• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.167-181
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• 2009

Based on Ricatti equation $XA^{-1}X=B$ for two (positive invertible) operators A and B which has the geometric mean $A{\sharp}B$ as its solution, we consider a cubic equation $X(A{\sharp}B)^{-1}X(A{\sharp}B)^{-1}X=C$ for A, B and C. The solution X = $(A{\sharp}B){\sharp}_{\frac{1}{3}}C$ is a candidate of the geometric mean of the three operators. However, this solution is not invariant under permutation unlike the geometric mean of two operators. To supply the lack of the property, we adopt a limiting process due to Ando-Li-Mathias. We define reasonable geometric means of k operators for all integers $k{\geq}2$ by induction. For three positive operators, in particular, we define the weighted geometric mean as an extension of that of two operators.

• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.487-490
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• 1995

This paper discisses the effects geometric errors on the measurement of error motions of rotor with the cylindrical capacitive displacement sensor. Analytic model of the measuring process with this sensor is derived and this model shows that the effect of geometric errors of sensor is larger than that of rator on the measurement of error motions of rotor. The computer simulation shows effect of periodic errors in this sensor on the measuring orbit.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.127-140
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• 2010

This paper focuses on a number of criteria that enable controlling the influence of geometric simplification on the quality of finite element (FE) computations. To perform the mechanical simulation of a component, the corresponding geometric model typically needs to be simplified in accordance with hypotheses adopted regarding the component's mechanical behaviour. The method presented herein serves to compute an a posteriori indicator for the purpose of estimating the significance of each feature removal. This method can be used as part of an adaptive process of geometric simplification. If a shape detail removed during the shape simplification process proves to be influential on mechanical behaviour, the particular detail can then be reinserted into the simplified model, thus making it possible to readapt the initial simulation model. The fields of application for such a method are: static problems involving linear elastic behaviour, and linear thermal problems with stationary conduction.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.587-591
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• 1996

Usually triangular patches are used to transfer geometric shape in Rpaid Prototyping CAM system. STL, a list of triangles, is de facto in RP industry. Because STL has no topology data, it can cause errornous results. So, STL should be verified before using. After adding support structures to anchor the part to the platform and to prevent sagging or distortion, slicing and layer by layer manufacturing process are done. But triangular patch is surface model and cannot provide dufficient information on geometry in the above processes. So, geometric modeling is necessary in verifying STL, adding support structures, and slicing. It is natural that triangle based modeling is the best when traingular patches are used as input. Considering support structures, solid and faces coexist in RP process. Therefore non-manifold modeler is required. In this study, triangle based non-manifold geometric modeling is proposed for RP system consitent with STL input.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1129-1140
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• 2005

A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.6
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• pp.9-15
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• 2011

Any relative deformation between the cutting tool and the workpiece at machining point results directly in geometric and dimensional errors. The sources of relative deformations between the cutting tool and the workpiece at the contact point may be due to vibration, thermal deformation and cutting forces. In this paper, geometric error prediction of workpiece in turning has been investigated. To reach this goal, turning experiments are carried out according to selected cutting conditions. The variable cutting conditions are cutting speed, depth of cut and feed rate. The results will be useful as a guidance to select cutting conditions to improve the geometrical accuracy.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.5
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• pp.469-475
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• 2010

This paper presents a method of classifying discolored defects of metal pads using geometric texture for AFVI (Automated Final Vision Inspection) systems. In PCB manufacturing process, the metal pads on PCB can be oxidized and discolored partly due to various environmental factors. Nowadays the discolored defects are manually detected and rejected from the process. This paper proposes an efficient geometric texture feature, SUTF (Symmetry and Uniformity Texture Feature) based on the symmetric and uniform textural characteristics of the surface of circular metal pads for automating AFVI systems. In practical experiments with real samples acquired from a production line, 30 discolored images and 1232 roughness images are tested. The experimental results demonstrate that the proposed method using SUTFs provides better performance compared to Gabor feature with 0% FNR (False Negative Rate) and 1.46% FPR (False Positive Rate). The performance of the proposed method shows its applicability in the real manufacturing systems.

• Research in Mathematical Education
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• v.11 no.3
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• pp.209-218
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• 2007

The purpose of this study is to create an interactive tool Geometry Player for geometric explorations. In designing this software, we referred to van Hiele's geometric learning theory of and Duval's cognitive comprehension theory of geometric figures. With Geometry Player, it is easy to construct and manipulate dynamic geometric figures. Teachers can easily present the dynamic process of geometric figures in class, and students can use it as a leaning tool to construct geometric concepts by themselves. It is hoped that Geometry Player can be a useful assistant for teachers and a nice partner for students. A brief introduction to Geometry Player and some application examples are included in this paper.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.60-70
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• 2020

The outfitting design of ships and offshore structures is mainly undertaken in a restricted space. Pipes occupying a large portion of outfitting design are normally manufactured outside the shipyard. This complicated manufacturing process results in frequent delivery delays. Inevitable design modifications and material changes have also resulted in inefficient pipe installation works. In this study, an algorithm is proposed to systematically determine the pipe installation sequence. An accurate and fast algorithm to identify the geometric relationship of piping materials is presented. To improve the calculation efficiency, the interference is gradually examined from simplified to complicated shapes. It is demonstrated that the calculation efficiency is significantly improved with successive geometric operations such as back-face culling and use of bounding boxes. After the final installation sequence is determined, the entire installation process is visualized in a virtual reality environment so that the process can be rendered and understood for a full-scale model.