• Journal of the Korean Society for Precision Engineering
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• v.16 no.4 s.97
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• pp.95-101
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• 1999

In this paper, we propose a dynamic model of an escalator which can be used to build a design database. The model permits to estimate the forces applied to the structure by calculating three primary types of forces; the torque required to operate the escalator, the reaction forces at part interconnection points, and contact forces between parts. These forces can then be used to calculate dynamic stresses in the structure which is required to estimate the durability of the structure. Result of the computer model are compared with testing results. This simulation model is used to construct a design database. So when we design a new escalator, this design database can be used to make a new simulation model which makes it possible for us to do a Knowledge-Based-Design.

• The KSFM Journal of Fluid Machinery
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• v.1 no.1 s.1
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• pp.7-16
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• 1998

An interactive mode of grid generation system has been developed for a Navier-Stokes design procedure of axial flow compressors. The present grid generator adopts the multiblock H-grid structure, which simplifies the creation of computational grids about complex turbomachinery geometries and facilitate the manipulation of multiple grid blocks for multirow flow fields. The numerical algorithm adopts the combination of the algebraic and elliptic method to create the internal grids efficiently and quickly. The system consists of four separated modules, which are linked together with a common graphical user interface. The system input is made of the results of the preliminary design. The final grids generated from each module of the system are used as the preprocessor for the performance prediction of the two-or three-dimensional flow simulation inside the blade passage. Application to the blade design of the LP compressor was demonstrated to be very reliable and practical in support of design activities. This customized system are coupled strongly with the design procedure of the turbomachinery cascades using the Navier-Stokes technique.

• The Mathematical Education
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• v.55 no.1
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• pp.1-19
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• 2016

Given the importance of understanding the equal sign in developing early algebraic thinking, this paper investigated how a total of 695 students in grades 2~6 understood the equal sign. The students completed a questionnaire with three types of items (equation structure, equal sign definition, and open equation solving) based on the construct map by four different levels of understanding the equal sign. The questionnaire was analyzed by Rasch model. The results showed that about 80% of the students were at least Level 3 which means a basic relational understanding of the equal sign. However, the success rates varied across grades and it was noticeable that about 70% of the second graders remained at Level 1 or 2 which maintains an operational understanding of the equal sign. The results of item types demonstrated that item difficulty for the advanced relational thinking was the highest and this is the same even for the Level 4 students. This paper is expected to investigate elementary school students' understanding of the equal sign and provide implications of how to deal with the equal sign in the elementary school.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.109-128
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• 2009

This study aimed to investigate students' learning process by examining their perception process of problem structure and mathematization, and further to suggest an effective teaching and learning of mathematics to improve students' problem-solving ability. Using the qualitative research method, the researcher observed the collaborative learning of two middle school students by providing problem-posing activities of five lessons and interviewed the students during their performance. The results indicated the student with a high achievement tended to make a similar problem and a new problem where a problem structure should be found first, had a flexible approach in changing its variability of the problem because he had advanced algebraic thinking of quantitative reasoning and reversibility in dealing with making a formula, which related to developing creativity. In conclusion, it was observed that the process of problem posing required accurate understanding of problem structures, providing students an opportunity to understand elements and principles of the problem to find the relation of the problem. Teachers may use a strategy of simplifying external structure of the problem and analyzing algebraical thinking necessary to internal structure according to students' level so that students are able to recognize the problem.

• School Mathematics
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• v.13 no.3
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• pp.405-422
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• 2011

In this study, we consider the meaning of one-to-one correspondence through theoretical background under operation of matrix. On algebraic point of view, its significance is 'through one-to-one correspondence from a set with given structure, become a methods in order to induce an algebraic system in to a new set.' That is a key idea making isomorphic structure. Such process experiences necessity of mathematical fact, as well as the deep understanding of one-to-one correspon -dence. Also that becomes a base for develop a various mathematical concepts, such as matrix, exponential laws, symmetric difference, permutation and so on. This study help teachers and students to understand of mathematical concepts meaningfully and to facilitate teacher's professional development.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.1
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• pp.21-27
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• 2002

Inspection and shape measurement of three-dimensional objects are widely needed in industries for quality monitoring and control. A number of visual or optical technologies have been successfully applied to measure three-dimensional surfaces. However, those conventional visual or optical methods have inherent shortcomings such as occlusion and variant surface reflection. X-ray vision system can be a good solution to these conventional problems, since we can extract the volume information including both the surface geometry and the inner structure of any objects. In the x-ray system, the surface condition of an object, whether it is lambertian or specular, does not affect the inherent characteristics of its x-ray images. In this paper, we propose a three-dimensional x-ray imaging method to reconstruct a three dimensional structure of an object out of two dimensional x-ray image sets. To achieve this by the proposed method, two or more x-ray images projected from different views are needed. Once these images are acquired, the simultaneous algebraic reconstruction technique(SART) is usually utilized. Since the existing SART algorithms have several shortcomings such as low performance in convergence and different convergence within the reconstruction volume of interest, an advanced SART algorithm named as USART(uniform SART) is proposed to avoid such shortcomings and improve the reconstruction performance. Because, each voxel within the volume is equally weighted to update instantaneous value of its internal density, it can achieve uniform convergence property of the reconstructed volume. The algorithm is simulated on various shapes of objects such as a pyramid, a hemisphere and a BGA model. Based on simulation results the performance of the proposed method is compared with that of the conventional SART method.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.571-595
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• 2021

In this paper we study the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, where u^k = 0 and p is a prime. A ℤ_pℤ_p[u]/k>-linear code of length (r + s) is an R_k-submodule of ℤ^r_p × R^s_k with respect to a suitable scalar multiplication, where R_k = ℤ_p[u]/k>. Such a code can also be viewed as an R_k-submodule of ℤ_p[x]/r - 1> × R_k[x]/s - 1>. A new Gray map has been defined on ℤ_p[u]/k>. We have considered two cases for studying the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, and determined the generator polynomials and minimal spanning sets of these codes in both the cases. In the first case, we have considered (r, p) = 1 and (s, p) ≠ 1, and in the second case we consider (r, p) = 1 and (s, p) = 1. We have established the MacWilliams identity for complete weight enumerators of ℤ_pℤ_p[u]/k>-linear codes. Examples have been given to construct ℤ_pℤ_p[u]/k>-cyclic codes, through which we get codes over ℤ_p using the Gray map. Some optimal p-ary codes have been obtained in this way. An example has also been given to illustrate the use of MacWilliams identity.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.111-120
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• 2018

This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.997-1017
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• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2016

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.