• Computers and Concrete
• /
• v.30 no.4
• /
• pp.243-256
• /
• 2022

The static analysis of spinning functionally graded (FG) nanotube on the basis of the nonlocal strain gradient theory (NSGT) is presented. The high-order beam theory is employed for mathematical modeling of the tube structures according to the Sinusoidal shear deformation beam theory. The energy conservation principle is operated to generate the equations. The centrifugal force is assumed along the tube length due to the rotating of the tube, moreover, the nanotube is made of functionally graded material (FGM) composed of ceramic and metal phases along the tube radius direction. The generalized differential quadratic method (GDQM) is utilized to solve the formulations. Finally, the numerical results are discussed in detail to examine the impact of different relevant parameters on the bending the buckling behavior of the rotating nanotube.

• Communications of Mathematical Education
• /
• v.25 no.1
• /
• pp.207-219
• /
• 2011

The purpose of this article is to study characteristics of diabolical cube in geometric point of view, and to present educational materials and direction for efficient diabolical cube activities in gifted education upon systematical analysis of methods of finding solutions. We can apply inclusion-exclusion Method to find all possible combination of solutions in diabolical cube activities not as trial-and-error method but as analytical method. Through teacher's questions and problem posing in activities using diabolical cube, we systematically came up with most solution and case of all possible combinations be solution in classifying properties of pieces and combining selected pieces.

• Communications of Mathematical Education
• /
• v.23 no.1
• /
• pp.39-51
• /
• 2009

The purpose of this article is to study characteristics of tangram as instructional media in combinatorialgeometric point of view, and to present basic materials and direction for efficient tangram activities in gifted education upon systematical analysis of methods of finding solutions. We can apply x=a+2b+4c to find all possible combination of solutions in tangram activities not as trial-and-error method but as analytical method. Through teacher's questions and problem posing in activities using tangram, we systematically came up with most solution and case of all possible combinations be solution in classifying properties of pieces and combining selected pieces.

• Communications of Mathematical Education
• /
• v.37 no.3
• /
• pp.467-482
• /
• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.

• Structural Engineering and Mechanics
• /
• v.25 no.6
• /
• pp.653-674
• /
• 2007

This paper discusses the application of piezoelectric sensors used for evaluation of damping ratio of PVC plastics. The development of the mathematical formulation based on the Empirical Mode Decomposition for calculating the damping coefficient and natural frequency of the system is presented. A systematic experimental and analytical investigation was also carried out to demonstrate the integrity of several methods commonly used to evaluate the damping of materials based on a single degree freedom formulation. The influence of the sensors' location was also investigated. Besides the commonly used methods, a newly emerging time-frequency method, namely the Empirical Mode decomposition, is also employed. Mathematical formulations based on the Hilbert-Huang formulation, and a frequency spacing technique were also developed for establishing the natural frequency and damping ratio based on the output voltage of a single piezoelectric sensor. An experimental investigation was also conducted and the results were compared and verified with Finite Element Analysis (FEA), revealing good agreement.

• East Asian mathematical journal
• /
• v.32 no.4
• /
• pp.501-518
• /
• 2016

In this paper, we analyzed the correlation among scores of the mathematics B-type grade of College Scholastic Ability Test(CSAT), scores of Mathematics Level Assessment(MLA) and written test scores of Basic Mathematics Subject(BMS) made by students. Especially, we examined the relationship between CSAT grade with results of MLA and results of BMS through survey of students who changed their grades and learned about reasons. In addition, we analyzed error types for the descriptive problem solving in BMS written tests..

• Journal of Drive and Control
• /
• v.11 no.1
• /
• pp.14-24
• /
• 2014

Variable displacement vane-type oil pumps represent one of the most innovative pump types for industrial applications, especially for engine lubrication systems. This paper presents a complete and accurate mathematical model for a typical variable displacement vane-type oil pump. Firstly, its theoretical model is revised. Secondly, an analysis of power loss factors of this pump type is carefully investigated to optimize the modeling accuracy. Finally, the estimated pump performance using the complete pump model is verified by numerical simulations in comparison with the practical tests.

• Research in Mathematical Education
• /
• v.15 no.3
• /
• pp.251-259
• /
• 2011

Metaphor is the main representations of teachers' practical knowledge, which can help students to understand mathematics better. Through the recording and quantitative analysis of video cases of expert teachers in mathematics classroom, there are some results after analysis: 1) Teachers use many metaphors in the classroom and most of that are structural-ontological metaphors, which takes a certain period of time. 2) Teachers use the metaphors mainly in the teaching process of introduce and explore by the form of question-answer. 3) During the process of concept teaching, the metaphors from the real-world examples can promote the students have more motivation to study. During the process of procedure teaching, the metaphors from similar materials can promote the students to understand the operational skill better.

• Transactions of Materials Processing
• /
• v.11 no.5
• /
• pp.394-404
• /
• 2002

The drawbead model for a three-dimensional a finite element analysis of sheet metal forming processes is developed. The mathematical models of the basic drawbeads like circular drawbead, stepped drawbead, and squared drawbaed are first derived using the bending theory, belt-pulley equation, and Coulomb friction law. Next, the experiments for finding the drawing characteristics of the drawbead are performed. Based on mathematical models and drawing test results, expert models of basic drawbeads are then developed employing a linear multiple regression method. For the expert models of combined drawbeads such as the double circular drawbead, double stepped drawbead, circular-and-stepped drawbead, etc., those of the basic drawbeads are summed. Finally, in order to verify the expert models developed, the drawing characteristics calculated by the expert models of the double circular drawbead and circular-and-stepped drawbead are compared with those obtained from the experiments. The predictions by expert models agree well with the measurements by experiments.

• Journal of the Society of Naval Architects of Korea
• /
• v.44 no.2 s.152
• /
• pp.148-153
• /
• 2007

Two typical impact loadings, shock wave and gas bubble pulse, due to UNDEX(UNDerwater EXplosion), should be considered together for the closest response analysis of structure subjected to UNDEX to a reality. Since these two impact loadings have different response time bands, however, their response characteristics of structure are different from each other. It is impossible to consider these effectively under the current computational environment and the mathematical model has not yet been developed. Whereas Hicks model approximates the fluid-structure interaction due to gas bubble pulse as virtual mass effect, treating the flow by the response of gas bubble after shock wave as incompressible ideal fluid contrary to the compressible flow due to shock wave, Geers-Hunter model could make the closest response analysis of structure under UNDEX to a real one as a mathematical model considering the fluid-structure interaction due to shock wave and gas bubble pulse together using acoustic wave theory and DAA(Doubly Asymptotic Approximation). In this study, the application and effectiveness of integrated dynamic response analysis of submerged structure was examined with the analysis of the shock wave and gas bubble pulse together.