• 한국수학사학회지
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• 제26권4호
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• pp.233-243
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• 2013

The Erlangen program is a scholastic plan by German mathematician Felix Klein, in which he, based on group theory, made a reassessment of geometry as well as an attempt to generally organize it. In this paper, I will introduce the historical and scholastic background of the Erlangen program, overview the process of its formation, and provide some comments regarding its historical significance.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제7권1호
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• pp.43-56
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• 2003

In late 19C, German mathematician Felix Klein declaired "Erlangen program" to reform mathematics education in Germany. The main ideas of "Erlangen program" contain the importance of instructing the concepts of functions and groups in school mathematics. After one century from that time, the importance of concepts of groups revived by Bourbaki in the sense of the algebraic structure which is the most important structure among three structures of mathematics - algebraic structure. ordered structure and topological structure. Since then, many mathematicians and mathematics educators devoted to work with the concepts of group for school mathematics. This movement landed on Korea in 21C, and now, the concepts of groups appeared in element mathematics text as plane rigid motion. In this paper, we state the rigid motions centered the symmetry - an important notion in group theory, then summarize the results obtained from some classroom activities. After that, we discuss the responses of children to concepts of groups.of groups.

• 한국수학사학회지
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• 제17권4호
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• pp.77-86
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• 2004

펠릭스 쿨라인은 현대 기하학이 나아갈 새로운 방향을 제시하여 현대 수학에 큰 영향을 미쳤을 뿐만 아니라 수학 교육의 개혁을 주도하여 유능한 과학자들이 탄생하는 데 크게 기여하였다. 2004년 7월 국제 수학 교육 위원회(ICME)에서 처음으로 펠릭스 클라인 메달이 수여된 것을 계기로, 클라인이 에를랑겐 대학교에 교수로 취임되면서 강연하였던 ‘에를랑겐 계획’을 소개하고 그가 현대 수학과 수학 교육에 끼친 영향을 고찰하고자 한다.

• 한국언어정보학회:학술대회논문집
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• 한국언어정보학회 2002년도 Language, Information, and Computation Proceedings of The 16th Pacific Asia Conference
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• pp.411-420
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• 2002

The left-associative grammar model (LAG) has been applied successfully to the morphologic and syntactic analysis of various european and asian languages. The algebraic definition of the LAG is very well suited for the application to natural language processing as it inherently obeys de Saussure's second law (de Saussure, 1913, p. 103) on the linear nature of language, which phrase-structure grammar (PSG) and categorial grammar (CG) do not. This paper describes the so-called Loom-LAGs (LLAG) -a specialization of LAGs for the analysis of natural language. Whereas the only means of language-independent abstraction in ordinary LAG is the principle of possible continuations, LLAGs introduce a set of more detailed language-independent generalizations that form the so-called loom of a Loom-LAG. Every LLAG uses the very smut loom and adds the language-specific information in the form of a declarative description of the language -much like an ancient mechanised Jacquard-loom would take a program-card providing the specific pattern for the cloth to be woven. The linguistic information is formulated declaratively in so-called syntax plans that describe the sequential structure of clauses and phrases. This approach introduces the explicit notion of phrases and sentence structure to LAG without violating de Saussure's second law iud without leaving the ground of the original algebraic definition of LAG, LLAGS can in fact be shown to be just a notational variant of LAG -but one that is much better suited for the manual development of syntax grammars for the robust analysis of free texts.

• 대한방사선기술학회지:방사선기술과학
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• 제44권6호
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• pp.655-661
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• 2021

Positron emission tomography (PET) images is affected by acquisition time, short acquisition times results in low gamma counts leading to degradation of image quality by statistical noise. Noise2Void(N2V) is self supervised denoising model that is convolutional neural network (CNN) based deep learning. The purpose of this study is to evaluate denoising performance of N2V for PET image with a short acquisition time. The phantom was scanned as a list mode for 10 min using Biograph mCT40 of PET/CT (Siemens Healthcare, Erlangen, Germany). We compared PET images using NEMA image-quality phantom for standard acquisition time (10 min), short acquisition time (2min) and simulated PET image (S2 min). To evaluate performance of N2V, the peak signal to noise ratio (PSNR), normalized root mean square error (NRMSE), structural similarity index (SSIM) and radio-activity recovery coefficient (RC) were used. The PSNR, NRMSE and SSIM for 2 min and S2 min PET images compared to 10min PET image were 30.983, 33.936, 9.954, 7.609 and 0.916, 0.934 respectively. The RC for spheres with S2 min PET image also met European Association of Nuclear Medicine Research Ltd. (EARL) FDG PET accreditation program. We confirmed generated S2 min PET image from N2V deep learning showed improvement results compared to 2 min PET image and The PET images on visual analysis were also comparable between 10 min and S2 min PET images. In conclusion, noisy PET image by means of short acquisition time using N2V denoising network model can be improved image quality without underestimation of radioactivity.

• Investigative Magnetic Resonance Imaging
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• 제4권2호
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• pp.113-119
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• 2000

목적 : 산소호흡을 이용한 뇌의 관류 자기공명영상의 임상적용 가능성을 알고자 하였다. 대상 및 방법 정상 성인 지원자 2명과 3명의 환자, 각각 모야모야병 환자 1명, 뇌경색환자 1명, 뇌수막종 환자 1명을 대상으로 하였으며, 1.5 Tesla의 자기공명영상 장치를 이용하여 뇌의 자화율 대조 (susceptibility contrast) echo planar image (EPI) 방법으로 뇌영역을 10 slice씩 25회(검사시간은 검사당 1.6초) 영상을 얻었다. 검사자는 안면마스크를 착용한 상태로 스캔 시작 8초 후부터 35초가지 산소 15 liter/min를 실내 공기와 혼합되어 흡입되도록 하였다. 획득된 영상을 Magnetom Vision (Siemens Medical Systems, Erlangen, Germany)의 VB31C 프로그램을 이용하여 산소투여전(3골 번째 검사)과, 산소투여 후의 초기 (12-18 번째 검사)와 후기(19-25 번째 검사) 군으로 나누었다. 초기 및 후기 군과 산소투여전 군의 신호차이는 Z-score 0.7 내지 1.0으로 하여 여러번 영상후 처리를 반복하여 difference map을 얻어서, T1 강조영상에 중첩시켜 관류 영상을 얻었다. 모야모야병 환자는 추가로 Gd-DTPA를 0.1 mmol/kg급속주사 후 동일한 방법으로 관류 영상을 얻어 산소호흡에 의한 관류 영상과 비교하였다. 결과 : 산소 공급 후에 시행한 자화율 대조 EPI 방법으로 2명의 지원자와 각각 1예의 모야모야병, 뇌경색, 뇌수막종 증례에서 혈류 분포를 반영하는 관류 영상을 얻을 수 있었다. 모야모야병 1예의 산소 호흡에 의한 관류 영상은 Gd-DTPA투여후의 관류 영상과 유사한 양상을 보였다. 결론 : 산소호흡을 이용한 자화율 대조 EPI 방법은 향후 뇌의 관류 자기공명영상 방법으로 적용이 가능하리라고 생각된다.