• 한국수학사학회지
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• 제31권2호
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• pp.73-91
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• 2018

This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.

• 정보처리학회논문지A
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• 제12A권2호
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• pp.95-102
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• 2005

부동소수점 나눗셈에서 많이 사용하는 뉴톤-랍손 부동소수점 역수 알고리즘은 일정한 횟수의 곱셈을 반복하여 역수를 계산한다. 본 논문에서는 오차가 정해진 값보다 작아질 때까지 곱셈을 반복해서 역수를 계산하는 가변 시간 뉴톤-랍손 부동소수점 역수 알고리즘을 제안한다. 'F'의 역수 계산은 초기값 $'X_0=\frac{1}{F}{\pm}e_0'$에 대하여, $'X_{i+1}=X=X_i*(2-e_r-F*X_i),\;i\in\{0,\;1,\;2,...n-1\}'$을 반복한다. 중간 곱셈 견과는 소수점 이하 p비트 미만을 절삭하며, 절삭 오차는 $'e_r=2^{-p}'$보다 작다. p는 단정도실수에서 27, 배정도실수에서 57이다. $'X_i=\frac{1}{F}+e_i{'}$라 하면 $'X_{i+1}=\frac{1}{F}-e_{i+1},\;e_{i+1}이 된다. $'\mid(2-e_r-F*X_i)-1\mid<2^{\frac{-p+2}{2}}{'}이면, $'e_{i+1}<4e_r{'}$이 부동산소수점으로 표현 가능한 최소값보다 작이지며, $'X_{i+1}\fallingdotseq\frac{1}{F}'$이다. 본 논문에서 제안한 알고리즘은 입력 값에 따라서 곱셈 횟수가 다르므로, 평균 곱셈 횟수를 계산하는 방식을 유도하고, 여러 크기의 근사 역수 테이블$(X_0=\frac{1}{F}{\pm}e_0)$에서 단정도실수 및 배정도실수의 역수 계산에 필요한 평균 곱셈 횟수를 계산한다. 이들 평균 곱셈 횟수를 종래 알고리즘과 비교하여 본 논문에서 제안한 알고리즘의 우수성을 증명한다. 본 논문에서 제안한 알고리즘은 오차가 일정한 값보다 작아질 때까지만 반복 연산을 수행하므로 역수 계산기의 성능을 높일 수 있다. 또한 최적의 근사 역수 테이블을 구성할 수 있다. 본 논문의 연구 결과는 디지털 신호처리, 컴퓨터 그라픽스, 멀티미디어, 과학 기술 연산 등 부동소수점 계산기가 사용되는 분야에서 폭 넓게 사용될 수 있다.

• 약학회지
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• 제34권2호
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• pp.112-116
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• 1990

8-Acyl-2-hydroxyphenzaine -5, 10-dioxides and 8-acyl-2-aminophenazine-5, 10-dioxides bearing n-butanoyl, n-hexanoyl and n-octanoyl groups were synthesized. It was attempted to observe the effect of phenazine dioxide derivatives on the hepatic xanthine oxidase activity in this study. As the activity of xanthine oxidase, the key enzyme in the generation of superoxide anion radical ($O_2$), was measured in the presence of phenazine dioxide derivatives, the action of 8-acyl-2-hydroxyphenazine-5,10-dioxide derivatives inhibited with increase of numbers of carbon atom bearing 8-acyl group. Moreover, when plotted on double reciprocal form, the Vmax value decrease as increase of numbers of carbon atom bearing acyl groups without affecting the Km value. However, the hepatic xanthine oxidase activity was not changed by 8-acyl-2-aminophenazine-5,10-dioxide derivatives.

• Journal of Forest and Environmental Science
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• 제26권1호
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• pp.1-7
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• 2010

Species diversity is one of the most important specifications of biological societies. Diversity of organisms, measurement of variety and examination of those hypotheses that are about reasons of diversity are such as affairs that have been desired by the ecologists for a long time. In this research, diversity of plant species in forest region, numbers of 60 sample plots in 256.00 square meters have been considered in random - systematic inventory was considered. In each sample plot, four micro-plots in 2.25 square meters in order to study on herbal cover, were executed that totally 240 micro-plots were considered. At each plot six diversity indices in relation to physiographic factors (slope, geographical aspect and altitude from the sea level) were studied. The results indicate that species diversity is more in the northern direction and also species diversity in slops less than 30% has the most amounts. Factor of altitude from the sea level did not have meaningful relation with species diversity. Through study on correlation of the numbers of species in sample plots with indices and also process and role of indices in different processors of analysis, Simpson's reciprocal index was suggested as suitable index in this type of studies.

• 정보처리학회논문지A
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• 제12A권5호
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• pp.413-420
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• 2005

부동소수점 제곱근 계산에 많이 사용하는 뉴톤-랍손 부동소수점 역수 제곱근 알고리즘은 일정한 횟수의 곱셈을 반복하여 역수 제곱근을 계산한다. 본 논문에서는 뉴톤-랍손 역수 제곱근 알고리즘의 반복 과정의 오차를 예측하여 오차가 정해진 값보다 작아지는 시점까지 반복 연산하는 알고리즘을 제안한다. `F`의 역수 제곱근 계산은 초기값 '$X_0={\frac{1}{\sqrt{F}}}{\pm}e_0$'에 대하여, '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$'을 반복한다. 중간 곱셈 결과는 소수점 이하 p 비트 미만을 절삭하며, 절삭 오차는 '$e_r=2^{-p}$' 보다 작다. p는 단정도실수에서 28, 배정도실수에서 58이다. '$X_i={\frac{1}{\sqrt{F}}}{\pm}e_i$'라고 하면 '$X_{i+1}={\frac{1}{\sqrt{F}}}-e_{i+1}$, $e_{i+1}{<}{\frac{3{\sqrt{F}}{{e_i}^2}}{2}}{\mp}{\frac{{Fe_i}^3}{2}}+2e_r$이 된다. '$|{\frac{\sqrt{3-e_r-{FX_i}^2}}{2}}-1|<2^{\frac{\sqrt{-p}{2}}}$'이면,'$e_{i+1}<8e_r$이 부동소수점으로 표현 가능한 최소값보다 작아지며, '$X_{i+1}\fallingdotseq{\frac{1}{\sqrt{F}}}$'이다. 본 논문에서 제안한 알고리즘은 입력 값에 따라서 곱셈 횟수가 다르므로, 평균 곱셈 횟수를 계산하는 방식을 도출하고, 여러 크기의 근사 역수 제곱근 테이블($X_0={\frac{1}{\sqrt{F}}}{\pm}e_0$)에서 단정도실수 및 배정도실수의 역수 제곱근 계산에 필요한 평균 곱셈 횟수를 계산한다 이들 평균 곱셈 횟수를 종래 알고리즘과 비교하여 본 논문에서 제안한 알고리즘의 우수성을 증명한다. 본 논문에서 제안한 알고리즘은 오차가 일정한 값보다 작아질 때까지만 반복하므로 역수 제곱근 계산기의 성능을 높일 수 있다. 또한 최적의 근사 역수 제곱근 테이블을 구성할 수 있다. 본 논문의 연구 결과는 디지털 신호처리, 컴퓨터 그라픽스, 멀티미디어, 과학 기술 연산 등 부동소수점 계산기가 사용되는 분야에서 폭 넓게 사용될 수 있다.

• East Asian mathematical journal
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• 제32권4호
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• pp.565-587
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• 2016

The purpose of this study was to analyze the understanding of the meaning of fraction division and fraction division algorithm of elementary mathematical gifted students through the process of problem posing and solving activities. For this goal, students were asked to pose more than two real-world problems with respect to the fraction division of ${\frac{3}{4}}{\div}{\frac{2}{3}}$, and to explain the validity of the operation ${\frac{3}{4}}{\div}{\frac{2}{3}}={\frac{3}{4}}{\times}{\frac{3}{2}}$ in the process of solving the posed problems. As the results, although the gifted students posed more word problems in the 'inverse of multiplication' and 'inverse of a cartesian product' situations compared to the general students and pre-service elementary teachers in the previous researches, most of them also preferred to understanding the meaning of fractional division in the 'measurement division' situation. Handling the fractional division by converting it into the division of natural numbers through reduction to a common denominator in the 'measurement division', they showed the poor understanding of the meaning of multiplication by the reciprocal of divisor in the fraction division algorithm. So we suggest following: First, instruction on fraction division based on various problem situations is necessary. Second, eliciting fractional division algorithm in partitive division situation is strongly recommended for helping students understand the meaning of the reciprocal of divisor. Third, it is necessary to incorporate real-world problem posing tasks into elementary mathematics classroom for fostering mathematical creativity as well as problem solving ability.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제8권2호
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• pp.97-113
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• 2004

The purpose of this study is to develop instructional methods for the formalized algorithm through informal knowledge in teaching division of fractions. The following results have been drawn from this study: First, before students learn formal knowledge about division of fractions, they knowledge or strategies to solve problems such as direct modeling strategies, languages to reason mathematically, and using operational expressions. Second, students could solve problems using informal knowledge which is based on partitioning. But they could not solve problems as the numbers involved in problems became complex. In the beginning, they could not reinvent invert-and-multiply rule only by concrete models. However, with the researcher's guidance, they can understand the meaning of a reciprocal number by using concrete models. Moreover, they had an ability to apply the pattern of solving problems when dividend is 1 into division problems of fractions when dividend is fraction. Third, instructional activities were developed by using the results of the teaching experiment performed in the second research step. They consist of student's worksheets and teachers' guides. In conclusion, formalizing students' informal knowledge can make students understand formal knowledge meaningfully and it has a potential that promote mathematical thinking. The teaching-learning activities developed in this study can be an example to help teachers formalize students' informal knowledge.

• 한국동물학회지
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• 제13권4호
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• pp.112-126
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• 1970

This paper deals with cytogenetical and cytochemical studies of the carp (Cyprinus carpio), the funa (Carassius carassius) and their hybrids. When kept under a confined condition, the carp and the funa mate andcan produce hybrids. Reciprocal crosses are also possible with similar results. The hybrids grow regularly with no observed abnormalities in the course of their development. They rank intermediate between the parent species in several characters. The hybrid males are completely sterile, while a hybrid female laid eggs in backcrossing. The spermatogenetic activity in hybrid testes is greatly disturbed. The chromosomes as observed in spermatogonial devision of hybrids are 100 in number, being the total sum of the haploid numbers of the parents, 50 for the carp and 50 for the funa. Meiosis in the hybrid testes is highly disturbed being arrested at early stages of the meiotic prophase. Most of the germ-cells undergo pycnotic degeneration during the period from late leptotene, and no spermatozoa are produced. In some hybrid specimens, the gonads show mosaic structures composed of testicular and ovarian elements, anevidence suggesting that sterility is associated with intersexuality caused by genetic unbalance between the parent species. The DNA amount in spermatogonial nuclei of thehybrids is approximately the same as that of liver nuclei, showing the 2n value. The DNA amount in the pachytene nuclei of the hybrids is less than the 4n value, while the parent species have the reduced amount of DNA in their pachytene nuclei. A consideration was made that the reduced amount of DNA in the hybrid cells may cause the disturbance of cellular activity leading to the subsequent degeneration of cells. Some aspects of enzymatic pattern in the carp, funa and their hybrids are. going on.

• 농업과학연구
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• 제9권2호
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• pp.494-506
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• 1982

보문산의 교목림(喬木林) 군집(群集)을 대상(對象)으로 수종(樹種)의 종군분유(種群分類)와 천이(遷移)계열(系列)을 추정(推定)하기 위하여 $20{\times}20m$의 quadrat를 22개소(個所) 선정하였다. 교목(喬木) 및 토양(土壤)의 분석(分析)에는 reciprocal ave raging(RA) ordination 방법(方法)을 사용하였으며, 다음과 같은 결과(結果)를 얻었다. 1. 보문산에 출현(出現)한 교목(喬木) 수종(樹種)은 20종(種)이었으며, 우세종(優勢種)은 Quercus variabilis, Pinus densiflora, Alnus hirsuta, Pinus rigida 등(等)이다. 2. RA ordination으로 분석(分析)한 결과(結果) 보문산의 교목(喬木) 군집(群集)은 Pinus rigida와 Quercus variabilis-Pinus densiflora 군(群)으로 구별(區別)된다. 3. 천이계열(移系列)에서 교목림(喬木林) 군집(群集)의 극상(極相)은 Quercus variabilis로 추정(推定)된다. 4. 토양(土壤) 요인(要因)으로는 T-N, $NO_3^-$, $NH_4^+$, $P_2O_5$, 유기물, C. E. C, pH, $K^+$, $Ca^{{+}{+}}$, $Mg^{{+}{+}}$가 분석(分析)되었으며, 토양(土壤) 환경(環境)을 지배하는 주성분(主成分)은 T-N, $NO_3$, $NH_4^+$, $P_2O_5$라고 사료(思料)된다.

• Mycobiology
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• 제38권2호
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• pp.89-96
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• 2010

This study evaluated the optimal vegetative growth conditions and molecular phylogenetic relationships of eleven strains of Agrocybe cylindracea collected from different ecological regions of Korea, China and Taiwan. The optimal temperature and pH for mycelial growth were observed at $25^{\circ}C$ and 6. Potato dextrose agar and Hennerberg were the favorable media for vegetative growth, whereas glucose tryptone was unfavorable. Dextrin, maltose, and fructose were the most effective carbon sources. The most suitable nitrogen sources were arginine and glycine, whereas methionine, alanine, histidine, and urea were least effective for the mycelial propagation of A. cylindracea. The internal transcribed spacer (ITS) regions of rDNA were amplified using PCR. The sequence of ITS2 was more variable than that of ITS1, while the 5.8S sequences were identical. The reciprocal homologies of the ITS sequences ranged from 98 to 100%. The strains were also analyzed by random amplification of polymorphic DNA (RAPD) using 20 arbitrary primers. Fifteen primers efficiently amplified the genomic DNA. The average number of polymorphic bands observed per primer was 3.8. The numbers of amplified bands varied based on the primers and strains, with polymorphic fragments ranging from 0.1 to 2.9 kb. The results of RAPD analysis were similar to the ITS region sequences. The results revealed that RAPD and ITS techniques were well suited for detecting the genetic diversity of all A. cylindracea strains tested.