• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.11
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• pp.17-26
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• 1993

In this paper, a VlSI architecture for Reed-Solomon (RS) decoder based on the Berlekamp algorithm is proposed. The proposed decoder provided both erasure and error correcting capability. In order to reduc the chip area, we reformulate the Berlekamp algorithm. The proposed algorithm possesses a recursive structure so that the number of cells for computing the errata locator polynomial can be reduced. Moreover, in our approach, only one finite field multiplication per clock cycle is required for implementation, provided an improvement in the decoding speed, and the overall architecture features parallel and pipelined structure, making a real time decoding possible. From the performance evaluation, it is concluded that the proposed VLSI architecture is more efficient in terms of VLSI implementation than the rcursive architecture based on the Euclid algorithm.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.30A no.11
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• pp.21-28
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• 1993

Decoding algorithm of noncyclic Reed-Solomon codes consists of four steps which are to compute syndromes, to find error-location polynomial, to decide error-location, and to solve error-values. There is a decoding method by which the computation of both error-location polynomial and error-evaluator polynimial can be avoided in conventional decoding methods using Euclid algorithm. The disadvantage of this method is that the same amount of computation is needed that is equivalent to solve the avoided polynomial. This paper considers the division method on polynomial on GF(2$^{m}$) systematically. And proposes a novel method to find error correcting polynomial by simple mathematical expression without the same amount of computation to find the two avoided polynomial. Especially. proposes the method which the amount of computation to find F (x) from the division M(x) by x, (x-1),....(x--${\alpha}^{n-2}$) respectively can be avoided. By applying the simple expression to decoding procedure on RS codes, propses a new decoding algorithm, and to show the validity of presented method, computer simulation is performed.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.6
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• pp.19-27
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• 1985

In most engineering problems the output of linear system could be expressed by a con-volution of finite input and impulse response. In this paper, the deconvolution algorithm based on the reconstruction of residue polynomials to get a convolution factor, impvlse response or system input, were considered. Two techniques, using a matrix and Euclid's algorithm were discussed. In the illustrated examples, the result showed high accuracy about 10-10 RMS error.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.103-121
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• 2017

Taxicab geometry was a typical non-Euclid geometry for mathematically gifted. Most educational material related quadratic curves on taxicab geometry for mathematically gifted served them to inquire the graph of the curves defined by focis and constant. In this study, we provide a shape of quadratic curves on taxicab geometry by applying three definitions(geometric algebraic definition, eccentricity definition, conic section definition).

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.53.3-53.3
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• 2019

Recent work by Ravanbakhsh et al. (2017), Mathuriya et al. (2018) showed that convolutional neural networks (CNN) can be trained to predict cosmological parameters from the visual shape of the large scale structure, i.e. the filaments, clusters and voids of the cosmic density field. These preliminary works used the dark matter density field at redshift zero. We build upon these works by considering realistic mock galaxy catalogues that mimic true observations. We construct light-cones that span the redshift range appropriate for current and near future cosmological surveys such as LSST, EUCLID, WFIRST etc. In summary, we propose a novel multi-image input CNN to track the evolution in the morphology of large scale structures over cosmic time to constrain cosmology and the expansion history of the Universe.

• Proceedings of the Korean Society of Computer Information Conference
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• 2024.01a
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• pp.85-88
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• 2024

안개 영상은 먼지, 안개 등의 원인으로 영상 내의 물체가 흐리게 보이며, 빛의 산란으로 인하여 영상의 밝기가 높다. 기존의 다크 채널 방식은 하늘 영역을 따로 처리하지 않고, 안개 영상에서 얻어지는 다크채널을 바탕으로 전달량을 추정한다. 이러한 방식은 안개 영상 내 하늘 영역이 왜곡되는 문제가 발생하게 된다. 이와 같은 문제점을 해결하기 위하여 본 논문에서는 영상의 반전, 유클리드, 그리고 감마보정을 이용한 적응형 전달량을 추정하여 성능을 개선하였다.

• School Mathematics
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• v.5 no.4
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• pp.421-440
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• 2003

It is difficult for the learner to understand completely the ratio concept which forms a basis of proportional reasoning. And proportional reasoning is, on the one hand, the capstone of children's elementary school arithmetic and, the other hand, it is the cornerstone of all that is to follow. But school mathematics has centered on the teachings of algorithm without dealing with its essence and meaning. The purpose of this study is to analyze the essence of ratio concept from multidimensional viewpoint. In addition, this study will show the direction for improvement of ratio concept. For this purpose, I tried to analyze the historical development of ratio concept. Most mathematicians today consider ratio as fraction and, in effect, identify ratios with what mathematicians called the denominations of ratios. But Euclid did not. In line with Euclid's theory, ratio should not have been represented in the same way as fraction, and proportion should not have been represented as equation, but in line with the other's theory they might be. The two theories of ratios were running alongside each other, but the differences between them were not always clearly stated. Ratio can be interpreted as a function of an ordered pair of numbers or magnitude values. A ratio is a numerical expression of how much there is of one quantity in relation to another quantity. So ratio can be interpreted as a binary vector which differentiates between the absolute aspect of a vector -its size- and the comparative aspect-its slope. Analysis on ratio concept shows that its basic structure implies 'proportionality' and it is formalized through transmission from the understanding of the invariance of internal ratio to the understanding of constancy of external ratio. In the study, a fittingness(or comparison) and a covariation were examined as the intuitive origins of proportion and proportional reasoning. These form the basis of the protoquantitative knowledge. The development of sequences of proportional reasoning was examined. The first attempts at quantifying the relationships are usually additive reasoning. Additive reasoning appears as a precursor to proportional reasoning. Preproportions are followed by logical proportions which refer to the understanding of the logical relationships between the four terms of a proportion. Even though developmental psychologists often speak of proportional reasoning as though it were a global ability, other psychologists insist that the evolution of proportional reasoning is characterized by a gradual increase in local competence.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.1-24
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• 2009

The applications of ratio and similarity have been in need of everyday life from ancient times. Euclid's elements Ⅴand Ⅵ cover ratio and similarity respectively. In this note, we have done a comparative analysis to button down the contents of ratio and similarity covered by the math text books used in Korea, Euclid's elements and the math text books used in Japan and America. As results, we can observe some differences between them. When math text books used in Korea introduce ratio, they presented it by showing examples unlike math text books used in America and Japan which present ratio by explaining the definition of it. In addition, in the text books used in Korea and Japan, the order of dealing with condition of similarity of triangles and the triangle proportionality is different from that of the text books used in America. Also, condition of similarity of triangles is used intuitively as postulate without any definition in text books used in Korea and Japan which is different from America's. The manner of teaching depending on the way of introducing learning contents and the order of presenting them can have great influence on student's understanding and application of the learning contents. For more desirable teaching in math it is better to provide text books dealing with various learning contents which consider student's diverse abilities rather than using current text books offering learning contents which are applied uniformly.

• Korean Institute of Interior Design Journal
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• v.20 no.6
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• pp.145-152
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• 2011

Salvador Dali put a title of his work as 'A Propos of the Treatise on Cubic Form by Juan de Herrera' at 1960. Through this work which is consisted in cube frame surrounding black and white letter squares and nails in the sky, he directly referred about the cube which were showed in his pictures. To understand the meaning of this work, Dali's paintings and Juan de Herrera's design and architectural ideas are analysed by building. His concerning about absolute existence like god and nuclear takes the cubic form by Juan de Herrera instead of pictorial tendencies of Cubism, however pictorial elements such as sky and nails were still used in the work. He use alphabet letter as pattern consisting wall and symbol representing 'Juan de Herrera', moreover number '2' is taken to show up line attribute. Dali had several design develop process, and finally he reached an new stage called 'Hypercube'. Hypercube can distinguish from Cubism and Herrera's architectural idea, and it will be free from objective world based in Euclid geometry. Although cubic is the simplest shape. It can contain the variety of developments in these fields - philosophy, architecture, painting and etc.- from Platon to nuclear physics and coexists in a picture of Salvador Dali.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.43-54
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• 2006

The purpose of this paper, followed by 'Nature$\cdot$Human, and Golden Section I ', is to study aesthetic consciousness, mentality model and body proportion of human, and the golden section applied to architecture and hand axe of stone age. In particular, handaxes of one million years ago have shown that they had critical competency to the basis of art and mathematics in the future. Furthermore, without pen, paper and ruler, the existence of mentality model made fundamental conversion of mathematics possible. Different sizes of handaxes were made by maintaining the equal golden section. This was the first example in relation to the principle mentioned in 'Stoicheia' by Euclid which was published hundred thousands of years later.