##### Linear Summing Formulas of Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers

Yüksel Soykan

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/jamcs/2019/v33i330176

In this paper, we present linear summation formulas for generalized Pentanacci numbers and generalized Gaussian Pentanacci numbers. Also, as special cases, we give linear summation formulas of Pentanacci and Pentanacci-Lucas numbers; Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.

##### On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method

B. M. Ikramul Haque, A. K. M. Selim Reza, Md. Mominur Rahman

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/jamcs/2019/v33i330177

A modified approximate analytic solution of the cubic nonlinear oscillator “ ” has been obtained based on an iteration procedure. Here we have used the truncated Fourier series in each iterative step. The approximate frequencies obtained by this technique show a good agreement with the exact frequency. The percentage of error between exact frequency and our fifth approximate frequency is as low as 0.009%. The calculation with this technique is very easy. This easily-calculated modified technique accelerates the rapid convergence, reduces the error and increases the validity range of the solution.

##### An Accurate System for Face Detection and Recognition

Abdelmgeid A. Ali, Tarek Abd El-Hafeez, Yosra Khalaf Mohany

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/jamcs/2019/v33i330178

During the last few years, Local Binary Patterns (LBP) has aroused increasing interest in image processing and computer vision. LBP was originally proposed for texture analysis, and has proved a simple yet powerful approach to describe local structures. It has been extensively exploited in many applications, for instance, face image analysis, image and video retrieval, environment modeling, visual inspection, motion analysis, biomedical and aerial image analysis, remote sensing. Face recognition is an interesting and challenging problem, and impacts important applications in many areas such as identification for law enforcement, authentication for banking and security system access, and personal identification among others. In this paper we are concerned with face recognition in a video stream using Local Binary Pattern histogram with processed data. First we will detect faces by using a combination of Haar cascade files that uses skin detection, eye detection and nose detection as input of LBP to increase the accuracy of the proposed recognition system. Also, our system can be used to build a dataset of faces and names to be used in a recognition step. The experimental results have shown that the proposed system can achieve accuracy of recognition up to 96.5% which was better than the relevant methods.

##### Modelling the Effect of Hartmann Number on Transient Period, Viscous Dissipation and Joule Heating in a Transient MHD Flow over a Flat Plate Moving at a Constant Velocity

B. M. Nyamai

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2019/v33i330179

This study is designed to investigate the effect of Hartmann number on transient period, Joule heating and viscous dissipation in an incompressible MHD (Magneto-Hydrodynamics) flow over a flat plate moving at a constant velocity. The governing momentum equation is non-dimensionalized and solved by the Laplace transform technique. The solution is decomposed into transient part and steady state part and then the effect of Hartmann number on transient period concerning velocity and its two related quantities (Joule heating and viscous dissipation) is analyzed. It was found out that when Hartmann number is increased the transient period is shortened and it was the same for the three quantities. In addition, the steady state solutions for both Joule heating and viscous heating were found to be equal. Even though velocity decreases when the Hartmann number is increased, the opposite was discovered for both Joule heating and viscous heating. Graphical analysis indicated that transient period changes considerably if Hartmann number is between 0 and 2. This study will find use in those industrial areas where magnetic fields are used to control liquid / molten metals in open channels.

##### Construction and Determination of Irreducible Polynomials in Galois elds, GF(2m)

Abraham Aidoo, Kwasi Baah Gyam, Fengfan Yang

Journal of Advances in Mathematics and Computer Science, Page 1-6
DOI: 10.9734/jamcs/2019/v33i330181

This work is about Construction of Irreducible Polynomials in Finite fields. We defined some terms in the Galois field that led us to the construction of the polynomials in the GF(2m). We discussed the following in the text; irreducible polynomials, monic polynomial, primitive polynomials, eld, Galois eld or nite elds, and the order of a finite field. We found all the polynomials in $$F_2[x]$$ that is, $$P(x) =\sum_{i=1}^m a_ix^i : a_i \in F_2$$ with $$a_m \neq 0$$ for some degree $m$ which
led us to determine the number of irreducible polynomials generally at any degree in $$F_2[x]$$.