu, Legendre, pseudo-Zernike and Krawtchouk invariant moments and even more of invariant analytical Fourier-Mellin transform for multi-oriented, multi-scaled and noisy printed Eastern Arabic numerals recognition. These descriptors are used to extract the features from all numeral images. For this purpose in order to pre-process each one of them, we have used the median filter and the thresholding technique for enhancing its quality, while for recognizing each unknown numeral we have exploited the support vectors machine. Furthermore for carrying out efficiently this comparison, we introduce new concepts which are the threshold and the interval of stability of each invariant descriptor and for each Eastern Arabic numeral. The experiments that we have obtained have provided very satisfactory results.

Open Access Original Research Article

Parameters Determination for the Design of Bevel Gears Using Computer Aided Design (Bevel CAD)

B. O. Akinnuli, O. O. Agboola, P. P. Ikubanni

Journal of Advances in Mathematics and Computer Science, Page 537-558
DOI: 10.9734/BJMCS/2015/18411

This paper prescribes a Computer Aided approach to the design of bevel gears. The approach utilizes standard design equations and standard data on bevel gears; linking them together using a Programming language(C#) to develop this special software (Bevel CAD) that designs and determines the strengths and dimensions of bevel gears. This study reviews the Procedural steps (algorithms) involved in the design of bevel gears and the development of the software package (Bevel CAD) which is to be used in designing bevel gears. When material required are selected based on the area of application, the software will make use of the data provided using the C# to determine the required; speed and velocity of the bevel gear, number of teeth, speed ratio, dynamic load, endurance strength and maximum wear load for the design bevel gear. The Bevel CAD’s performance was verified by comparing the results of Algorithm calculation and the software’s results. The Bevel CAD was confirmed effective as the minor differences obtained between the results were due to approximation errors. The Bevel CAD increases productivity but reduces drudgery of enormous calculations; hence, making it a recommended tool for industries and tertiary institutions for the designing of bevel gears.