• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.485-494
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• 1998

This study is on the theory of Piaget's reflective abstraction and the mechanism of the development of knowledge and the history of algebra and its application to understand the difficulties that many students have in learning algebra. Piaget considers the development of knowledge as a linear process. The stages in the construction of different forms of knowledge are sequential and each stage begins with reorganization. The reorganization consists of the projection onto a higher level from the lower level and the reflection which reconstructs and reorganizes within a lager system that is transferred by profection. Piaget shows that the mechanisms mediating transitions from one historical period to the next are analogous to those mediating the transition from one psychogenetic stage to the next and characterizes the mechanism as the intra, inter, trans sequence. The historical development of algebra is characterized by three periods, which are intra inter, transoperational. The analysis of the history of algebra by the mechanism explains why the difficulties that students have in learning algebra occur and shows that the roles of teachers are important to help students to overcome the difficulties.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권3호
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• pp.965-983
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• 2014

Concurrent behaviors of multithreaded programs cannot be described effectively by automata-based models. Thus, concurrent program intrusion attempts cannot be detected. To address this problem, we proposed the process algebra-based detection model for multithreaded programs (PADMP). We generate process expressions by static binary code analysis. We then add concurrency operators to process expressions and propose a model construction algorithm based on process algebra. We also present a definition of process equivalence and behavior detection rules. Experiments demonstrate that the proposed method can accurately detect errors in multithreaded programs and has linear space-time complexity. The proposed method provides effective support for concurrent behavior modeling and detection.

• 산업경영시스템학회지
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• 제35권3호
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• pp.155-162
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• 2012

This study proposes an integrated approach that uses both a fuzzy service FMEA (failure mode and effect analysis) and HOQ (house of quality) matrix algebra in designing and improving a service system. The fuzzy service FMEA methodology applies the customer satisfaction to the fuzzy RPN model. We fuzzify only the service satisfaction that consist in two failure factors, intangible service and tangible service, to more effectively assess the customer satisfactions on service encounters. Proposed fuzzy service satisfactions with triangle membership function are defuzzified by using the Fuzzy Inference System, and these are eventually identified the ranks on the potential fail points. HOQ matrices are constructed from cause-effect relationships. It is possible for these relationship matrix to find a linear approximation solution on the engineering attributes. Thus, in order to demonstrate how the proposed methods work, practical sample of the A/S part in S Electronic Co. provides for the ranking of the engineering attributes which has been successfully implemented.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -2
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• pp.1103-1106
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• 2000

Recently, the research on computer graphics (CG) has been actively studied and developed. Namely, many surface/solid models have been proposed in the field of computer aided geometric design as well as the one of CG. Since it is difficult to visualize the complex shape exactly, an approximation by generating a set of meshes is usually used. Therefore it is important to guarantee the quality of the approximation in consideration of the computational cost. In this paper, a mesh generation algorithm will be proposed for a surface defined by linear tie algebra The proposed algorithm which considers the quality in the meaning of validation of invariants obtained by the mesh.

• 한국철도학회논문집
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• 제12권2호
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• pp.267-275
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• 2009

Max-Plus 대수란, 선형 대수(linear algebra)에서의 더하기(addition) 연산과 곱하기(multiplication)연산을 최대값(maximization), 더하기(addition)로 각각 대체한 비선형 시스템을 말한다. Max-Plus 대수는 전통적인 의미의 선형 대수에서 다뤄지는 고유값(eigenvalue), 고유벡터(eigenvector), 안전성(stability) 등의 개념이 Max-Plus 대수에서도 그대로 적용되고, 그것의 의미 또한 실제 시스템의 다양한 해석을 가능케 하고 있어, 최대값 연산과 더하기 연산으로 이루어진 이산 사건 시스템(discrete event system)을 분석할 수 있는 유용한 도구가 된다. 이러한 이산 사건 시스템의 대표적인 예가 바로 환승을 고려한 열차 스케줄이다. 현재 수도권에는 1호선${\sim}$8호선, 인천 1호선, 분당선, 중앙선 등 11개 노선의 도시 철도가 운영되고 있다. 각 노선들은 서울 Metro, 서울도시철도공사, KORAIL 등 서로 다른 운영사에 의해 운영되고 있어서 각 노선의 스케줄 또한 노선간의 환승을 고려하지 않은 채 독립적으로 작성되고 있는 실정이다. 이러한 독립적인 열차 스케줄은 승객들의 긴 환승시간으로 이어진다. 본 연구에서는 Max-flus대수 방법론에 대한 자세한 설명을 기초로 1호선과 2호선, 4호선의 주요 환승역인 사당역과 신도림역, 시청역, 동대문역을 중심으로 Max-Plus 대수 방법론의 적용 가능성을 검토해 보았다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권1호
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• pp.15-28
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• 2018

Recently Machine Learning algorithms are widely used to process Big Data in various applications and a lot of these applications are executed in run time. Therefore the speed of Machine Learning algorithms is a critical issue in these applications. However the most of modern iteration Machine Learning algorithms use a successive iteration technique well-known in Numerical Linear Algebra. But this technique has a very low convergence, needs a lot of iterations to get solution of considering problems and therefore a lot of time for processing even on modern multi-core computers and clusters. Tchebychev iteration technique is well-known in Numerical Linear Algebra as an attractive candidate to decrease the number of iterations in Machine Learning iteration algorithms and also to decrease the running time of these algorithms those is very important especially in run time applications. In this paper we consider the usage of Tchebychev iterations for acceleration of well-known K-Means and SVM (Support Vector Machine) clustering algorithms in Machine Leaning. Some examples of usage of our approach on modern multi-core computers under Apache Spark framework will be considered and discussed.

• 한국콘텐츠학회논문지
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• 제8권5호
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• pp.276-286
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• 2008

본 논문에서는 컴퓨터 대수 시스템을 기반으로 하는 웹 저작 환경과 베이지언 추론망을 적용한 학습자 진단 환경이 포함된 이공계 수학용 적응적 이러닝 시스템 개발에 대하여 소개하였다. 본 시스템을 활용하면 교수자는 컴퓨터 대수 시스템을 수식처리 엔진으로 하며 웹을 인터페이스로 하는 이공계 수학용 웹 콘텐츠를 쉽게 생성할 수 있다. 구체적으로 선형대수, 미분방정식 및 이산수학의 영역에서 콘텐츠 개발의 예를 소개하였다. 또한 학습자의 지식 영역별 수준을 조건부 확률을 이용한 통계적 추론에 의해 진단하여 그 결과에 따라 피드백을 생성하는 적응적 이러닝 웹 콘텐츠를 만들 수 있다. 본 시스템을 사용하여 개발한 이공계 수학용 웹 콘텐츠를 평가하기 위하여 그 결과물을 대학 강의에 적용하였고, 설문지 조사를 통하여 콘텐츠 사용에 대한 학습자의 반응을 평가하였다.

• Industrial Engineering and Management Systems
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• 제8권3호
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• pp.155-161
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• 2009

We focus on discrete event systems with a structure of parallel processing, synchronization, and no-concurrency. We use max-plus algebra, which is an effective approach for controller design for this type of system, for modeling and formulation. Since a typical feature of this type of system is that the initial schedule is frequently changed due to unpredictable disturbances, we use a simple model and numerical examples to examine the possibility of applying the concepts of the feeding buffer and the project buffer of critical chain project management (CCPM) on max-plus linear discrete event systems in order to control the occurrence of an undesirable state change. The application of a CCPM-based framework on a max-plus linear discrete event system was proven to be effective.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권9호
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• pp.3458-3481
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• 2021

Existing methods for blind identification of linear block codes without a candidate set are mainly built on the Gauss elimination process. However, the fault tolerance will fall short when the intercepted bit error rate (BER) is too high. To address this issue, we apply the reverse algebra approach and propose a novel "two-step-screening" algorithm by solving the linear error equations on the binary Galois field, or GF(2). In the first step, a recursive matrix partition is implemented to solve the system linear error equations where the coefficient matrix is constructed by the full codewords which come from the intercepted noisy bitstream. This process is repeated to derive all those possible parity-checks. In the second step, a check matrix constructed by the intercepted codewords is applied to find the correct parity-checks out of all possible parity-checks solutions. This novel "two-step-screening" algorithm can be used in different codes like Hamming codes, BCH codes, LDPC codes, and quasi-cyclic LDPC codes. The simulation results have shown that it can highly improve the fault tolerance ability compared to the existing Gauss elimination process-based algorithms.

• 대한수학회지
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• 제45권5호
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• pp.1203-1220
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• 2008

Let V be an arbitrary system of weights on an open connected subset G of ${\mathbb{C}}^N(N{\geq}1)$ and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let $HV_b$ (G, E) and $HV_0$ (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings ${\phi}:G{\rightarrow}G$ and operator-valued analytic mappings ${\Psi}:G{\rightarrow}B(E)$ which generate weighted composition operators and invertible weighted composition operators on the spaces $HV_b$ (G, E) and $HV_0$ (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.