• 전자공학회논문지B
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• 제33B권11호
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• pp.150-158
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• 1996

Physiological observations reported and the perceptual phenomena that some simple arrays of discrete dots are perceived as a continuous curve, and others are perceived as an angular contour or as consisting of separate goups of dots. The perception of continuous curves versus discondinuous angles is mainly determined by the relative orientations of the dots, i.e., by the angles between sucessive virtual lines, whereas the length of the virtual lines gives little influence. It is important that the perception of dot stimuli is presented by vitual lines between dots in visual information processing. In this paper, on the basis of these facts of physiological observations, some experimental results on the perception of visual lines form dot stimuli are shown. Triples of the dots used in the experiment are similar to those of smith & Vos' physiological experiments.

• 대한수학회보
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• 제52권4호
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• pp.1133-1138
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• 2015

In 1956, $Je{\acute{s}}manowicz$ conjectured that, for any positive integer n and any primitive Pythagorean triple (a, b, c) with $a^2+b^2=c^2$, the equation $(an)^x+(bn)^y=(cn)^z$ has the unique solution (x, y, z) = (2, 2, 2). In this paper, under some conditions, we prove the conjecture for the primitive Pythagorean triples $(a,\;b,\;c)=(4k^2-1,\;4k,\;4k^2+1)$.

• 한국멀티미디어학회논문지
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• 제21권2호
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• pp.158-165
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• 2018

Since a large amount of multimedia image has dramatically increased, it is important to search semantically relevant image. Thus, several semantic image annotation methods using RDF(Resource Description Framework) model in mobile environment are introduced. Earlier studies on annotating image semantically focused on both the image tag and the context-aware information such as temporal and spatial data. However, in order to fully express their semantics of image, we need more annotations which are described in RDF model. In this paper, we propose an annotation method inferencing with RDFS entailment rules and user defined rules. Our approach implemented in Moment system shows that it can more fully represent the semantics of image with more annotation triples.

• ETRI Journal
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• 제39권4호
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• pp.455-466
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• 2017

This study focuses on a method for sequential data augmentation in order to alleviate data sparseness problems. Specifically, we present corpus expansion techniques for enhancing the coverage of a language model. Recent recurrent neural network studies show that a seq2seq model can be applied for addressing language generation issues; it has the ability to generate new sentences from given input sentences. We present a method of corpus expansion using a sentence-chain based seq2seq model. For training the seq2seq model, sentence chains are used as triples. The first two sentences in a triple are used for the encoder of the seq2seq model, while the last sentence becomes a target sequence for the decoder. Using only internal resources, evaluation results show an improvement of approximately 7.6% relative perplexity over a baseline language model of Korean text. Additionally, from a comparison with a previous study, the sentence chain approach reduces the size of the training data by 38.4% while generating 1.4-times the number of n-grams with superior performance for English text.

• 한국수학사학회지
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• 제20권1호
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• pp.45-56
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• 2007

수학을 배운 사람이라면 수십 년이 지나서도 기억되고 회자되는 것으로 피타고라스의 정리를 꼽을 수 있다. 그런데 역사적으로 이 정리를 중요한 위치로 자리 잡게 한 역할은 피타고라스 이전, 고대 바빌로니아 시대의 이름 모를 사람들의 노력 이었으며 이를 보여주는 흔적 중 하나가 'Plimpton 322‘라는 점토판을 들 수 있다. 본 고에서는 피타고라스의 정리를 완성하게 영감을 준 Plimpton 322의 내용을 소개하며 적혀 있는 숫자들의 해석과 함께 그 시대의 뛰어난 수학적 수준을 재조명해 보고자 한다.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.167-174
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• 2002

A group G is said to be (l, n, n)-generated if it is a quotient group of the triangle group T(p,q,r)=(x,y,z|x$\^$p/=y$\^$q/=z$\^$r/=xyz=1). In [15], the question of finding all triples (l, m, n) such that non-abelian finite simple groups are (l , m, n)-generated was posed. In this paper we partially answer this question for the sporadic group He. We continue the study of (p, q, r) -generations of the sporadic simple groups, where p, q, r are distinct primes. The problem is resolved for the Held group He.

• 대한수학회논문집
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• 제35권3호
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• pp.745-757
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• 2020

A set {a₁, a₂, …, a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of a torsion group of elliptic curves E_k constructed by a Diophantine triple {F_2k, F_2k+2, 4F_2k+1F_2k+2F_2k+3}, and find all integer points on the elliptic curve under assumption that rank(E_k(ℚ)) = 2.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제17권4호
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• pp.279-290
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• 2013

Presently, there has been growing interests in using mathematics' history in teaching mathematics [Katz, V. & Tzanakis, C. (Eds.) (2011). Recent Developments on Introducing a Historical Dimension in Mathematics Education. Washington, DC: Mathematical Association of America]. Thus, this article introduces some work of scholars from ancient East Indian culture like Bhaskara (AD 1114-1185) and Arabic culture such as Ibn Qurrah (AD 9th c) that are related to Pythagoras Theorem. In addition, some Babylonian creative works related to Pythagorean triples found in a tablet known as 'Plimpton 322', and an application of the Pythagorean Theorem found in another tablet named 'Yale Tablet' are presented. Applications of computer animation of dissection Motion Operations concept in 2D and 3D using dynamic software like Geometer's-Sketchpad and Cabri-II-and-3D. Nowadays, creative minds are attracted by the recent stampede in the advances of technological applications in visual literacy; consequently, innovative environments that would help young students, gifted or not, acquiring meaningful conceptual understanding would immerge.

• Bulletin of the Korean Chemical Society
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• 제32권12호
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• pp.4195-4198
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• 2011

Intramolecular ${\pi}-{\pi}$ and ${\sigma}-{\pi}$ interactions are omnipresent for numerous energetic and structural phenomena in nature, and the exact description of these nonbonding interactions plays an important role in the accurate prediction of the three-dimensional structures for numerous interesting molecular systems such as protein folding and polymer shaping. We have selected two prototype molecular systems for benchmarking calculations of intramolecular ${\pi}-{\pi}$ and ${\sigma}-{\pi}$ interactions. Accurately describing conformational energy of such systems requires highly elaborate but very expensive ab initio methods such as coupled cluster singles, doubles, and (triples) (CCSD(T)). Our calculations reveal a double hybrid density functional incorporating dispersion correction (B2PLYP-D) that agrees excellently with the CCSD(T) results, indicating that B2PLYP-D can serve as a practical method of choice.

• 대한수학회논문집
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• 제19권2호
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• pp.355-373
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• 2004

An extended directed triple system of order v, denoted by EDTS(v), is a pair (V, (equation omitted)) where V is a v-set and (equation omitted) is a set of transitive triples of elements of V such that every ordered pair of elements of V is contained in exactly one member of (equation omitted). We obtain a necessary and sufficient condition for the existence of cyclic EDTS(v)s, and when k=1 or 2, we also obtain a necessary and sufficient condition for the existence of k-rotational EDTS(v)s.