• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1149-1161
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• 2021

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

• Korean Journal of Microbiology
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• v.39 no.4
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• pp.223-229
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• 2003

The purpose of this work was to perform the characterization of NAD(P)H-nitroreductase isolated from Stenotrophomonas sp. OK-5 capable of degrading 2,4,6-trinitrotoluene (TNT). Initially, NADP(H)-nitroreductase by a series of purification processes including ammonium sulfate precipitation, DEAE-sepharose, andQ-sepharose was prepared. From samples harvested from fraction collector, three different fractions (I, II & III)having the enzyme activity of NAD(P)H-itroreductase were detected. Specific activities of three fractions I, II,and III of NAD(P)H-nitroreductase were determined to approximately 5.06 unit/mg, 4.95 unit/mg and 4.86 unit/mg, and concentrated to 10.5, 9.8, and 8.9-fold compared to crude extract, respectively. Among these three fractions,the fraction I of NAD(P)H-nitroreductase demonstrated the highest specific activity in this experiment. Several factors affecting on the enzyme activity of NAD(P)H-nitroreductase (fractions I, II & III) were investigated.The optimum temperature of all NAD(P)H-nitroreductase (fractions I, II & III) was 30oC, and the optimal pH was approximately 7.5. Metal ions such as Ag+, Cu2+, Hg2+ inhibited approximately 80% enzyme activity of all NAD(P)H-nitroreductase, and the enzyme activities were decreased about 30-40% inhibition in the presence of Mn2+ or Ca2+. However, Fe3+ showed stimulatory effect on the enzyme activity. The molecular weights of NAD(P)H-nitroreductase (fractions I, II & III) were measured about 27 kDa on the SDS-PAGE.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.25-43
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• 2009

The fraction concept consists of various meanings and is one of the abstract and difficult in elementary school mathematics. This study intends to find out the implication for introducing the fraction concept by comparing mathematics textbooks of Korea and Singapore. Both countries' students peformed well in recent TIMMSs. Some implications are as follows; The term 'equal' is not defined and the results of various 'equal partitioning' activities can not easily examined in Korea's mathematics textbook. And contexts of introducing fractions as a quotient and a ratio are unnatural in Korea's mathematics textbook in comparison with Singapore's mathematics textbook. So these ideas should be reconsidered in order to seek the direction for improvement of it. And Korea's textbooks need the emphasis on the fraction as a measure and on constructing fraction concept by unit fraction.

• School Mathematics
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• v.5 no.2
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• pp.259-273
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• 2003

A fraction is one of the most important concepts that students have to learn in elementary school. But it is a challenge for students to understand fraction concept because of its conceptual complexity. The focus of fraction learning is understanding the concept. Then the problem is how we can facilitate the conceptual understanding and estimate it. In this study, Moore's concept understanding scheme(concept definition, concept image, concept usage) was adopted as an theoretical framework to investigate students' fraction understanding. The questions of this study were a) what concept image do students have\ulcorner b) How well do students solve fraction problems\ulcorner c) How do students use fraction concept to generate fraction word problem\ulcorner By analyzing the data gathered from three elementary school, several conclusion was drawn. 1) The students' concept image of fraction is restricted to part-whole sub-construct. So is students' fraction understanding. 2) Students can solve part-whole fraction problems well but others less. This also imply that students' fraction understanding is partial. 3) Half of the subject(N=98) cannot pose problems that involve fraction and fraction operation. And some succeeded applied the concept mistakenly. To understand fraction, various fraction subconstructs have to be integrated as whole one. To facilitate this integration, fraction program should focus on unit, partitioning and quantity. This may be achieved by following activities: * Building on informal knowledge of fraction * Focusing on meaning other than symbol * Various partitioning activities * Facing various representation * Emphasizing quantitative aspects of fraction * Understanding the meanings of fraction operation Through these activities, teacher must help students construct various faction concept image and apply it to meaningful situation. Especially, to help students to construct various concept image and to use fraction meaningfully to pose problems, much time should be spent to problem posing using fraction.

• Korean Journal of Food Science and Technology
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• v.47 no.1
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• pp.6-12
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• 2015

This study was performed to determine the optimal hydrolysis conditions for the production of hydrolysates, including water-soluble dietary fiber from Chinese cabbage, with commercial enzymes. The optimal pH and temperature for hydrolysis of the hemicellulose fraction were pH 5.0 and $40^{\circ}C$, and optimal enzyme concentrations were 45 units and 21 units for Shearzyme plus and Viscozyme L, respectively. The yields of the hydrolysate including the water-soluble dietary fiber from the hemicellulose fraction by Shearzyme plus and Viscozyme L were 22.64 and 24.73%, respectively, after a 72 h reaction. The molecular weight distribution of alcohol-insoluble fiber was characterized by gel chromatography; degradation of hemicellulose increased with increasing reaction time. Our results indicate that the hemicellulose fraction was degraded to water-soluble dietary fiber by enzymatic hydrolysis, and its hydrolysate could be utilized as new watersoluble food materials.

• 한국태양에너지학회:학술대회논문집
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• 2008.11a
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• pp.245-250
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• 2008

This study is on the availability of solar thermal energy in Korean high-rise apartment complex depending on the installation type of solar collectors to roof or facade of building. Firstly, solar access evaluation on the roof and the facade of apartment buildings was carried out. The total thermal load of each apartment unit and building was investigated and matched with the energy which was produced by solar thermal systems on the facade. The considered layout patterns of apartment buildings were '一type', 'alternative 一type', 'ㄱtype' and 'ㅁtype' and that was analyzed in prior studies. Extensive dynamic hourly energy simulations with the solar thermal system were Performed with the TRNSYS of SEL. We assumed that the apartment complex is composed of 9 buildings and located in Daejeon. The collectors are the heat-pip evacuated tube collectors and the number of collectors are 45 tubes We assumed that the collectors are installed on the balcony of each unit and the angle of incilnation is $90^{\circ}$. As a result, the supply amount of solar thermal systems is about 4,850,086kJ/hr and the solar fraction is about 66%. The solar fraction according to each azimuth is about 66% on the south, 62% on the south-east $30^{\circ}$ and 56% on the south-east $60^{\circ}$. So, we quantitatively got a line on the optimal azimuth for installing the solar thermal systems. The solar fraction has differences from 5% to 15% of each floor, 6th, 12th and 20th and those tendencies are same in analyzed each 4 types of the apartment complexes.

• The Mathematical Education
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• v.60 no.1
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• pp.1-19
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• 2021

This study investigates students' conceptions of fractions from a measurement approach while providing a technological environment designed to support students' understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students' constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field's understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.

• Journal of Pharmacopuncture
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• v.25 no.2
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• pp.121-129
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• 2022

Objectives: The chemical composition of cactus pear seed oil (Opuntia ficus-indica [L.] Mill.) was analyzed in terms of its fatty acid composition, tocopherol content, phenolic identification, and the oil's phenolic-rich fraction antioxidant power was determined. Methods: Fatty acid profiling was performed by gas chromatography coupled to an FI detector. Tocopherols and phenolic compounds were analyzed by LC-FLD/UV, and the oil's phenolic-rich fraction antioxidant power was determined by phosphomolybdenum, DPPH assay and β-carotene bleaching test. Results: Fatty acid composition was marked by a high unsaturation level (83.22 ± 0.34%). The predominant fatty acid was linoleic acid (66.79 ± 0.78%), followed by oleic acid (15.16 ± 0.42%) and palmitic acid (12.70 ± 0.03%). The main tocopherol was γ-tocopherol (172.59 ± 7.59 mg/kg. In addition, Tyrosol, vanillic acid, vanillin, ferulic acid, pinoresinol, and cinnamic acid were identified as phenolic compounds in the analyzed seed oil. Moreover, the oil's phenolics-rich fraction showed a significant total antioxidant activity, scavenged DPPH up to 97.85%, and effectively protected β-carotene against bleaching (97.56%). Conclusion: The results support the potential use of cactus pear seed oil as a functional food.

• Nuclear Engineering and Technology
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• v.55 no.1
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• pp.109-118
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• 2023

In this paper, the evaluation method of fluidelastic instability (FEI) of newly designed steam generator tubing in pressurized water reactor (PWR) nuclear power plants is discussed. To obtain the parameters for prediction of the critical velocity of FEI for steam generator tubes, experimental research is carried out, and the design parameters are determined. Using CFD numerical simulation, the tube array scale of the model experiment is determined, and the experimental device is designed. In this paper, 7 groups of experiments with void fractions of 0% (water), 10%, 20%, 50%, 75%, 85% and 95% were carried out. The critical damping ration, fundamental frequency and critical velocity of FEI of tubes in flowing water were measured. Through calculation, the total mass and instability constant of the immersed tube are obtained. The critical damping ration measured in the experiment mainly included two-phase damping and viscous damping, which changed with the change in void fraction from 1.56% to 4.34%. This value can be used in the steam generator design described in this paper and is conservative. By introducing the multiplier of frequency and square root of total mass per unit length, it is found that the difference between the experimental results and the calculated results is less than 1%, which proves the rationality and feasibility of the calculation method of frequency and total mass per unit length in engineering design. Through calculation, the instability constant is greater than 4 when the void fraction is less than 75%, less than 4 when the void fraction exceeds 75% and only 3.04 when the void fraction is 95%.

• The Mathematical Education
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• v.56 no.2
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• pp.193-212
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• 2017

This study focuses on cuisenaire rods that can be used when teaching fractions to elementary school students. First of all, this study critically examines the use of cuisenaire rods in learning of fraction proposed by various researches. Then, based on this review, this study explores in detail the use of cuisenaire rods in teachers' manuals developed from the revised curriculum by 2009 and in lessons related to fraction. The results of this study show that there are subtle differences in how to use cuisenaire rods in learning fractions and these subtle differences have a significant impact on students' understanding of the fractions. Therefore, the teachers should be able to accurately grasp the differences and utilize appropriate methods for teaching purpose. The followings are some of the implications for teachers or textbook developers when using cuisenaire rods in fraction learning: First, we should use cuisenaire rods in ways that can fully exploit the interpretations of the fraction as a part-whole and the fraction as a ratio. Second, we should focus on quantitative reasoning with unit to determine what each cuisenaire rod refers to. Third, it is necessary to take a more careful and sensitive approach to the use of cuisenaire rods. Teachers and textbook developers should constantly explore ways to make good use of mathematical manipulatives to help students understand conceptually in fractional learning. Furthermore, when teaching various mathematical topics using different manipulatives, I expect that there will be sufficient discussions and specific studies on how to use each of these manipulatives.