• Journal for History of Mathematics
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• v.11 no.1
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• pp.47-51
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• 1998

We consider how the speculation of infinity has been established through Cantor's idea. Also this paper deals with a problem of infinity in view of the application of our real life, as well as the theoretical meaning.

• Proceedings of The Korean Society of Agricultural and Forest Meteorology Conference
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• 2012.07a
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• pp.59-61
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• 2012

• Korean Journal of Veterinary Research
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• v.40 no.1
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• pp.17-26
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• 2000

The regional distribution and relative frequencies of endocrine cells were studied immunohistochemically (PAP methods) in the alimentary tract and pancreas of the toad, Bufo bufo gargarizans Cantor using specific antisera against bovine Sp-1/chromogranin (BCG), serotonin, bombesin, gastrin, substance P (SP), somatostatin, insulin, glucagon, pancreatic polypeptide (PP), vasoactive intestinal polypeptide (VIP) and secretin. Nine kinds of endocrine cells were identified in this study. Spherical or spindleshaped immunoreactive (IR) cells were located in the gastric glands of stomach regions, in the basal portion of the epithelium of intestinal tract or esophagus, and in the exocrine or pancreatic islets with variable frequencies. In the alimentary tract, BCG-IR cells were found in the fundus and pylorus with rare and a few frequencies, respectively. Serotonin-IR cells were demonstrated in the whole alimentary tract including the esophagus. Bombesin- and SP-IR cells were restricted to the stomach regions and gastrin-IR cells were restricted to the pylorus. Somatostatin-IR cells were detected throughout the whole alimentary tract except for the large intestine, However, insulin-, glucagon-, PP-, VIP- and secretin-IR cells were not detected in the alimentary tract. In the pancreas of toad, the distribution and relative frequency of endocrine cells were similar to those of other mammals. Insulin-IR cells were located in the central portion of the pancreatic islets and interspaces of exocrine portions, and glucagon-, somatostatin- and PP-IR cells were detected in the marginal regions of the pancreatic islets and interspaces of exocrine. However, other IR cells were not found in the pancreas. In conclusion, the regional distribution and relative frequency of the endocrine cells in the alimentary tract and pancreas of the toad were similar to other anuran species but some differences which might be caused by feeding habits and species specification were also observed.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.357-364
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• 2006

We study Hausdorff and packing dimensions of subsets of a general coding space with a generalized ultra metric from a multifractal spectrum induced by a self-similar measure on a self-similar Cantor set using a function satisfying a H${\ddot{o}}$older condition.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.469-475
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• 2004

We generalize S. Ikeda's results for perturbed cantor sets showing how we get the dimensions for deformed self-similar sets.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.527-532
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• 2008

We compare a coding space which has an ultra metric with the unit interval which has an associated generalized dyadic expansion. The two spaces are not homeomorphic but dimensionally equivalent in the sense that the Hausdorff and packing dimensions of the corresponding distribution sets in the two spaces coincide.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.37
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• pp.233-240
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• 1996

Julia set, Fatou set와 Mandelbrot set 가 컴퓨터에 의하여 도형화된 후부터 혼돈 역학체계 (chaotic dynamical system)에 대한 연구가 모든 학계에 비상한 관심을 모으고 있으며 특히 수학자들에 의하여 많은 연구가 이루어지고 있다. 또한 혼돈 역학체계를 기초로 하여 컴퓨터 그래픽스를 이용한 후랙탈(fractal)들의 매혹적인 시각적 표현으로 인하여 최근들어 과학자들 뿐 아니라 일반대중의 후랙탈에 대한 관심이 매우 높아지고 있다. 후랙탈이란 말은 라틴어 fractus(부서진 상태를 뜻함)에서 유래되었으며 1975년 Mandelbrot가 수학 및 자연계의 비정규적 패턴들에 대한 체계적 고찰을 담은 자신의 에세이의 표제를 주기 위해서 만들었다(〔6〕). 후랙탈을 기술하는데 있어서 가장 중요한 양은 차원(dimension)으로, 예컨데 Cantor 1/3 집합은 길이 1인 선분으로부터 시작하야 매 단계마다 모든 선분들의 가운데 1/3을 잘라내는 것을 무한히 반복함으로써 얻어지는데 이 집합의 Lebesgue measure는 0이지만 후랙탈 차원은 log2/log3 로 정수차원이 아닌 실수차원을 갖으며 또한 Cantor 1/3집합은 연속이 아니면서 점도 선도 아닌 집합인 것이다. 이 논문에서는 Box counting dimension 과 Hausdorff dimension에 대한 몇 가지 정의를 하고 정리 2.6, 정리2.7 및 정리 3.3을 증명함으로써 어떤 성질을 갖는 후랙탈의 가장 중요한 양인 후랙탈 차원에 대하여 논의 하고자 한다.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.53-68
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• 2009

From ancient Greek times, the infinite concepts had debated, and then they had been influenced by Hebrew's tradition Kabbalab. Next, those infinite thoughts had been developed by Roman Catholic theologists in the medieval ages. After Renaissance movement, the mathematical infinite thoughts had been described by the vanishing point in Renaissance paintings. In the end of 1800s, the infinite thoughts had been concreted by Cantor such as Set Theory. At that time, the set theoretical trend had been appeared by pointillism of Seurat and Signac. After 20 century, mathematician $M\ddot{o}bius$ invented <$M\ddot{o}bius$ band> which dimension was more 3-dimensional space. While mathematicians were pursuing about infinite dimensional space, artists invented new paradigm, surrealism. That was not real world's images. So, it is called by surrealism. In contemporary arts, a lot of artists has made their works by mathematical material such as Mo?bius band, non-Euclidean space, hypercube, and so on.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.477-484
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• 2007

Let h : M ${\rightarrow}$ M be an almost periodic homeomorphism of a compact metric space M onto itself. We prove that h is topologically transitive iff every element of M has a dense orbit. It follows as a corollary that an almost periodic homeomorphism of a compact metric space onto itself can not be chaotic. Some additional related observations on a Cantor set are made.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.691-699
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• 1997

The following statement is known as the generalized Hilbert-Smith conjecture : If G is a compact group and acts effectively on a manifold, then G is a Lie group. In this paper we prove that the generalized Hilbert-Smith conjecture is equivalent to the following : A known, but has never been published before.