• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1737-1751
• /
• 2015

For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

• Solar Energy
• /
• v.12 no.3
• /
• pp.94-106
• /
• 1992

The optimum water temperature was maintained for Misgurnus anguillicaudatus(CANTOR) in winter season by solar thermal heating. The optimum temperature ranges for the Misgurnus anguillicaudatus(CANTOR) were experimentally estimated, i.e. for the body length $7{\sim}9cm$ and body weight $4{\sim}6g$, the optimum temperature range was $21{\sim}23^{\circ}C$. For the body length $9{\sim}11cm$ and body weight $6{\sim}8g$, it was $23{\sim}25^{\circ}C$, And for the body length $11{\sim}13cm$ and body weight $8{\sim}10g$, it was $25{\sim}27^{\circ}C$. The Misgurnus anguillicaudaus(CATOR) with the body weight $5{\sim}10g$ and body length $8{\sim}15cm$ grew relativeiy fast but the bigger ones with body weight above 15g, grew relatively slow and total average weight increment was about $50{\sim}80g$ per month.

• The Korean Journal of Zoology
• /
• v.6 no.2
• /
• pp.6-10
• /
• 1963

가물치( Ophicephalus argus CANTOR) 2 년생(168$\pm$4g)107마리를 대조군과 실험적으로 나누고 실험군에는 일시에 2.9mg/kg 체동의 potassium cyanide을 배근에 직접 주사하였다. 약물 처리후 시간의 경과에 따라 나타나는 Albumin/Blbulin(A/G)비, 총혈청단백질량, hematocrit 비 및 간장 및 신장의 중량변화를 측정하였다. 약물 처리 직후는 A/G 비 , 총혈청단백질량 및 hematocrit 비는 각각 현저하게 감소되었으나 많은 시간이 경과함에 따라 점차 증가되어 228시간이후는 거의 대조군과 그것과 가까운 결과를 얻었다. 그러나 간장과 신장의 중량은 약물 처리 직후는 오히려 약간 증가되는 상태였으나 , 48시간이후 급히 감소되었다가 점차 역시 대조군과 가까운 결과를 나타냈다. 이상의 결과로서 KCN가 어류의 호흡 억제작용뿐만 아니라 단백질대사에도 영향을 미치는 것으로 생각된다.

• East Asian mathematical journal
• /
• v.25 no.3
• /
• pp.229-245
• /
• 2009

G. Cantor gave a deep influence to the society of mathematics in many ways, especially in the set theory. It is important for gifted and talented high school students in mathematics to understand the Euler constant and the fractal dimension of the Cantor set in a heuristic sense. On the historic basis of mathematics and the standard of high school students, we give the teaching method for the talented high school student to understand them better. Further we introduce the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs distribution and its first moment. We hope that from these topics, the gifted and talented students in mathematics will have insight in the analysis of mathematics.

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

• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.13-19
• /
• 2016

In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.

• The Korean Journal of Zoology
• /
• v.7 no.2
• /
• pp.6-12
• /
• 1964

The present paper deals with the changes in serum protein fraction, total serum protein, hematocrit, red blood cell, haemoglobin, and weight of liver or kidney : body weight ratio of irradiated and non-irradiated snake head, Ophicephalus argus(CANTOR) . Irrardiation doses are 2537$\AA$-7 minutes (7M) and 2537$\AA$-15 minutes (15M). Serum electrophoretic patterns showed a marked decrease in albumin fraction at 1, 3, 9, 12 and 15 days on 7M group and 15 M group. On both experimental groups percentage increases in $\alpha$1 and $\beta$ fractions occurred at different time periods in general but are interpreted as only apparent changes accompanying the greater albumin fall. ${\gamma}$-Globulin decreased at 1, 6 and 15 days on 7M group. and at 1, 3, 6 and 9 days on 15M group. Also, A/G ratio was significantly low in groups subjected to above conditions as compared to the controls. A/G ratio decreased at 3 and 15 days remarkably on both groups. On the average, the reductions in the A/G ratio were not proportional to themagnitude of ultraviolet-light. Total protein of serum changed according to suggestive changes in electrophoretic patterns of serum . Total protein of serum declined at 1, 3, 6, 9 and 12 day periods on 7M groups and at 1, 3, 9, 12 and 15 day-periods on 15 M group, and increased approaching control values at 15 and 18 day-periods on both groups. Hematocrit increased remarkably at 1, 3, 6 and 12 days and decreased at 9 and 15 days on 7M group, and increased throughout the sampling period on 15M . Red blood cell decreased throughout the sampling period and increased slightly at 6 days on 7 M group and decreased at 1, 6, 9, 15 and 18 days and increased remarkably at 3 and 12 days on 15M group. Hemoglobin decreased remarkably at 1 day-period and increased at other days on both groups. The liver weight was not remarkably changed after whole body irradiation on both groups. and kidney was increased from 1st day on 7M group and 3 rd day on 15M group respectively. It appears that changes in electropphoretic patterns of serum, A/G ratio, total protein of serum, hematocrit, red blood cell, hemoglobin, and liver or kidney weight act to the detriment of the animal following non-ionizing irradiation.

• The Korean Journal of Zoology
• /
• v.8 no.2
• /
• pp.28-32
• /
• 1965

It is well known that many kinds of chemical or metalic agent which were ionized or undissociated at toxified external medium and remarkable effect occurred to the fresh water fish. The effects of hydrogen ion concentration on serum protein of fresh water fish, (phycephalus argus CANTOR) had not been reported yet. In this point, authors attempted to study the changes of A/G ratio, total protein, hemoglobin, hematocrit, RBC , liver and kidney weight of snake head in the above environment. 95 snake heads were subjected to external medium with PH-4.5 and A/G ratio, hematocrit, hemoglobin, total protein, RBC, and liver & kidney weight were measured at 32.80, 15202000 and 272 hours respectively. In whole experimental period, L 1 and L2 globulin increased, on the other, albumin decreased as compare with control . Hence, the A/G ratio decreased remarkably . Though, total protein increased prominently through the whole experimental period, hematocrit, hemoglobin, RBC, increased only at 80 hours, and then decreased as compared to the control. Liver weight revealed distinctive increase at 80 hours, but no remarkable change could be seen there after. Hence, kidney weight revealed continuous rise. By these results, it may be said that as snake head were subjected to external medium with PH-4.5, this environmental factor influenced protein metabolism , blood component and organs.

• The Korean Journal of Zoology
• /
• v.8 no.2
• /
• pp.42-46
• /
• 1965

가물치 (Ophicephalus argus CANTOR) ♂♀를 재료로 하여 두 실험군으로 나누어서 대조군에 부치사량인 25-${\gamma}$의 137Cs-${\gamma}$ 선을 조사하고 실험군에는 250${\gamma}$의 137Cs-${\gamma}$선을 조사 즉후 adrenaline (0.5cc/80g$\pm$18%)을 매일 투여하여 약 23$^{\circ}C$에서 사육하면서 혈청단백질의 전기영동상과 총혈청단백질의 변화를 1, 4, 7, 10 , 13 및 1일구간으로 분리 즉 시일적 경과로 조사하였다. 한편 가물치에서의 ${\gamma}$선 치사량은 310${\gamma}$이다. 1) 양군에서 일반적으로 1, 4, 7, 10 및 13 일구에 현저한 albumin 분설의 감소가 나타났다. 즉 대조군인 adrenaline 비투여 대조군에서 a1 및 a2 globulin 분설의 증가와 실험군이 adrenaline 투여 대조군에서 a1 및 $\beta$-globulin 분설의 증가에 다른 albumin 분설의 감소가 나타났다. 따라서 A/G 비고 역시 시일적 경과에 따라 감소된 치를 나타내었다. 그러나 특히 adrenabine 투여 대조군의 1 일간에서 A/G비가 현저하게 감소의 지체성을 나타내었다. 2) 총혈청단백질량은 양군에서 일반적으로 1, 4 및 7일구에서 현저하게 감소되나 13 미치 16 이구에서 가물치의 정상치로 근접된 치를 나타내었다. 그러나 특히 adrenaline 투여 조사군에서 4 및 7일구에서 현저하게 감소의 지체성을 나타내었다. 3) 상기의 결과로 미루어보다 명백하게 혈청단백질에 미치는 adrenaline 처리의 방어효과가 ${\gamma}$선 조사후 특히 초기상태에서 현저하게 초래된다고 생각도니다.

• Journal of the Korean School Mathematics Society
• /
• v.3 no.1
• /
• pp.211-217
• /
• 2000

본 논문의 목적은 G. Cantor 에 의하여 출발된 집합론을 보통집합 이론이라고 구별하여 부를 때, 보통 집합 이론이 그 바탕에 깔고 있는 논리적 제한 점들 곧, 배중률이라든지 모순의 법칙 등을 어떻게 보완할 수 있을 것인가\ulcorner 하는 점과 그러한 점을 보완하여야 할 필요성에 대하여도 생각하고자 한다. 그런 관점에서 보통집합 이론과 퍼지집합 이론의 기본개념을 상호 비교함으로써 앞서 제기한 문제의 보완 요소를 찾아보려고 한다. 실제에 있어 인간의 사고 가운데에서는 중간을 배제하는 일이 없음에도 불구하고 이를 수학적으로 접근하고 표현하는 수단이 부족함으로 인하여 부자연스러운 논리의 법칙을 받아들일 수밖에 없었던 것도 사실이다. 특히, 논리적 응용력이 부족한 중등과정의 학생들에게 있어서 수학이 전적으로 2가 논리에 의하여 지배되고 있다는 방식으로만 지도하는 것은 여러 가지 측면에서 그 내용의 보완이 요구된다. 보다 다양한 수학적 표현의 여지를 열어주는 지도법은 쉼없이 연구되어야 할 것이다. 무엇보다도 배우는 학생들이 보다 폭 넓은 사고의 영역을 소유하고, 그를 바탕으로 창의적이고 자유로운 발상이 이어 질 수 있도록 하기 위하여는 교사의 수학적 시야가 보다 넓고 유연해져야 한다함은 재론할 필요가 없을 것이다. 그런 의미에서 본 논문이 작은 역할을 할 수 있기를 바란다.