• Industrial Engineering and Management Systems
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• v.7 no.1
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• pp.23-33
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• 2008

This paper proposes an approach to monitoring and scheduling methods for repetitive MIMO-FIFO DESs. We use max-plus algebra for modeling and formulation, known as an effective approach for controller design for this type of system. Because a certain type of linear equations in max-plus algebra can represent the system's behavior, the principal concerns in past researches were how to solve the equations. However, the researches focused mainly on analyses of the relation between inputs and outputs of the system, which implies that the changes or the slacks of internal states were not clarified well. We first examine several properties of the corresponding state variables, which contribute to finding and tracing the float times in each process. Moreover, we provide a rescheduling method that can take into account delays or changes of the internal states. These methods would be useful in schedule control or progress management.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.531-535
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• 1996

Computer aided conceptual solution of engineering problems can be effectively implemented by qualitative reasoning based on a physical model. Qualitative reasoning needs modeling paradigm which provides intellignet control of modeling assumptions and robust inferences without quantitative information about the system. We developed reasoning method using new algebra of qualitative mathematics. The method is applied to a conceptual design scheme of anadaptive control system of cutting process. The method identifies differences between proportional and proportional-integral control scheme of cutting process. It is shown that unfeasible investment could be prevented in the early conceptual stage by the qualitative reasoning procedures proposed in this paper.

• School Mathematics
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• v.9 no.1
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• pp.141-160
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• 2007

The purpose of this paper was to evaluate how students apply prior knowledge or experience in solving algebra word problems from the chain of signification-based perspective. Three middle school students were evaluated in this case study. The results showed that the subjects formed similarities in the process of applying knowledge needed for solving a problem. The student A and C used semi-open-end formulas and closed formulas as solutions. They then formed concrete shape for each solution using the chain of signification that was applied for solution by forming procedural similarity. At this time, the chain of signification could be the combination of numbers, words, and pictures (such as diagrams or graphs) or just numbers or words. On the other hand, the student C who recognized closed formulas and her own rule as a solution method could not formulate completely procedural similarity due to many errors arising from number information. Nonetheless, all of the subjects showed something in common in the process of coming up with a algorithm that was semi-open-end formula or closed formula.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.1-14
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• 2009

Since western mathematics and astronomy had been introduced in Chosun dynasty in the 17th century, most of Chosun mathematicians studied Shu li jing yun(數理精蘊) for the western mathematics. In the last two decades of the 19th century, Chosun scholars have studied them which were introduced by Japanese text books and western missionaries. The former dealt mostly with elementary arithmetic and the latter established schools and taught mathematics. Lee Sang Seol(1870~1917) is well known in Korea as a Confucian scholar, government official, educator and foremost Korean independence movement activist in the 20th century. He was very eager to acquire western civilizations and studied them with the minister H. B. Hulbert(1863~1949). He wrote a mathematics book Su Ri(數理, 1898-1899) which has two parts. The first one deals with the linear part(線部) and geometry in Shu li jing yun and the second part with algebra. Using Su Ri, we investigate the process of transmission of western mathematics into Chosun in the century and show that Lee Sang Seol built a firm foundation for the study of algebra in Chosun.

• School Mathematics
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• v.11 no.3
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• pp.527-546
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• 2009

This study was designed to gain insights into instrumental genesis process of CAS in Korean high school students and to explore its practical potentials in secondary mathematics education. Two activities, such as Concept-Centered Mathematics Activity based on CAS and Problem Solving Activities, were constructed and executed to 10th Grade seven students for twelve class hours. The finding on the students' activities are as follows : it is meaningful in mathematics education, especially in algebra education, in that the CAS based concept centered mathematics activity offers great opportunities to deal with high-qualified application problems. The problem solving activities based on the instrumented CAS may have an influence on the sequence of mathematics curriculum, e.g. the optimization problems may precede the calculus problems such as derivatives in high school. The results of this study to investigate the instrumental genesis of CAS in mathematical activities will give insights into the secondary mathematics curriculum to prepare the CAS in Korea.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.369-382
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• 2009

In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.138-143
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• 2002

This paper describes a framework for extending GIS databases to support moving object data type and query language. The rapid progress of wireless communications, positioning systems, and mobile computing devices have led location-aware applications to be essential components for commercial and industrial systems. Location-aware applications require GIS databases system to represent moving objects and to support querying on the motion properties of objects. For example, fleet management applications may require storage of information about moving vehicles. Also, advanced CRM(Customer Relationship Management) applications may require to store and query the trajectories of mobile phone users. In this trend, maintaining consistent information about the location of continuously moving objects and processing motion-specific queries is challenging problem. We formally define a data model and query language for mobile objects that includes complex evolving spatial structure, and propose core algebra to process the moving object query language. Main profit of proposed moving objects query language and algebra is that proposed model can be constructed on the top of GIS databases.

• Journal of the Korea Society for Simulation
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• v.17 no.4
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• pp.241-247
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• 2008

In this study we consider an M/D/1 queue with a finite buffer. Due to the finiteness of the buffer capacity arriving customers can not join the system and turn away without service when the buffer is full. Even though a computational method for blocking probabilities in an M/D/1/K queue is already known, it is very complex to use. The aim of this study is to propose a new way to compute blocking probability by using (max,+)-algebra. Our approach provide a totally different and easier way to compute blocking probabilities and it is, moreover, immediately applicable to more generous queueing systems.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.437-456
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• 2003

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra $S(L^2_{a,b}[0,T])$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.

• Journal for History of Mathematics
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• v.26 no.4
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• pp.245-257
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• 2013

Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.