Open Access Original Research Article

Design of a Hardware Circuit for Integer Factorization Using a Big Boolean Algebra

Ali Muhammad Rushdi, Sultan Sameer Zagzoog, Ahmed Said Balamesh

Journal of Advances in Mathematics and Computer Science, Page 1-25
DOI: 10.9734/JAMCS/2018/40369

An Integer factorization is an intractable problem that might be handled in real time via hardware solution. Such a solution requires the extension of propositional logic to higher-order logics (e.g., first-order predicate logic) or the enlargement of two-valued Boolean algebra to a ‘big’ Boolean algebra. The paper derives a hardware circuit that factorizes a 6-bit integer X into two integers Y and Z of sizes 5 bits and 3 bits, respectively. The paper employs Boolean-equation solving techniques employing relatively large (8-variables and 6-variables) Karnaugh maps. The underlying Boolean algebra has 6 generators, 26 = 64 atoms, and 264 ≈ 1.8  1019 elements. The solution obtained for the 6-bits problem is easily and readily reduced to obtain or reproduce solutions for the problem in which X has 5 bits, 4 bits, and 3 bits, respectively. The feasibility of the proposed techniques is demonstrated and methods to study the scaling, complexity and automation issues are suggested. An automated version of the method is expected to compete well with the best solver available which currently handles up to 12 bits for the integer X to be factored.

Open Access Original Research Article

Efficient Image Registration Using Discrete Orthogonal Stockwell Transform and SIFT

Hossam-E M. Shamardan

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2018/40026

Image registration is a vital step for most of recent image processing applications. In this paper, a novel approach for magnetic resonance images (MRI) registration based on artificial neural network (ANN) is proposed. The ANN achieves the state-of-the-art performance for estimation problems, hence it has been adopted for estimating the registration parameters. The ANN is fed by joined features extracted from both of spatial and frequency domains. The Scale Invariant Feature Transform (SIFT) is used for extracting the spatial domain features while The Discrete Orthogonal Stockwell Transform (DOST) coefficients are used as frequency domain features. The combined features provide a robust foundation for the registration process. Many experiments were performed to test the success of the new approach. The simulation results demonstrate that the proposed approach yields a better registration performance with regard to both the accuracy, and the robustness versus noise conditions.

Open Access Original Research Article

Improved FTWeightedHashT Apriori Algorithm for Big Data using Hadoop-MapReduce Model

Sarem M. Ammar, Fadl M. Ba-Alwi

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2018/39635

The most significant problem of data mining is the frequent itemset mining on big datasets. The best-known basic algorithm for frequent mining itemset is Apriori. Due to the drawbacks of Apriori algorithm, many improvements have been done to make Apriori better, efficient and faster. We have reviewed over 100 papers related to this work that include enhancements be done to improve Apriori algorithm. Weighted based Apriori and Hash Tree based Apriori are the most significant improvements. One of the recent papers integrated the weight concept of weighted Apriori and Hash tree construction concept of Hash Tree Apriori to produce a hybrid Apriori algorithm named WeightedHashT. In this paper, we aim to propose a new approach to improve WeightedHashT Apriori algorithm on big data using Hadoop-MapReduce model by employing the transaction filtering technique. The experiment of this work using different datasets manifests that the proposed algorithm is efficient and effective regarding execution time.

Open Access Original Research Article

Lomax-Modified Weibull Distribution: A New Generalization

R. M. Mandouh

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/JAMCS/2018/38975

In this paper, the Lomax-Modified Weibull distribution with five parameters is introduced as a new generalization of Modified Weibull distribution introduced by Sarhan and Zaindin (2009). Some properties of the new distribution are obtained. Estimation of the five unknown parameters will be discussed in the view of the likelihood and Bayesian principals. Also, a numerical example is provided.

Open Access Original Research Article

Cubic B-Spline Collocation and Adomian Decomposition Methods on 4th Order Multi-point Boundary Value Problems

E. U. Agom, F. O. Ogunfiditimi, B. E. A. Eno, I. M Esuabana

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/JAMCS/2018/40656

In this paper, Cubic B-Spline collocation method (CBSCM) and Adomian Decomposition Method (ADM) are applied to obtain numerical solutions to fourth-order linear and nonlinear differential equations. The CBSCM was based on finite element method involving collocation method with cubic B-spline as a basis function. While ADM was based on multistage decomposition method. We discovered in the illustrative examples considered, that result by ADM were compatible with the closed form solutions well over twenty, in some cases over thirty, decimal places and with extremely minimal absolute errors. Results by CBSCM gave correct solutions to atmost six decimal places with sizeable absolute errors. These has further revealed the importance and superiority of ADM over CBSCM in providing semi-analytic solution to this class of differential equations.