• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.93-108
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• 2011

A ring R is called left weakly np- injective if for each non-nilpotent element a of R, there exists a positive integer n such that any left R- homomorphism from $Ra^n$ to R is right multiplication by an element of R. In this paper various properties of these rings are first developed, many extending known results such as every left or right module over a left weakly np- injective ring is divisible; R is left seft-injective if and only if R is left weakly np-injective and $_RR$ is weakly injective; R is strongly regular if and only if R is abelian left pp and left weakly np- injective. We next introduce the concepts of left weakly pp rings and left weakly C2 rings. In terms of these rings, we give some characterizations of (von Neumann) regular rings such as R is regular if and only if R is n- regular, left weakly pp and left weakly C2. Finally, the relations among left C2 rings, left weakly C2 rings and left GC2 rings are given.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.2
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• pp.121-131
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• 2011

An object oriented programming(OOP) framework is presented to solve plane elastostatic contact problems by means of the boundary element method(BEM). Unified modeling language(UML) is chosen to describe the structure of the program without loss of generality, even though all implemented codes are written with C++. The implementation is based on computational abstractions of both mathematical and physical concepts associated with contact mechanics involving geometrical nonlinearities and the corner node problems for multi-valued traction. The overall class organization for contact analysis is discussed in detail. Numerical examples are also presented to verify the accuracy of the developed BEM program.

• Structural Engineering and Mechanics
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• v.23 no.1
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• pp.63-74
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• 2006

In this paper, the scattering of harmonic elastic anti-plane shear waves by two collinear cracks in functionally graded materials is investigated by means of nonlocal theory. The traditional concepts of the non-local theory are extended to solve the fracture problem of functionally graded materials. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially with coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips.

• Education of Primary School Mathematics
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• v.6 no.2
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• pp.85-91
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• 2002

The purpose of this study is to analyze elementary students' understanding the relationship between perimeter and area in geometric figures. In this study, the questionaries were used. In the survey, the subjects were elementary school students in In-cheon city. They were 86 students of the fifth grade, 86 of the sixth. They were asked to solve the problems which was designed by the researcher and to describe the reasons why they answered like that. Study findings are as following; Students have misbelief about the concept of the relationship between perimeter and area in geometric figures. Therefore, 1 propose the method fur teaching about the relationship between perimeter and area in geometric figures. That is teaching via problem solving.. In teaching via problem solving, problems are valued not only as a purpose fur learning mathematics but also a primary means of doing so. For example, teachers give the problem relating the concepts of area and perimeter using a set of twenty-four square tiles. Students are challenged to determine the number of small tiles needed to make rectangle tables. Using this, students can recognize the concept of the relationship between perimeter and area in geometric figures.

• Smart Structures and Systems
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• v.14 no.2
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• pp.159-189
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• 2014

One of the most important requirements in the evaluation of existing structural systems and ensuring a safe performance during their service life is damage assessment. Damage can be defined as a weakening of the structure that adversely affects its current or future performance which may cause undesirable displacements, stresses or vibrations to the structure. The mass and stiffness of a structure will change due to the damage, which in turn changes the measured dynamic response of the system. Damage detection can increase safety, reduce maintenance costs and increase serviceability of the structures. Artificial Neural Networks (ANNs) are simplified models of the human brain and evolved as one of the most useful mathematical concepts used in almost all branches of science and engineering. ANNs have been applied increasingly due to its powerful computational and excellent pattern recognition ability for detecting damage in structural engineering. This paper presents and reviews the technical literature for past two decades on structural damage detection using ANNs with modal parameters such as natural frequencies and mode shapes as inputs.

• Journal of Electrical Engineering and Technology
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• v.13 no.4
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• pp.1515-1527
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• 2018

This paper presents a sensorless speed control of IPMSM (Interior Permanent Magnet Synchronous Motor) using the high-frequency (HF) square wave injection method. In the proposed HF pulsating square wave injection method, injection voltage is applied into the estimated d-axis of rotor and high-frequency induced q-axis current is considered to estimate the rotor position. Conventional square wave injection methods may need complex demodulation process to find rotor position, while in the proposed method, an easy demodulation process based on the rising-falling edge of the injected voltage and carrier induced q-axis current is implemented, which needs less processing time and improves control bandwidth. Unlike some saliency-based sensorless methods, the proposed method uses maximum torque per ampere (MTPA) strategy, instead of zero d-axis command current strategy, to improve control performance. Furthermore, this paper directly uses resultant d-axis current to detect the magnet polarity and eliminates the need to add an extra pulse injection for magnet polarity detection. As experimental results show, the proposed method can quickly find initial rotor position and MTPA strategy helps to improve the control performance. The effectiveness of the proposed method and all theoretical concepts are verified by mathematical equations, simulation, and experimental tests.

• School Mathematics
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• v.12 no.1
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• pp.1-15
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• 2010

The study presented in this paper, which serves as a pilot study for a future comprehensive project, was to investigate how students deal with the concepts of infinity and limit. Based on the communicational approach to cognition, according to which mathematics is a kind of discourse, we tried to identify the characteristics of students' discourse on the topics. Four American and four Korean students were interviewed in English on limits and infinity and their discourse was scrutinized with an eye to common characteristics as well as culture, age, and education-related differences.

• School Mathematics
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• v.16 no.2
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• pp.285-301
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• 2014

Because a development figure is treated restrictively in elementary school, not only there are brought out the concept image, but also the definition of the development figure in textbook in not unique. Furthermore, since the comparison and analysis of 'definition element' between the materials in textbook are nor carried out, its educational value as well as the teaching for concepts and objectives does not give rise to public discussion. In this note, we will investigate the definition and teaching of the development figure in Korea and Japan. And through three viewpoints of its definition and related debate, we will consider the fundamental understanding and objectiveness of a development figure, and suggest its mathematical application. This study will promote teachers's critical and didactical insight for the didactical transposition.

• Journal of Power Electronics
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• v.6 no.2
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• pp.104-113
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• 2006

Satellites have provided the impetus for the orderly development of reliability engineering research and analysis because they tend to have complex systems and hence acute problems. They were instrumental in developing mathematical models for reliability, as well as design techniques to permit quantitative specification, prediction and measurement of reliability. Reliability engineering is based on implementing measures which insure an item will perform its mission successfully. The discipline of reliability engineering consists of two fundamental aspects; $(1^{st})$ paying attention to details, and $(2^{nd})$ handling uncertainties. This paper uses some of the basic concepts, formulas and examples of reliability theory in application. This paper emphasizes the practical reliability analysis of a Low Earth Orbit (LEO) Micro-satellite power subsystem. Approaches for specifying and allocating the reliability of each element of the power system so as to meet the overall power system reliability requirements, as well as to give detailed modeling and predicting of equipment/system reliability are introduced. The results are handled and analyzed to form the final reliability results for the satellite power system. The results show that the Electric Power Subsystem (EPS) reliability meets the requirements with quad microcontrollers (MC), two boards working as main and cold redundant while each board contains two MCs in a hot redundant.

• Korean Institute of Interior Design Journal
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• v.17 no.3
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• pp.156-164
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• 2008

Through staggering advancements of technology and network as we know them as digital revolution, we have established a foundation of space in which we can express reality by eliminating the boundaries between expression, space, and movement. There are many ongoing approaches that aim to overcome the physically-fixed property of space where the mathematical-geometric notion of Voronoi Diagram is one of them. Although the repetitive increment based on self-organization during the process in which space is generated by the Voronoi Diagram forms a pattern and focuses on the formation, its pattern is not restricted to a single method of expression but evolves over self-control. The result of having analyzed spaces generated by the Voronoi Diagram in this study can be summarized as follows. First, the Voronoi computation method with self-organization property creates multiple levels, increments, and evolves through feedbacks among changes with the slightest order and in the absence of control. Secondly, after forming a pattern through such feedbacks comes the differentiation phase due to the presence of different properties. Thirdly, a space that has gone through the generation process retransforms through active interaction between changes and it obtains ambiguous boundaries and a repetitive pattern. This leads to an evolution of space through repetitive increments based on self-organization. Such flexible space creation is supported by various digital technologies where we believe a converging application of these studies, sciences, engineering concepts, and space design is and effective and new method in terms of space creation.