• Journal for History of Mathematics
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• v.31 no.2
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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.

• The KIPS Transactions:PartA
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• v.12A no.2 s.92
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• pp.95-102
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal which is widely used for a floating point division, calculates the reciprocal by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the reciprocal of a floating point number F, the algorithm repeats the following operations: '$'X_{i+1}=X=X_i*(2-e_r-F*X_i),\;i\in\{0,\;1,\;2,...n-1\}'$ with the initial value $'X_0=\frac{1}{F}{\pm}e_0'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 27 for the single precision floating point, and 57 for the double precision floating point. Let $'X_i=\frac{1}{F}+e_i{'}$, these is $'X_{i+1}=\frac{1}{F}-e_{i+1},\;where\;{'}e_{i+1}, is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to $'\frac{1}{F}{'}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables $(X_0=\frac{1}{F}{\pm}e_0)$ with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal unit. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia scientific computing, etc.

• YAKHAK HOEJI
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• v.34 no.2
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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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• v.26 no.1
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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.

• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.413-420
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal square mot calculates it by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal square root algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the rediprocal square root of a floating point number F, the algorithm repeats the following operations: '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$' with the initial value is '$X_0=\frac{1}{\sqrt{F}}{\pm}e_0$'. The bits to the right of p fractional bits in intermediate multiplication results are truncated and this truncation error is less than '$e_r=2^{-p}$'. The value of p is 28 for the single precision floating point, and 58 for the double precision floating point. Let '$X_i=\frac{1}{\sqrt{F}}{\pm}e_i$, there is '$X_{i+1}=\frac{1}{\sqrt{F}}-e_{i+1}$, where '$e_{i+1}{<}\frac{3{\sqrt{F}}{{e_i}^2}}{2}{\mp}\frac{{Fe_i}^3}{2}+2e_r$'. If '$|\frac{\sqrt{3-e_r-{FX_i}^2}}{2}-1|<2^{\frac{\sqrt{-p}{2}}}$' is true, '$e_{i+1}<8e_r$' is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to '$\frac{1}{\sqrt{F}}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications Per an operation is derived from many reciprocal square root tables ($X_0=\frac{1}{\sqrt{F}}{\pm}e_0$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• East Asian mathematical journal
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• v.32 no.4
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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.

• Education of Primary School Mathematics
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• v.8 no.2 s.16
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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.

• The Korean Journal of Zoology
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• v.13 no.4
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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.

• Korean Journal of Agricultural Science
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• v.9 no.2
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• pp.494-506
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• 1982

The community structure and dynamic succession of forest were determinated on the quadrat plots selected randomly at the Mt. Bomun. The plot size was $20{\times}20m$, and analysis of vegetation and soil 'data we re adapted reciprocal averaging(RA) ordination method. 1. The numbers of tree species were twenty, and dominant species were Quercus variabilis, Pinus densiflora, Alnus hirsuta, and Pinus rigida. 2. The forest of Mt. Bomun was found to be composed of Pinus rigida community and Quercus-Pinus community through RA ordination method. 3. The community of Quercus variabilis was assumed to be dominant in the succession of forest. 4. The soil factors, such as total-N, $NO_3$, $NH_4^+$, $P_2O_5$, organic matter, C. E. C., pH, $K^+$, $Ca^{{+}{+}}$ and $Mg^{{+}{+}}$, were analyzed. Total-N, $NO_3^-$, $NH_4^+$, and $P_2O_5$ were assumed to be the main factors of the soil.

• Mycobiology
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• v.38 no.2
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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.