• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.561-577
• /
• 2002

In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed.

• International Journal of Precision Engineering and Manufacturing
• /
• v.3 no.4
• /
• pp.54-63
• /
• 2002

In recent years, mechanical systems such as high speed vehicles and railway trains moving on elastic beam structures have become a very important issue to consider. In this paper, a general approach, which can predict the dynamic behavior of a constrained mechanical system moving on a flexible beam structure, is proposed. Various supporting conditions for the foundation support are considered for the elastic beam structure. The elastic structure is assumed to be a non-uniform and linear Bernoulli-Euler beam with a proportional damping effect. Combined differential-algebraic equation of motion is derived using the multi-body dynamics theory and the finite element method. The proposed equations of motion can be solved numerically using the generalized coordinate partitioning method and predictor-corrector algorithm, which is an implicit multi-step integration method.

• International Journal of Precision Engineering and Manufacturing
• /
• v.3 no.4
• /
• pp.64-71
• /
• 2002

Recently, mechanical systems such as a high-speed vehicles and railway trains moving on flexible beam structures have become a very important issue to consider. Using the general approach proposed in the first part of this paper, it is possible to predict motion of the constrained mechanical system and the elastic structure, with various kinds of foundation supporting conditions. Combined differential-algebraic equation of motion derived from both multibody dynamics theory and finite element method can be analyzed numerically using a generalized coordinate partitioning algorithm. To verify the validity of this approach, results from the simply supported elastic beam subjected to a moving load are compared with the exact solution from a reference. Finally, parametric study is conducted for a moving vehicle model on a simply supported 3-span bridge.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.04a
• /
• pp.252-259
• /
• 1999

One of the most important factors for a proper design of a slender compression member may be the exact determination of the elastic critical load of that member. In the cases of non-prismatic compression member, however, there are times when the exact critical load becomes impossible to determinate if one relies on the neutral equilibrium method or energy principle. Here in this paper, the approximate critical loads of symmetrically or non-symmetrically tapered members are computed by finite element method. The two parameters considered in this numerical analysis are the taper parameter, $\alpha$ and the sectional property parameters, m. The computed results for each sectional property parameter, m are presented in an algebraic equation which agrees with those by F.E.M The algebraic equation can be easily used by structural engineers, who are engaged in structural analysis and design of non-prismatic compression member.

• Research in Mathematical Education
• /
• v.14 no.1
• /
• pp.33-50
• /
• 2010

The mathematical thinking which transforms important mathematical content and developed into mathematical structure is a vital process in building up mathematical ability as mathematical knowledge based on structure. Such process based on students' recognition of mathematical concept. Developing mathematical thinking into mathematical structure happens when different cognitive units are connected and compressed to form schema of solution, which could happen through some guided problems. The effort of arithmetic approach in problem solving did not necessarily provide students the structure schema of solution. The using of equation to solve the problem is based on the schema of building equation, and is not necessary recognizing the structure of the solution, as the recognition of structure may be lost in the process of simplification of algebraic expressions, leaving only the final numeric answer of the problem.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.25 no.10
• /
• pp.1166-1172
• /
• 1988

This paper presents an efficient method of analyzing linear time-varying systems via Taylor polynomials. While the approach suggested by Sparis and Mouroutsos gives an implicit form for unknown state vector and requires to solve a linear algebraic equation with large dimension when the number of terms increases, the method proposed in this paper shows an explicit form and has no need to solve any linear algebraic equation.

• Journal of Institute of Control, Robotics and Systems
• /
• v.12 no.5
• /
• pp.497-504
• /
• 2006

This paper presents a new technique that derives the dynamic acceleration bounds of multiple cooperating robot systems from given individual torque limits of robots. A set of linear algebraic homogeneous equation is derived from the dynamic equations of multiple robots with friction contacts. The mobility of the robot system is analyzed by the decomposition of the null space of the linear algebraic equation. The acceleration bounds of multiple robot systems are obtained from the joint torque constraints of robots by the medium of the decomposed null space. As the joint constraints of the robots are given in the infinite norm sense, the resultant acceleration bounds of the systems are described as polytopes. Several case studies are presented to validate the proposed method in this paper.

• East Asian mathematical journal
• /
• v.37 no.4
• /
• pp.401-426
• /
• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• Communications of Mathematical Education
• /
• v.2
• /
• pp.181-191
• /
• 1997

The purpose of this study is to provide the primary sources to improve the problem solving performance by analyzing the errors and the strategies selection of the high school students when solving given algebraic problems. To attain the purpose of this study, the questions for investigation in this study are : 1. What are the differences / similarities in the patterns of errors committed by successful and unsuccessful problem-solvers when solving particular algebraic problems ? 2. What are the error types chosen by unsuccessful problem-solvers when solving particular algebraic problems? 3. Do students utilize checking, either locally or globally, when solving particular algebraic problems? Twenty students were drawn out of 10th grade students in J girls' high school in Yengi -gun, Chung-Nam, for this study. The problem-solving test was used as a test instrument. From the data, the verbal protocols and the written protocols were analyzed by the patterns. The conclusions drawn from the results obtained in the present study are as follows: First, in solving particular algebraic problems, when the problems were solved with one strategy, most students didn't give any consideration to other strategies. So mathematics teachers should teach them to use the various strategies, and should develop the problems to be used the various strategies. Second, in solving particular algebraic problems, errors on notions or transformations of equations were found. Thus, the basic knowledges related to equation should be taught. In addition, most unsuccessful students seleted the strategies inadequately to solve the problems because of misunderstanding the problems. So, to improve the problem solving performance the processes of 'understanding problem' should be emphasized to students. Third, although the unsuccesful students used the 'checking' processes when solving the problems, most of them did not find the errors because of misconceptions related to the problems, carelessness, and unskillfulness of checking. Thus, students must be taught more carefully and encouraged to use the checking.

• Journal of Electrical Engineering and Technology
• /
• v.11 no.5
• /
• pp.1486-1491
• /
• 2016