• Journal for History of Mathematics
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• v.26 no.4
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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.

• Education of Primary School Mathematics
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• v.7 no.1
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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.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.77-86
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• 2004

Felix Klein profoundly influenced mathematical developments throughout the world by showing a new direction for modem geometry. He also influenced the lives of excellent scientists like Einstein by reforming mathematical education. The first Felix Klein medal of the Internal Commission on Mathematical Instruction was awarded at ICME-10 in July of 2004. In this article, we discuss Klein's Erlangen Program and investigate his influence on modem mathematics and mathematical education with this medal as momentum.

• Proceedings of the Korean Society for Language and Information Conference
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• 2002.02a
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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.

• Journal of radiological science and technology
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• v.44 no.6
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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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• v.4 no.2
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• pp.113-119
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• 2000

Purpose : To know the possibility of clinical application of MRI using oxygen inhalation as a perfusion MRI Materials and methods : Two healthy volunteers and three patients of one moyamoya disease, one acute infarction and one meningioma were studied using a 1.5 Tesla MRI unit. Oxygen (15 liters/min) mixed with room air was given using face mask from 8 second to 35 second during the study. Images were acquired 25 times (scan time per study were 1.6 seconds) using susceptibility contrast EPI (echo planar image) sequence. Difference maps were acquired by early (study 12-18), and late (study 19-25) O2 inhalation image groups minus pre-O2 inhalation image group (study 3-9) with a Z-score of 0.7-1.0 using VB31C program of Magneton Vision. The resulting perfusion images were created by superimposition of difference maps on corresponding T1 weighted anatomic images. On moyamoya patient, similar perfusion images were acquired after Gd-DTPA injection, and compared with O2 inhalation perfusion images. Results ; The author can get the perfusion images of the brain by oxygen inhalation with susceptibility contrast EPI sequence at the volunteers, and the patient of moyomoya disease, acute infarction and meningioma. On moyamoya patient, perfusion images with O2 inhalation are similar with perfusion images by Gd-DTPA injection. Conclusion 1 This study has demonstrated that the susceptibility contrast EPI by oxygen inhalation can be used as the clinically useful perfusion MRI technique