• Communications of Mathematical Education
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• v.26 no.4
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• pp.351-362
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• 2012

Until the 1950s, linear algebra was considered only as one of abstract and advanced mathematics subject among in graduate mathematics courses, mainly dealing with module in algebra. Since the 1960s, it has been a main subject in undergraduate mathematics education because matrices has been used all over. In Korea, it was considered as a course only for mathematics major students until 1980s. However, now it is a subject for all undergraduate students including natural science, engineering, social science since 1990s. In this paper, we investigate the early history of linear algebra and its development from a historical perspective and mathematicians who made contributions. Secondly, we explain why linear algebra became so popular in college mathematics education in the late 20th century. Contributions of Chinese and H. Grassmann will be extensively examined with many newly discovered facts.

• Korean Institute of Interior Design Journal
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• v.24 no.5
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• pp.21-30
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• 2015

The visual expression system of space realized in Baroque aesthetics is basically grounded on the philosophical view to the world of the time, that is to say the changes of the thinking system in the Renaissance and ontology based on it. Structural aesthetics in Baroque freed from Plato's system of harmony but grounded on Leibniz's process philosophy formed a crucial background to highlight the formal nature of the whole and build a structure based on the inclusive principle of formativity. Also, to solve problems to realize the order and consistency of forms from the whole, Baroque adopted the nonlinear and nonphysical formative system as the principle of building space in works of art. Combining the order system of nature in the Renaissance with manneristic dynamicity as well as formative principle taking shape geometrically, it did establish a variety of aesthetic concepts based on the results of infiniteness and exaggeration expressed from the two forces, the Renaissance and mannerism. This study has found that such Baroque aesthetics did overcome classical planeness and draw continuous mobility from the structures and forms based on that with the transborder concepts of structures, the components of space, as an ultimate system of formative expression. Moreover, this author has drawn and analyzed with the cases of the 17th-century art and architecture the transborder elements manifesting the nature of diverse formative visual elements produced in artistic expressions with that principle of aesthetics, that is the intangible concept of Baroque. Based on that, this researcher intends to come up with technical solutions to solve a lot of environmental and architectural problems we are severely facing nowadays in terms of environmental, physical, and emotional aspects with the theoretical clues and results acceptable to this contemporary era.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.139-152
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• 2017

In this paper, we examine how secondary school mathematics textbooks on calculus introduce the history of calculus. In order to identify the problem, we consider the Babylonian integration by trapezoidal rule, which was made to calculate the location of Jupiter in 350-50 B.C., and the integration by the method of the rotating plate of ibn al-Haytham in Egypt, about 1000 years. In conclusion, our secondary school mathematics textbooks describe Newton and Leibniz as inventing calculus and place their roots in ancient Greece. The origin of the calculus is in Babylonia and the Faṭimah Dynasty (909-1171) (Egypt) and it is desirable that the calculus is developed in Europe after the development of the power series in India, and that the value of Asia Africa is introduced in the textbooks.

• Journal of Korean Philosophical Society
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• v.117
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• pp.249-273
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• 2011

In this paper, I suggest a discourse on some delicate relations between the philosophy and the cinema, or between the visualizing philosophical reflection and the contemplating cinematic imagination. In this context, G. Deleuze is not a simple philosopher and Director Hong, not a director. Each is a kind of metonymy. Deleuzean style of philosophizing asks for Hong's nomadic style of producing cinema. and of course in the same manner, the latter asks for the former. The latter visualizes the speculative empiricism of the former, the former crystalizes the visual esthetics of the latter. To speak with Deleuzean vocabularies, it is not possible for the State Apparatus to capture the diverse works of director Hong. Because each of them is a kind of War Machine which always slips from every tackle of State Apparatus. Deleuzean key word 'genetic becomming' is a main concept of Hong's works. The point is not to dispose the theses 'becomming' of his works in the line of series but to release them in the line of rupture. My paper would show the sharp ridicules director Hong had poured on the conservative circle of the cinema in the context of Deleuzean nomadology.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.38.2-38.2
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• 2019

S0 galaxies are mostly known to be formed in dense environments from spiral progenitors. Recently, however, a new formation scenario has been suggested that field S0s can be formed from elliptical progenitors. The Sombrero galaxy (M104, NGC 4594) is a massive disk galaxy located in the field environment, and its morphological type has been controversial from Sa to E. Thus, it is an ideal target to test the new scenario. We trace the giant halo of M104 with globular clusters to test this scenario. From the wide images obtained with CFHT/MegaCam, we find a large number of globular clusters in this galaxy. We also confirm their membership by measuring the radial velocities from the spectra obtained with MMT/Hectospec. The color distribution of these globular clusters is bimodal, and blue (metal-poor) globular clusters are more spatially widely spread than red (metal-rich) globular clusters. This indicates that M104 hosts a giant metal-poor halo as well as an inner metal-rich halo. Combining this result with the fact that M104 is unusually massive and brighter than other spiral galaxies, we infer that M104 was indeed a massive elliptical galaxy that had formed a metal-rich halo by gas-rich mergers and a metal-poor halo by gas-poor mergers. In addition, we find young star clusters around the disk of M104, which shows that the disk formed after the spheroidal halos had formed. In conclusion, we suggest that M104 was originally a massive elliptical galaxy and was transformed to a lenticular galaxy by acquiring its disk later.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.38.4-38.4
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• 2019

Ultra-diffuse galaxies (UDGs) are intriguing in the sense that they are much larger than dwarf galaxies but have much lower surface brightness than normal galaxies. To date, UDGs have been found only in the local universe. Taking advantage of deep and high-resolution HST images, we search for UDGs in massive galaxy clusters in the distant universe. In this work, we present our search results of UDGs in three massive clusters of the Hubble Frontier Fields: Abell 2744 (z=0.308), Abell S1063 (z=0.348), and Abell 370 (z=0.375). These clusters are the most distant and massive among the host systems of known UDGs. The color-magnitude diagrams of these clusters show that UDGs are mainly located in the faint end of the red sequence. This means that most UDGs in these clusters consist of old stars. Interestingly, we found a few blue UDGs, which implies that they had recent star formation. The radial number densities of UDGs clearly decrease in the central region of the clusters in contrast to those of bright galaxies which keep rising. This implies that a large fraction of UDGs in the central region were tidally disrupted. These features are consistent with those of UDGs in nearby galaxy clusters. We estimate the total number of UDGs (N(UDG)) in each cluster. The abundance of UDGs shows a tight relation with the virial masses (M_200) of thier host systems: M_200 \propto N(UDG)^(1.01+/-0.05). This slope is found to be very close to one, indicating that efficiency of UDGs does not significantly depend on the host environments. Furthermore, estimation of dynamical masses of UDGs indicates that most UDGs have dwarf-like masses (M_200 < 10^11 M_Sun), but a few UDGs have $L{\ast}$-like masses (M_200 > 10^11 M_Sun). In summary, UDGs in distant massive clusters are found to be similar to those in the local universe.

• Journal of the Architectural Institute of Korea Planning & Design
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• v.34 no.9
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• pp.87-96
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• 2018

The purpose of this study is to get a more fundamental definition of the term Architecture and Geonchuk through analyzing the origin and reception of the terminus technicus Architektonike. In Latin world the greek term Architektonike was adopted and replaced the term Constructio by Vitruvius and has played a significant role in the history of architecture. In the late 19th Century however, the word Architecture was translated into Geonchuk(建築) and has been dominantly used in countries such as Korea, Japan, and China. But the difference of the denotation between them has not yet been fully evaluated. The term Geonchuk signifies much the same as the Tektonik and remains as such in the architectural discourse. In this context, this study goes back to refer to the philosophy of Metaphysics by Aristotle. In his book the term Architektonike was defined for the first time as terminus technicus, and the philosophies in later Ages of Leibniz or of Kant adopted it to signify the world view in accordance with the time. However, the original thought of the Architektonike disappeared in architectural practice and has been used in most cases as a substitute for Oikodomike which denotes house-building. The usage of this word in later time shows that it lost its foundation to be interpreted not only in terms of principium cognoscendi, but also in terms of principium reale. From this the literal usage of the term architecture and Geonchuk has seldom to do with its original meaning and denotation of Architektonike and also they lost the status of terminus technicus for the discourse of arche which encompasses the meaning of both principle and universal order.

• Journal of The Geomorphological Association of Korea
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• v.25 no.4
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• pp.63-75
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• 2018

The lower marine terrace 1 and 2 surfaces distributed between Ulsan and Pohang coast in the southeastern coast of the Korean penninsula have been correlated with MIS 5e and 5a (or 5c) by amino acid dates, 14C dates, wide-spread tephra correlation and pollen analysis respectively. In this study, to test the reliability of the OSL method for the estimation of the numerical burial age of marine sediment deposits, we analyzed the samples from the marine terraces which have been known as typical marine terraces formed during MIS 5e and MIS 5a in the above-mentioned coast. The burial ages of the marine deposit of the lower marine terrace 1 and 2, with paleoshoreline altitudes of 18m to 19m and 10m to 11m respectively, both showed about the same age of 60 ka BP. The lower marine terraces 1 and 2, however, were divided into two terrace surfaces by a clear terrace cliff. Besides, the OSL dates of the lower and upper parts of the lower marine terrace 2 of the Bonggil coast showed the reversed burial ages. In the lower marine terrace 1 of the Sanhari coast, almost the same burial ages were derived from both the lower part (marine rounded gravel layer) and the upper part (terrestrial angular gravel layer) of the terrace deposit. Therefore, at the present time, judging from only the OSL dates measured in this study, it could be argued that the OSL method is not the best for the estimation of forming periods of the lower marine terraces 1 and 2 and their classification.

• Structural Engineering and Mechanics
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• v.83 no.3
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• pp.293-304
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• 2022

In this work, a novel reliability approach for combined high and low cycle fatigue (CCF) estimation is developed by combining active learning strategy with least squares support vector machines (LS-SVM) (named as ALS-SVM) surrogate model to address the multi-resources uncertainties, including working loads, material properties and model itself. Initially, a new active learner function combining LS-SVM approach with Monte Carlo simulation (MCS) is presented to improve computational efficiency with fewer calls to the performance function. To consider the uncertainty of surrogate model at candidate sample points, the learning function employs k-fold cross validation method and introduces the predicted variance to sequentially select sampling. Following that, low cycle fatigue (LCF) loads and high cycle fatigue (HCF) loads are firstly estimated based on the training samples extracted from finite element (FE) simulations, and their simulated responses together with the sample points of model parameters in Coffin-Manson formula are selected as the MC samples to establish ALS-SVM model. In this analysis, the MC samples are substituted to predict the CCF reliability of turbine blades by using the built ALS-SVM model. Through the comparison of the two approaches, it is indicated that the reliability model by linear cumulative damage rule provides a non-conservative result compared with that by the proposed one. In addition, the results demonstrate that ALS-SVM is an effective analysis method holding high computational efficiency with small training samples to gain accurate fatigue reliability.

• Computers and Concrete
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• v.32 no.6
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• pp.577-594
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• 2023

Engineered cementitious composites with calcined clay limestone cement (LC³-ECC) as a kind of green, low-carbon and high toughness concrete, has recently received significant investigation. However, the complicated relationship between potential influential factors and LC³-ECC compressive strength makes the prediction of LC³-ECC compressive strength difficult. Regarding this, the machine learning-based prediction models for the compressive strength of LC³-ECC concrete is firstly proposed and developed. Models combine three novel meta-heuristic algorithms (golden jackal optimization algorithm, butterfly optimization algorithm and whale optimization algorithm) with support vector regression (SVR) to improve the accuracy of prediction. A new dataset about LC³-ECC compressive strength was integrated based on 156 data from previous studies and used to develop the SVR-based models. Thirteen potential factors affecting the compressive strength of LC³-ECC were comprehensively considered in the model. The results show all hybrid SVR prediction models can reach the Coefficient of determination (R²) above 0.95 for the testing set and 0.97 for the training set. Radar and Taylor plots also show better overall prediction performance of the hybrid SVR models than several traditional machine learning techniques, which confirms the superiority of the three proposed methods. The successful development of this predictive model can provide scientific guidance for LC³-ECC materials and further apply to such low-carbon, sustainable cement-based materials.