• Journal for History of Mathematics
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• v.22 no.3
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• pp.1-30
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• 2009

Frege's logicism has been frequently regarded as a development in number theory which succeeded to the so called arithmetization of analysis in the late 19th century. But it is not easy for us to accept this opinion if we carefully examine his actual works on real analysis. So it has been often argued that his logicism was just a philosophical program which had not contact with any contemporary mathematical practices. In this paper I will show that these two opinions are all ill-founded ones which are due to the misunderstanding of the theoretical place of Frege's logicism in the context of contemporary mathematical practices. Firstly, I will carefully examine Cantorian definition of real numbers and Frege's critiques of it. On the basis of this, I will show that Frege's aim was to produce the purely logical definition of ratios of quantities. Secondly, I will consider the mathematical background of Frege's logicism. On the basis of this, I will show that his standpoint in real analysis was much subtler than what we used to expect. On the one hand, unlike Weierstrass and Cantor, Frege wanted to get such real analysis that could be universally applicable. On the other hand, unlike most mathematicians who insisted on the traditional conceptions, he would not depend upon any geometrical considerations in establishing real analysis. Thirdly, I will argue that Frege regarded these two aspects - the independence from geometry and the universal applicability - as those which characterized logic itself and, by logicism, arithmetic itself. And I will show that his conception of real numbers as ratios of quantities stemmed from his methodological maxim according to which the nature of numbers should be explained by the common roles they played in various contexts to which they applied, and that he thought that the universal applicability of numbers could not be adequately explicated without such an explanation.

• Journal of the Korean Association of Geographic Information Studies
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• v.15 no.4
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• pp.114-123
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• 2012

This study is aimed to assess the stability of cable bridge by determining the geometric shape of the suspension bridge among the domestic coastal structures in public use after their completion of construction and the displacement of the target suspension bridge after public use. For this purpose, this study calculated the length between pylon piers for each period, sag, sag ratio and the displacement of pylon. Compared to the management standards for each step across different pylon behaviors of the target suspension bridge, this study found that the target suspension bridge behaves stably within the maintenance standards. To identify the behaviors of a suspension bridge accurately, the priority is put on the determination of geometric shape. Therefore, it is required to determine the surveyed shape model on a regular basis across public use period and increased traffics, which is expected to contribute considerably to ensuring the stability of the suspension bridge in its maintenance.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.2
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• pp.213-223
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• 2009

In geoid modelling field, it is very important the GPS/leveling data because it could be check-out the accuracy of gravimetric geoid and computed the hybrid geoid. In this study, GPS surveying was accomplished in the test area including mountainous area to improve the GPS/leveling data density in Korea. And the geometric geoidal heights was calculated using the GPS/leveling data in the test area and the accuracy of the geoidal heights was analyzed. For this study, GPS surveying was accomplished on the 211 1st and 2nd order benchmarks in Gyeongbuk province and 198 GPS/leveling data were achieved after both baseline analysis and network adjustment. Geometric geoidal heights were calculated using these 198 GPS/leveling data and the accuracy analysis was done by comparison with the geoidal heights from EGM2008 geopotential model. The results showed that the bias and standard deviation computed from 190 GPS/leveling data after gross removal was -0.185$\pm$0.079m. And also, the accuracy analyses according to the benchmark order, baseline length, and altitude were accomplished.

• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.239-261
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• 2008

This study presents results by the content areas in mathematics. Average performance is provided for five content areas: number, algebra, measurement, geometry, and data. Relative achievement is shown among the content areas for 4 countries in comparison to Korea. In number, Korea had lower average achievement than Singapore, especially for ratio proportion percent. Among 5 countries, Korea had the highest average achievement in algebra and geometry, but the lowest in attributes and units of measurement. In data, Korean students didn't learn the followings successfully: a) comparing characteristics of data sets and using mean, median, range, and shape of distribution, b) interpreting data sets (e.g., draw conclusions, make predictions, and estimate values between and beyond given data points), c) evaluating interpretations of data with respect to correctness and completeness of interpretation.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.8
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• pp.753-760
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• 2008

The present study is concerned with aerodynamic characteristics and reference trajectory generation of Hope-X in Approach/Landing phase. To create reference trajectory generation in A/L phase, detailed informations on lift and drag coefficients of Hope-X must be provided. To obtain these informations, aerodynamic characteristics of Hope-X are analyzed using the commercial CFD code, Fluent. The A/L phase is conceptually divided into three sub-phases: the Steepglide Slope phase for stability of vehicle, the Flare Maneuver phase for safety landing, the Circular Flare for smooth connecting with these both phases. The reference trajectory is obtained by determination of flight-path angle through geometrical formulas with consideration of aerodynamic coefficient and dynamic characteristic.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.24 no.1
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• pp.124-129
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• 2010

When a phenolic resin is carbonized by the leakage current flowing along its surface, the carbonization pattern is one of the most important factors to determine its carbonization characteristics. However, the typical carbonization pattern of a phenolic resin is too complicated to be analyzed by conventional Euclidean geometry. In most cases, such a complicated shape shows a fractal structure. It is possible, therefore, to examine the characteristics of the carbonization pattern regarding a given phenolic resin. In order to quantitatively investigate the carbonization pattern of the phenolic resin carbonized by a leakage current, in this paper, the fractal dimension of the carbonization pattern has been calculated as a function of the magnitude of a leakage current and the distance between two electrodes. For reliability of calculation, the correlation function as well as the box counting method has been used to calculate the fractal dimension. According to the result of calculation, the fractal dimension increases as the current increases at the constant electrode gap distance. However, there is no significant relation between the fractal dimension and the electrode gap distance at a constant current.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.11 no.1
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• pp.7-18
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• 1993

In analyzing whole surface of non-topographic objects, the design of multi-station photogrammetric network must involve a number of questions such as geometric configuration of exposure stations, imaging geometry, control point configuration or weight allowance of adjustments. Above all, the surveying of the interior of narrow longitudinal structures needs the design of special photogrammetric network. The main objective of this paper is to suggest the schemes for solving difficult problems attendant upon whole inside-surface analysis of structure and to improve the accuracy and reliability of final measurements. For it, the multi-station exposure network suitable to shape and size of the inside of the structure was designed. Then three dimensional data were acquired by bundle adjustments derived from multi-station photos and the effects of network design factors on accuracy of measurements were contemplated. Also, the algorithm for detection of blunders was developed here is expected to lead to improvement of the reliability of photogrammetric solutions.

• Journal of Navigation and Port Research
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• v.46 no.6
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• pp.471-482
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• 2022

This study aims to investigate the characteristics of wave generation in a deep ocean engineering basin and to develop a meta-model of the transfer function of the wavemaker that reflects the geometric characteristics of the deep ocean engineering basin. To this end, the two-dimensional frequency domain boundary element method was applied to achieve an efficient analysis that reflects the geometric characteristics of the deep ocean engineering basin. The developed numerical method was validated through comparison with the analytical solution. Numerical analyses were conducted for the boundary value problem of the wavemaker according to various periods and the positions of the movable bottom. The numerical results were used to investigate the effect of the geometric characteristics of the deep ocean engineering basin on the transfer function of the wavemaker, and the effect of depth on wave generation was checked by changing the position of the movable bottom. To efficiently utilize the various results of the boundary element method, a meta-model, an approximate model of the transfer function of the wave maker, was developed using a thin plate spline interpolation model. The validity of the developed meta-model was confirmed through a comparison of the results of the model tests.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.11
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• pp.1005-1012
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• 2011

In this paper, the effect of wrinkling on the failure behavior of thin membrane was studied using geometrically nonlinear shell element post-buckling analysis with global-local analysis strategy. In the analysis, double-edge notched and single-edge notched tensile specimen configurations were considered. The analyses were performed for both cases with allowing and suppressing the wrinkling deformation. The results were investigated focusing on the effect of wrinkle development on the variation of J-integral values at the cut tip. The effect of cut lengths and the specimen lengths were also systematically studied.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.2
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• pp.273-279
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• 2009

The descendants have a responsibility to conserve their cultural treasure and hand it down to posterity. Most of existing wooden properties, affected by environmental factors for many years, have been rebuilt or repaired many times. Kwandeogjeong, Cultural Properties Materials 322, has gone through rebuilding or repairing 11 times. It was natural that Kwandeogjeong lost its originality and attempt to restore it was made by Cultural Heritage Administration of Korea. But the restoration depends on a piece of picture, which was taken before 1900. It had been impossible to draw any data from the picture for restoration. In this study, I was able to obtain data for its restoration through geometrical analysis, using the vanishing point of the picture. These data were also used as preliminary data for its restoration.