An integral equation method for solving neumann problems on simply and multiply connected regions with smooth boundaries

This research presents several new boundary integral equations for the solution of Laplace’s equation with the Neumann boundary condition on both bounded and unbounded multiply connected regions. The integral equations are uniquely solvable Fredholm integral equations of the second kind with the generalized Neumann kernel. The complete discussion of the solvability of the integral equations is also presented. Numerical results obtained show the efficiency of the proposed method when the boundaries of the regions are sufficiently smooth

The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven

Graduate on Time: Factors of Failure in UiTM Cawangan Johor

The percentage of diploma students who graduate on time in UiTM Cawangan Johor for each semester was inadequate. Therefore, this study seeks to explore the factors that influence students to be unsuccessfully graduating on time. A sample of 17 extended full-time modes (SML) students in the semester of July – August 2018 (intersession semester) had been utilised as the primary data. In this research, the descriptive analytics study was also used. The students were asked an open-ended question to get the required information based on the objective of the study. In 30 minutes, 97 answers were received and recorded. Based on the answers obtained by the students, there are 10 categories that can be identified according to the similarities of answers given by the students. The 10 categories are then called the factors. It includes (1) learning abilities, (2) attitude towards learning, (3) time management, (4) system, (5) lecturer, (6) strategy, (7) low self-confidence, (8) peer, (9) lack of family support and (10) financial difficulties. This study is important because it attempts to generate research-based recommendations in order to improve the percentage of students who graduate on time in UiTM Cawangan Johor. The findings of the study may suggest new methods of activities or programmes that are needed to be taken into consideration by the university in the future. The increase in GOT students will only materialise if the actions have been taken, which is depending on the findings of this study

An integral equation method for solving exterior Neumann problems on smooth regions

This work develops a boundary integral equation method for numerical solution of the exterior Neumann problem. An integral equation for solving the exterior Neumann problem in a simply connected region is derived in this dissertation based on the exterior Riemann-Hilbert problem. In the first step the exterior Neumann problem is reduced to an exterior Riemann-Hilbert problem for the derivative of an auxiliary function which is analytic in the region. Then, the exterior Riemann-Hilbert problem is transformed to a uniquely solvable Fredholm integral equation on the boundary of the region. Once this equation is solved, the auxiliary function and the solution of the exterior Neumann problem can be obtained. The efficiency of the method is illustrated by some numerical examples

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.</jats:p

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.   </jats:p

The Effectiveness of Excellence Camp: A Study on Paired Sample

AbstractProblem solving is one of the important aspects in mathematics problem solving. Strengthening the basic knowledge and understanding the problem can guide the students to become better problem solver. The Mathematics Excellence Camp was conducted to recap the basic knowledge and expose the students to the problem-based learning. The study focused on the effectiveness of educational camp in improving students’ understanding in Mathematics. The camp was targeted on the repeaters of pre-Calculus students. Each day, the students were given the pre- test before the lesson began and post- test after the lesson ended. The study is statistically conducted indirectly to investigate the effectiveness of the program. The different mean values for pre-test and post-test were tested, and the hypothesis testing using paired sample t-test was used.. The results of the study are expected to have higher mean value for post-test than pre-test