• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.121-144
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• 2005

In this paper, we propose unconstrained and constrained posynomial Geometric Programming (GP) problem with negative or positive integral degree of difficulty. Conventional GP approach has been modified to solve some special type of GP problems. In specific case, when the degree of difficulty is negative, the normality and the orthogonality conditions of the dual program give a system of linear equations. No general solution vector exists for this system of linear equations. But an approximate solution can be determined by the least square and also max-min method. Here, modified form of geometric programming method has been demonstrated and for that purpose necessary theorems have been derived. Finally, these are illustrated by numerical examples and applications.

• Korean Journal of Computational Design and Engineering
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• v.9 no.4
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• pp.294-305
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• 2004

Highly detailed geometric models are rapidly becoming commonplace in computer graphics and other applications. These complex models, which is often represented as complex1 triangle meshes, mainly suffer from the vast memory requirement for real-time manipulation of arbitrary geometric shapes without loss of data. Various techniques have been devised to challenge these problems in views of geometric processing, not a representation scheme. This paper proposes the new mesh structure for the compact representation and the efficient handling of the highly complex models. To verify the compactness and the efficiency, the memory requirement of our representation is first investigated and compared with other existing representations. And then we analyze the time complexity of our data structure by the most critical operation, that is, the enumeration of the so-called one-ring neighborhood of a vertex. Finally, we evaluate some elementary modeling functions such as mesh smoothing, simplification, and subdivision, which is to demonstrate the effectiveness and robustness of our mesh structure in the context of the geometric modeling and processing.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.193-206
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• 2001

This study was designed to develop investigation- and exploration- activities on Euclidean geometry with an exploratory type software, Geometer's Sketchpad, and to gain insights into the geometric reasoning abilities of college students working with the software. A package of Euclidean geometric activities with GSP was developed and four college students worked on the several activities with GSP and their geometric reasoning process were analyzed. Results indicated that GSP helped students solve problems in the several ways: to make conjectures and discover theorems by providing precise construction and measurement; to discover their proofs by providing the visual images and its manipulation; and to make students easily apply "what-if"strategies and expand and deepen their activities. Students' geometric reasoning was highly depended on analytic methods and their abilities with synthetic methods were shown very limited.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.42-45
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• 2004

Electrochemical discharge machining (ECDM) has been found to be suitable for the micro-hole machining of nonconductive materials such as ceramics or glass compared with existing conventional and also non-conventional machining methods. However this machining process has some problems such as low geometric accuracy and low machining efficiency due to the random spark generation at the end of the electrode. This paper proposes the methods to improve the geometric accuracy of micro-hole using powder mixed ECDM process. The experimental results show the effects of powder producing improved geometric accuracy of machined hole and decreased concentration of spark energy.

• Korean Journal of Computational Design and Engineering
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• v.2 no.1
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• pp.1-10
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• 1997

Finding the optimum route of ship's pipes is complicated and time-consuming process. Experience of designers is the main tool in this process. To reduce design man-hours and human errors a design expert system shell and a geometric modeler is used to automate the design process. In this paper, a framework of the intelligent CAD system for pipe auto-routing is suggested, which consists of general-purpose expert system shell and a geometric modeler. The design expert system and the geometric modeling kernel have been integrated. The CADDS5 of Computervision is used as the overall CAD environment. The Nexpert Object of Neuron Data is used as the expert system shell. The CADDS5 ISSM is used as the interface that creates and modifies geometric models of pipes. Existing algorithms for the routing problem have been analyzed. Most of them are to solve the 2-D circuit routing problems. Ship piping system, specially within the engine room, is a complicated, large scale 3-D routing problem. Methods of expert system have been used to find the route of ship pipes on the main deck.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.9
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• pp.84-93
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• 1996

This paper describes the development of new feature positioning method which embedded into the top-down assembly modeling system supporting conceptual design. In this work, the user provides the geometric constraints representing the position and size of features, then the system calculates their proper solution. The use of geometric constraints which are easy to understand intuitively enables the user to represent his design intents about geometric shapes, and enables the system to propagate the changes automatically when some editing occurs. To find the proper solution of given constraints, the Selective Solving Method in which the redundant or conflict equations are detected and discarded is devised. The validity of feature shapes satisfying the constraints can be maintained by this technique, and under or over constrained user-defined constraints can also be estimated. The problems such as getting the initial guess, controlling the multiple solutions, and dealing with objects of rotational symmetry are also resolved. Through this work, the feature based modeling system can support more general and convenient modeling method, and keeps the model being valid during modifying models.

• Korean Journal of Computational Design and Engineering
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• v.9 no.1
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• pp.19-26
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• 2004

It is not possible to exchange parametric information of CAD models based on the current version of STEP (Standard for the Exchange of Product model data). The designer intents are lost during the transfer of CAD models. To resolve this problem, the macro-parametric approach had been proposed. To enable this approach, a set of standard modeling commands has been defined. Errors or missing elements of the standard modeling commands can be discovered by implementing macro-parametric translators. But there is a limit to discover problems only by using translators. This paper proposes a method to verify the standard modeling commands by implementing a geometric modeler. First, each argument of a modeling command is verified. Second, the set of the standard modeling commands is applied to geometric modeling of commercially available product parts. For the geometric modeling, nine test models have been selected.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• The Mathematical Education
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• v.49 no.1
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• pp.39-51
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• 2010

The purpose of this article is to study students' responses to non-routine problems which are presented by using solely numerals or symbolic figures. Such figures have no mathematical meaning but just symbolical meaning. Most students understand geometric figures more concrete objects than numerals because geometric figures such as circles and squares can be visualized by the manipulatives in real life. And since students need not consider (unvisible) any operational structure of numerals when they deal with (visible) figures, problems proposed using figures are considered relatively easier to them than those proposed using numerals. Under this assumption, we analyze students' problem solving processes of numeral problems and figural problems, and then find out when students' difficulties arise in the problem solving process and how they response when they feel difficulties. From this experiment, we will suggest several comments which would be considered in the development and application of both numerical and figural problems.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.89-102
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• 2001

Computer has been regarded as an alternative that could overcome the difficulties in the teaching and learning of mathematics. But the didactical problems of the computer-based environment for mathematics education could give us new obstacles. In this paper, first of all, we examined the application of the learning theories of mathematics to the computer environment. If the feedbacks of the computer are too immediate, students would have less opportunity to reflect on their thinking and focus their attention on the visual aspects, which leads to the simple abstraction rather than the reflective abstraction. We also examined some other Problems related to cognitive obstacle to learn the concepts of geometric figure and the geometric knowledge. Based on the analysis on the problems related to the computer-based environment of mathematics teaching and learning, we tried to find out the direction to use computer more adequately in teaching and learning geometry.