• Journal for History of Mathematics
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• v.21 no.2
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• pp.55-70
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• 2008

This study is about the Data which is one of Euclid's writing. It dealt with the organization of contents, formal system and mathematical meaning. First, we investigated the organization of contents of the Data. Second, on the basis of this investigation, we analyzed the formal system of the Data. It contains the analysis of described method of definition, proposition, proof and the meaning of 'given'. Third, we explored the mathematical meaning of the Data which can be classified as algebraic point of view, geometric point of view and the opposite point of view to 'The Elements'.

• East Asian mathematical journal
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• v.32 no.4
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• pp.483-500
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• 2016

Ancient Greek mathematician Euclid left three books about mathematics. It's 'The elements', 'The data', 'On divisions of figure'. This study is based on the analysis of Euclid's 'On divisions of figure'. 'On divisions of figure' is a book about the construction of the shape. Because, there are thirty six proposition in 'On divisions of figure', among them 30 proposition are for the construction. In this study, based on the 'On divisions of figure' we explore the direction for construction education. The results were as follows. First, the proposition of 'On divisions of figure' shall include the following information. It is a 'proposition presented', 'heuristic approach to the construction process', 'specifically drawn presenting', 'proof process'. Therefore, the content of textbooks needs a qualitative improvement in this way. Second, a conceptual basis of 'On divisions of figure' is 'The elements'. 'The elements' includes the construction propositions 25%. However, the geometric constructions contents in middle school area is only 3%. Therefore, it is necessary to expand the learning of construction in the our country mathematics curriculum.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.7
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• pp.1506-1511
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• 2004

The error control of digital transmission system is a very important subject because of the noise effects, which is very sensitive to transmission performance of the digital communication system It employs a modified Euclid's algorithm to compute the error-location polynomial and error-magnitude polynomial of input data. The circuit size is reduced by selecting the Modified Euclid's Algorithm with one Euclid Cell of mutual operation. And the operation speed of Decoder is improved by using ROM and parallel structure. The proposed Encoder and Decoder are simulated with ModelSim and Active-HDL and synthesized with Synopsys. We can see that this chip is implemented on Xilinx Virtex2 XC2V3000. A share of slice is 28%. nut speed of this paper is 45Mhz.

• Advances in aircraft and spacecraft science
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• v.7 no.3
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• pp.251-269
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• 2020

Euclid is an optical/near-infrared survey mission of the European Space Agency (ESA) to investigate the nature of dark energy, dark matter and gravity by observing the geometry of the Universe and the formation of structures over cosmological timescales. The Euclid spacecraft mechanical architecture comprises the Payload Module (PLM) and the Service Module (SVM) connected by an interface structure designed to maximize thermal and mechanical decoupling. This paper shortly illustrates the mechanical system of the spacecraft and the mechanical verification philosophy which is based on the Structural and Thermal Model (STM), built at flight standard for structure and thermal qualification and the Proto Flight Model (PFM), used to complete the qualification programme. It will be submitted to a proto-flight test approach and it will be suitable for launch and flight operations. Within the overall verification approach crucial mechanical tests have been successfully performed (2018) on the SVM platform and on the sunshield (SSH) subsystem: the SVM platform static test, the SSH structure modal survey test and the SSH sine vibration qualification test. The paper reports the objectives and the main results of these tests.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.173-192
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• 2013

It may be replacement proofs with understanding and explaining geometrical properties that was a remarkable change in school geometry of 2009 revised national curriculum for mathematics. That comes from the difficulties which students have experienced in learning proofs. This study focuses on one of those difficulties which are caused by the forms of proofs: using letters for designating some sides or angles in writing proofs and understanding some long sentences of proofs. To overcome it, this study aims to investigate the applicability of Byrne's method which uses coloured diagrams instead of letters. For this purpose, the proofs of three geometrical properties were taught to middle school students by Byrne's visual method using the original source, dynamic representations, and the teacher's manual drawing, respectively. Consequently, the applicability of Byrne's method was discussed based on its strengths and its weaknesses by analysing the results of students' worksheets and interviews and their teacher's interview. This analysis shows that Byrne's method may be helpful for students' understanding of given geometrical proofs rather than writing proofs.

• School Mathematics
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• v.9 no.4
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• pp.523-533
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• 2007

This article focused the meaning of Pythagoras' and Euclid's proof about the Pythagorean theorem in a historical and mathematical perspective. Pythagoras' proof using similarity is based on the arithmetic assumption about commensurability. However, Euclid proved the Pythagorean theorem again only using the concept of dissection-rearrangement that is purely geometric so that it does not need commensurability. Pythagoras' and Euclid's different approaches to geometry have to do with Birkhoff's axiom system and Hilbert's axiom system in the school geometry Birkhoff proposed the new axioms for plane geometry accepting real number that is strictly defined. Thus Birkhoff's metrical approach can be defined as a Pythagorean approach that developed geometry based on number. On the other hand, Hilbert succeeded Euclid who had pursued pure geometry that did not depend on number. The difference between the proof using similarity and dissection-rearrangement is related to the unsolved problem in the geometry curriculum that is conflict of Euclid's conventional synthetical approach and modern mathematical approach to geometry.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.6
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• pp.96-103
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• 2008

This paper proposes a new low-power and small-area Reed-Solomon decoder. The proposed Reed-Solomon decoder using a novel simplified form of the modified Euclid's algorithm can support low-hardware complexity and low-Power consumption for Reed-Solomon decoding. The simplified modified Euclid's algorithm uses new initial conditions and polynomial computations to reduce hardware complexity, and thus, the implemented architecture consisting of 3r basic cells has the lowest hardware complexity compared with existing modified Euclid's and Berlekamp-Massey architectures. The Reed-Solomon decoder has been synthesized using the $0.18{\mu}m$ Samsung standard cell library and operates at 370MHz and its data rate supports up to 2.9Gbps. For the (255, 239, 8) RS code, the gate counts of the simplified modified Euclid's architecture and the whole decoder excluding FIFO memory are only 20,166 and 40,136, respectively. Therefore, the proposed decoder can reduce the total gate count at least 5% compared with the conventional DCME decoder.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.1
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• pp.170-178
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• 2004

In this work a high speed 8-error correcting Reed-Solomon decoder is designed using the modified Euclid algorithm. Decoding algorithm of Reed-Solomon codes consists of four steps, those are, compute syndromes, find error-location polynomials, decide error-locations, and determine error values. The decoding speed is increased and the latency is reduced by using the parallel architecture in the syndrome generator and a faster clock speed in the modified Euclid algorithm block. In addition. the error locator polynomial in Chien search block is separated into even and odd terms to increase the overall speed of the decoder. All the functionalities of the decoder are verified first through C++ programs. Verilog is used for hardware description, and then the decoder is synthesized with a $.25{\mu}m$ CMOS TML library. The functionalities of the chip is also verified through test vectors. The clock speed of the chip is 250MHz, and the maximum data rate is 1Gbps.

• Publications of The Korean Astronomical Society
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• v.32 no.1
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• pp.251-255
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• 2017

Submillimetre and millimetre-wave surveys with Herschel and the South Pole Telescope have revolutionised the discovery of strong gravitational lenses. Their follow-ups have been greatly facilitated by the multi-wavelength supplementary data in the survey fields. The forthcoming Euclid optical/near-infrared space telescope will also detect strong gravitational lenses in large numbers, and orbital constraints are likely to require placing its deep survey at the North Ecliptic Pole (the natural deep field for a wide class of ground-based and space-based observatories including AKARI, JWST and SPICA). In this paper I review the current status of the multi-wavelength survey coverage in the NEP, and discuss the prospects for the detection of strong gravitational lenses in forthcoming or proposed facilities such as Euclid, FIRSPEX and SPICA.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.275-306
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• 2013

For two positive integers $m$ and $n$, let $\mathcal{P}_n$ be the open convex cone in $\mathbb{R}^{n(n+1)/2}$ consisting of positive definite $n{\times}n$ real symmetric matrices and let $\mathbb{R}^{(m,n)}$ be the set of all $m{\times}n$ real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$ that are invariant under the natural action of the semidirect product group $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ on the Minkowski-Euclid space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$. These invariant differential operators play an important role in the theory of automorphic forms on $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ generalizing that of automorphic forms on $GL(n,\mathbb{R})$.