In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equation with a smooth kernel. Using a sufficiently accurate numerical quadrature rule, we obtain super-convergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and 𝐿2-norm. Numerical examples are given to illustrate the theoretical results.

Sorting or ordering is an arrangement of a set of items of a list in a certain order. Several sorting algorithms and methods are available. In this paper, we focus on the simplest but not highly efficient bubble sort algorithm. Rearranging parallel computing, i.e., message passing interface (MPI), it is explained why parallel architectures are now mainstream. Recently, parallel computing has become one of the most important aspects of computer science and it has showed dominance especially in the field of analyzing high-performance problems. One of the major results is the type of data structure obtained by using 3D array of char, which shows faster result, instead of using a vector of string with extra overhead. The threads (slaves) sort part of the list and return to the master thread, which merges all small lists in one final sorted list. This study shows an increase in speed and efficiency with the increase in number of threads, indicating an increase in the efficiency of bubble sort algorithm.

Suppose that T is a tree. AbuHijleh has shown that T² is a divisor graph iff T is a caterpillar with diam(T) ≤ 5. In this paper we characterize when T³ and T⁴ are divisor graphs.

We used the monthly share prices of all Nigeria Share Price index from April, 2000 to January, 2014 to identify and model the volatility of asset return in the Nigerian Stock Exchange. We compared several ARMA-GARCH models that best fits the series. The result of our study shows that the ARMA(1,1)-GARCH (1,1) model best describes the volatility of the return. The volatility of the returns was found to be quite persistent, i.e. current volatility can be explained by past volatility that tends to persist over time.

Virtual Reality (VR) has been identified as one of the constructive medium to support the teaching-learning process. It is persistently explored by researchers in order to reap the most benefits from the technology in education. Among reasons for the usage of VR application in learning environment are due to its provision of interactivity among realistic complex structure of three-dimensional (3D) environment while giving the feel of being there to users. However, a broad framework and model to construct the theory and connection in this domain, particularly virtual reality for desktop or DesktopVR, has hardly been developed and evaluated. Therefore, the objective of this paper is to determine the features and relevant factors which may contribute to learning environment. This paper offers a theoretical model in designing DesktopVR for learning environment.

This paper contributes a scheme for solving linear optimal control problem in systems run by Volterra integral equations. At first, the original optimal control problem of Volterra integral equations is transformed into an integral problem via the Pontryagins maximum principle, and then, we applied homotopy analysis method (HAM) to solve the integral problem. The proposed method is compared with other methods. Numerical results show that the HAM method is more powerful and faster.

Mobile networks are changing and incorporating new services continuously. The Telecommunication industry in East Malaysia is still under progressing mode. The terrain and tropical rainforest conditions are the biggest challenge to design a good telecommunication infrastructure in Sarawak. This might be the reason that the service level figures are even poorer in Sarawak and the demand on mobile networks in Sarawak is comparatively high. This paper contains a performance evaluation of mobile telecommunication infrastructure in Kuching. The research has focused on propagation issues and the findings are the result of several propagation tests that in various propagation conditions. Since the paper has been written for research purposes, the vendors’ names in the study are not disclosed and are referred to as Provider A, B, and C. At the time of this research, only two vendors offered 4G services in Kuching.

This paper solves a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. Methodology is developed to transform the model into a general optimization problem, which is free from interval uncertainty. Relation between the original problem and the transformed problem is established. Finally, the proposed methodology is explained through a numerical example.

The high failure rates in mathematics courses have been a concerning matter in each semester at private universities. Studies about determining the causes of low mathematics achievement are very limited. The purpose of this study is to investigate the factors that affect low achievement in mathematics. In order to achieve this purpose, factor analysis was conducted to capture the potential factors which may affect achievement. Multiple linear regression was used to determine the factors that significantly affect the achievement in mathematics. A total of 111 students who enrolled in mathematics courses participated in the survey. This study revealed that one of the significant causes of low mathematics achievement is students’ educational background. Students who were not from science stream are at a disadvantage in achieving good performance in mathematics. Other factors of low mathematics achievement include race, age and students’ valuing of the importance of mathematics. One of the implications discussed in this paper is that mathematics educators must have several effective teaching strategies that suit students’ learning needs especially non-Chinese and older students. Such strategies might help educators achieve the desired learning outcomes and reduce failure rates.

The paper covers a research in the knowledge management area for automotive industries. A preliminary study on the knowledge management was conducted in the local automotive companies for obtaining an initial overview of the practice of knowledge management in the Malaysian automotive industry. The 72 managers and engineers from six automotive companies in Malaysia were the respondents for this study. The data were interpreted on the basis of weighted scores for each parameter. The final conclusions then were prepared on the basis of a knowledge management index (KMI). The interpretation of data reveals that the knowledge management index (KMI) in the three knowledge management aspects of (i) information technology, (ii) knowledge acquisition, and (iii) understanding and commitment were the highest while the knowledge management index (KMI) for the two other aspects of knowledge management aspects of (i) mechanism of assessment and (ii) acknowledgement were the lowest among the eleven considered aspects. From this data interpretation, it can be concluded that the practice of knowledge management in the Malaysian automotive industry was still in the early stage and need to be improved in order to guarantee the competitive success in the competitive world today.

The application of mathematical models of rainfall is crucial in order to have a better understanding in terms of rainfall characteristics. The rainfall models have been used widely to improve water management, to construct hydrological structures and as an input in climatological studies. In this study, the gamma distribution is used to fit the marginals of monthly rainfall data. The parameters of the gamma distribution, shape and scale, are estimated using the maximum likelihood estimation method. Then, the sum of monthly rainfall amounts is modelled using the McKay distribution for independent gamma variables. To illustrate the independent example, rainfall data is used between the months in monsoon season for Kuantan station. The fit between the observed and generated rainfall data is assessed using Kolmogorov-Smirnov goodness of fit test. The results show that the McKay distribution is suitable to model the sum of monthly rainfall amounts for two independent gamma variables. The model is also useful for generating synthetic rainfall amounts for independent months in simulation studies.

In this study, a steady stagnation point flow due to a permeable shrinking sheet with the slip effects is investigated. Employing similarity transformations, the governing boundary layer equations are transformed into the nonlinear ordinary differential equations. The transformed equations are figured out numerically using the shooting method. Results show that dual solutions for velocity and temperature distribution exist for a certain range of the shrinking parameter. The results also indicate that the skin friction coefficient and the local Nusselt number increase for the upper branch solution as the suction parameter increases. Meanwhile, for the lower branch solution, the skin friction coefficient decreases and the local Nusselt number increases as the suction parameter increases. It is also found that the velocity slip and suction process delay the boundary layer separation whereas the temperature slip does not affect the boundary layer separation.