Open Access Data Article

Numerical Solution of Volterra-Fredholm Integral Equations Using Hybrid Orthonormal Bernstein and Block-Pulse Functions

Mohamed A. Ramadan, Mohamed R. Ali

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/ARJOM/2017/34324

We have proposed an efficient numerical method to solve a class of mixed Volterra-Fredholm integral equations (VFIE’s) of the second kind, numerically based on Hybrid Orthonormal Bernstein and Block-Pulse Functions (OBH). The aim of this paper is to apply OBH method to obtain approximate solutions of nonlinear Fuzzy Fredholm Integro-differential Equations. First we introduce properties of Hybrid Orthonormal Bernstein and Block-Pulse Functions, we used it to transform  the  integral  equations  to  the system  of  linear algebraic equations then an iterative approach is proposed to obtain approximate solution of class of  linear algebraic equations, a numerical examples is presented to illustrate the proposed method. The error estimates of the proposed method is given.

Open Access Original Research Article

Decay for Solutions to Semilinear Regularity-Loss Type Equations with Memory

Shikuan Mao, Lin Wang

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/ARJOM/2017/33909

In this paper we consider the initial value problem of an inertial model for a generalized semilinear plate equation with memory in Rn (n ≥ 1). We study the decay and the regularity-loss property for this type of equations in the spirit of [1, 2]. The novelty of this paper is that we extend the order of derivatives from integer to fraction and refine the results in the related literature [1, 3].

Open Access Original Research Article

Effect of Physical and Virtual Manipulatives on the Mathematical Achievement of Junior High School Students in the Topic of Transformation in Ghana

Bosson-Amedenu Senyefia

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/ARJOM/2017/34238

There is a general perception that mathematics is difficult and many Junior High school students seem to struggle through mathematics lessons. The purpose of this study was to investigate the effect of physical (using mathematical set instruments) and virtual (using Geogebra software) manipulatives on the mathematical achievements of Junior High school students in the topic of Transformation (which is made up of rotation, reflection, enlargement/reduction by scale factor and translation). The topic was previously taught to the students by their teachers from their various schools. The researcher adopted a convenient sampling technique (with a sample size of 78 students) by making use of grade nine students (from 6 different Schools) who had enrolled in vacation classes at Ideal College of Ghana. Pretest-posttest control group experimental model, which is one of the quasi-experimental research designs, was used in the study. The students were randomly assigned to three different groups which consisted of two experimental groups and one control group. The pretest administered to all the groups showed that the mathematical achievements of the three groups were not significantly different. The data passed normality test and so ANOVA was applied in the analyses of pretest and posttest scores. One of the experimental groups was treated with physical manipulative and the other with a virtual manipulative. The control group was taught using the traditional method of teaching. One of the findings of the study showed that the use of manipulatives were significantly effective in increasing the achievement scores of the experimental groups. Another important finding showed that scores of low achievers were significantly improved when they were treated with manipulatives. Virtual manipulative proved to be more effective comparatively in increasing the achievements of grade nine students. It was recommended among many others that low achievers in mathematics should be given the opportunity to study with manipulatives.

Open Access Original Research Article

Problem Solving Framework for Mathematics Discipline

Evans Atteh, Emmanuel Appoh Andam, William Obeng– Denteh

Asian Research Journal of Mathematics, Page 1-11
DOI: 10.9734/ARJOM/2017/32586

This paper identifies a 4-step framework that can be implemented in almost every mathematics lesson and training setting to move learners towards problem solving effectively. This framework which is built upon existing ideas proposed over the years in the mathematics education discipline and best practices concerning cognitive development and effective teaching and learning environment including solved examples provides teachers with very useful guidelines for classroom instruction. Ultimately, this framework can be used to move students towards an active learning environment which is more effective and enjoyable for teachers and students for learning.

Open Access Original Research Article

Dynamic Behavior of Bernoulli-Euler Beam with Elastically Supported Boundary Conditions under Moving Distributed Masses and Resting on Constant Foundation

Adeoye Adebola Samuel, Akintomide Adeniyi

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/ARJOM/2017/33156

The dynamic behavior of uniform Bernoulli-Euler beam with elastically supported boundary conditions under moving distributed masses and resting on constant foundation is investigated in this research work. The governing equation is a fourth order partial differential equation with variable and singular co-efficients. In order to solve this equation, the method of Galerkin is used to reduce the governing differential equation to a sequence of coupled second order ordinary differential equation which is then simplified by applying the modified asymptotic method of Struble. The simplified equation is solved using the Laplace transform technique. The analysis of the closed form solution in this research work shows the conditions for resonance as well as the effects of beam parameters for moving force system only. The results in plotted graphs show that as the axial force, foundation modulus and shear modulus increase, the transverse deflection of the uniform Bernoulli-Euler beam with elastically supported boundary conditions decreases.