• Title/Summary/Keyword: Fractional Order

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A Comparative analysis on the Fraction Contents of Korean, Japanese, Singaporean, American, and Finnish Mathematics Textbooks (한국, 일본, 싱가포르, 미국, 핀란드의 수학 교과서에 제시된 분수 지도 내용의 비교·분석)

  • Lee, Dae Hyun
    • Education of Primary School Mathematics
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    • v.21 no.2
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    • pp.111-130
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    • 2018
  • In this study, I compared and analyzed the contents of Korean, Japanese, Singapore, American, and Finnish textbooks about fraction which is one of the important and difficult concepts in elementary school mathematics. This is aimed to get the implications for meaningful fractional teaching and learning by analyzing the advantages and disadvantages of the methods and time of introducing the concept because fraction has the diversity of the sub-concepts and the introducing methods or process. As a result of the analysis, the fraction was introduced as part-whole(area) in all five countries' textbooks, but the use of number line, conversion between improper fraction and mixed number, whether to deal with part-whole(set) model. Furthermore, there are differences in the methods in obtaining of the equivalent fraction and the order of arrangement in comparison of fraction. Through this analysis, we discussed the reconsideration of the introducing contexts of fractions, the use of number line when introducing fractions, and the problem of segmentation and classification of contents.

A Comparative Study on French and Korean Primary Mathematics Education (프랑스와 우리나라의 초등 수학교육 비교 연구: 수와 연산 영역을 중심으로)

  • Seo, Dong Yeop
    • Journal of Elementary Mathematics Education in Korea
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    • v.24 no.2
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    • pp.207-229
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    • 2020
  • The study examined on the general educational system, the structure of the document of mathematical curriculum, and the characteristics of the achievement standards written in the document of France in order to compare with Korean primary mathematics education. French pupils learn about 5% more hours than Korean sixth grade pupils, and French document of mathematical curriculum describes the contents included in the documents more concretely than us. There were a large differences in the subjects both of mixed calculations and division of fractions in the area of number and operations. The study proposed the necessity for researches on the concrete description of the document of mathematical curriculum, more concrete examples to use to teach pupils on the viewpoints of school mathematics, and the learning sequences and methods of the division of fractional numbers. At last we proposed to need rethink of the importances and teaching methods of calculations.

Damage index based seismic risk generalization for concrete gravity dams considering FFDI

  • Nahar, Tahmina T.;Rahman, Md M.;Kim, Dookie
    • Structural Engineering and Mechanics
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    • v.78 no.1
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    • pp.53-66
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    • 2021
  • The determination of the damage index to reveal the performance level of a structure can constitute the seismic risk generalization approach based on the parametric analysis. This study implemented this concept to one kind of civil engineering structure that is the concrete gravity dam. Different cases of the structure exhibit their individual responses, which constitute different considerations. Therefore, this approach allows the parametric study of concrete as well as soil for evaluating the seismic nature in the generalized case. To ensure that the target algorithm applicable to most of the concrete gravity dams, a very simple procedure has been considered. In order to develop a correlated algorithm (by response surface methodology; RSM) between the ground motion and the structural property, randomized sampling was adopted through a stochastic method called half-fractional central composite design. The responses in the case of fluid-foundation-dam interaction (FFDI) make it more reliable by introducing the foundation as being bounded by infinite elements. To evaluate the seismic generalization of FFDI models, incremental dynamic analysis (IDA) was carried out under the impacts of various earthquake records, which have been selected from the Pacific Earthquake Engineering Research Center data. Here, the displacement-based damage indexed fragility curves have been generated to show the variation in the seismic pattern of the dam. The responses to the sensitivity analysis of the various parameters presented here are the most effective controlling factors for the concrete gravity dam. Finally, to establish the accuracy of the proposed approach, reliable verification was adopted in this study.

Aerosol Sampling with Two Stage Filter Sampler and Seasonal Variation of Metal Components in the Atmosphere (이단 필터 샘플러에 의한 대기 부유분진의 포집 및 금속 성분의 계절별 거동에 관한 연구)

  • Lee, Yong-Keun;Kim, Nam-Hoon;Myung, No-Seung;Whang, Kyu-Ja
    • Journal of Korean Society for Atmospheric Environment
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    • v.4 no.2
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    • pp.20-27
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    • 1988
  • A simple two stage aerosol filter sampler which allows simultaneous and fractional collection of two different-size particles, coarse and fine, was constructed and applied to the collection of Seoul atmospheric particulate for inorganic analysis. The sampler consist of two 47-mm diameter filter holder, a pneumatic pump, and a flowmeter. Filtering rate normally runs around 20$\ell$/min for 8 hrs. Using the sampler, a series of seasonal aerosol samples were collected from June 1986 to March 1988 at Yonsei University campus, Seoul and subsequently analysed for ten environmentally important metals using an atomic absorption spectrometer and an inductively coupled plasma emission spectrometer. The analysed metals are Al, Cd, Cr, Cu, Fe, Mn, Ni, Pb, V, and Zn. The analytical results showed the following order of metal abundance; Al > Fe > Zn > Pb > Mn > Cu > V > Ni > Cr > Cd. Based upon their size distribution pattern, the analyzed matals could be clasified into two groups, those present primarily in coarse particle and those in fine particle. Fe, Al, Mn, V, and Cr belong to the former group while the rest to the latter. Most metal concentration were highest in spring or winter, and lowest in autumn. Statistical analysis showed strong correlations between Al and Fe, Pb and Zn, and Cu and Mn.

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Characteristics of trace analysis of potential diesel oxygenates using the factorial design in solid-phase microextraction with GC/FID (고체상미량분석법(SPME-GC/FID)에서 요인배치법을 이용한 디젤첨가제의 미량분석의 특성 평가)

  • Park, Jae-Sang;Chang, Soon-Woong
    • Analytical Science and Technology
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    • v.20 no.5
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    • pp.370-382
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    • 2007
  • In this study, solid-phase microextraction (SPME) technique using GC/FID was studied as a possible alternative to liquid-liquid extraction for the analysis of EGBE, DGBE, DBM and TGME in water, and an optimization condition of trace analysis of EGBE, DGBE, DBM and TGME using the factorial design was described. Experiments used a fractional factorial design method followed by central composite design allowing optimization of a number of factors as well as statical analysis of results. The response surface analysis showed that the extraction efficiency can be described by a second-order polynomial equation in which the salts concentration, extraction temperature, extraction time and sonication time are the major influences. Using DOE, a new data-dependent method was developed that improved the quantity of confidently analyzed EGBE, DGBE, DBM and TGME in water samples.

Statistical Optimization of Production Medium for Enhanced Production of Itaconic Acid Biosynthesized by Fungal Cells of Aspergillus terreus (Aspergillus terreus에 의해 생합성되는 이타콘산의 생산성 증가를 위한 통계적 생산배지 최적화)

  • Jang, Yong-Man;Shin, Woo-Shik;Lee, Do-Hoon;Kim, Sang-Yong;Park, Chul-Hwan;Jeong, Yong-Seob;Chun, Gie-Taek
    • KSBB Journal
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    • v.24 no.1
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    • pp.30-40
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    • 2009
  • Statistical optimization of the production medium was carried out in order to find an optimal medium composition in itaconic acid fermentation process. Itaconic acid utilized in the manufacture of various synthetic resins is a dicarboxylic acid biosynthesized by fungal cells of Aspergillus terreus in a branch of the TCA cycle via decarboxylation of cis-aconitate. Through OFAT (one factor at a time) experiments, six components (glucose, fructose, sucrose, soluble starch, soybean meal and cottonseed flour) were found to have significant effects on itaconic production among various carbon- and nitrogen-sources. Hence, using these six factors, interactive effects were investigated via fractional factorial design, showing that the initial concentrations of sucrose and cottonseed flour should be high for enhanced production of itaconic acid. Furthermore, through full factorial design (FFD) experiments, negative effects of $KH_2PO_4$ and $MgSO_4$ on itaconic acid biosynthesis were demonstrated, when excess amounts of the each component were initially added. Based on the FFD analysis, further statistical experiments were conducted along the steepest ascent path, followed by response surface method (RSM) in order to obtain optimal concentrations of the constituent nutrients. As a result, optimized concentrations of sucrose and cottonseed flour were found to be 90.4g/L and 53.8g/L respectively, with the corresponding production level of itaconic acid to be 4.36 g/L (about 7 fold higher productivity as compared to the previous production medium). From these experimental results, it was assumed that optimum ratio of the constituent carbon (sucrose) and nitrogen (cottonseed flour) sources was one of the most important factors for the enhanced production of itaconic acid.

Conjoint analysis by merging attributes (속성 병합에 의한 컨조인트 분석)

  • Lim, Yong B.;Park, Gahee;Chung, Jong Hee
    • Journal of Korean Society for Quality Management
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    • v.45 no.1
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    • pp.55-64
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    • 2017
  • Purpose: A large number of attributes with mixed levels are often considered in the conjoint analysis. The respondents may have difficulty with scoring their preferences accurately because of many attribute items involved in each survey question. We research on the technique for reducing the number of attribute items. Methods: In order to reduce the number of attribute items in a survey question, we make a new attribute by merging two original attributes. A 'No question' option is also included as a new level in a merged attribute. Results: We propose BIB $6^4$ design in the case where we have four attributes with 2 levels and 3 levels, respectively and then analyze all the respondents survey data generated by the repeated simulation study in order to compare various model selection methods. Conclusion: How to reduce the number of attribute items is proposed and how to design and analyze the survey data are illustrated.

Influence of barley grain treated with alkaline compounds or organic extracts on ex vivo site and extent of digestion of starch

  • Naseroleslami, Reza;Mesgaran, Mohsen Danesh;Tahmasbi, Abdolmansour;Vakili, Seyed Alireza;Ebrahimi, Seyed Hadi
    • Asian-Australasian Journal of Animal Sciences
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    • v.31 no.2
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    • pp.230-236
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    • 2018
  • Objective: Two ex vivo experiments were conducted to verify the effect of barley grain (Nusrat cultivar) treated with alkaline compounds (AC) including alum, ammonium, and sodium hydroxide or cation-exchanged organic extracts (OE) prepared from alfalfa hay, sugar beet pulp and Ulva Fasciata, on extent and digestion of starch. Methods: In the first study, the in vitro first order disappearance kinetic parameters of dry matter (DM), crude protein (CP) and starch were estimated using a non-linear model ($D_{(t)}=D_{(i)}{\cdot}e^{(-k_d{\cdot}time)}+I$, where: $D_{(t)}$ = potentially digestible residues at any time, $D_{(i)}$ = potentially digestible fraction at any time, $k_d$ = fractional rate constant of digestion (/h), I = indigestible fraction at any time). In the second experiment, the ruminal and post-ruminal disappearance of DM, CP, and starch were determined using in situ mobile nylon bag. Results: Barley grains treated with alum and alfalfa extract had a higher constant rate of starch digestion (0.11 and 0.09/h) than others. Barley grain treated with OE had a higher constant rate of CP digestion and that of treated with AC had a higher constant rate of starch digestion (0.08 and 0.11/h) compared with those of the other treatments. The indigestible fraction of starch treated with alum and sugar beet pulp extract was higher than that of the control group (0.24 and 0.25 vs 0.21). Barley grain treated with AC and OE had significant CP disappearance in the rumen, post-rumen and total tract, and also starch disappearance for post-rumen and total tract compared with the untreated (p<0.001). Conclusion: This study demonstrated that AC and OE might have positive effects on the starch degradation of the barley grain. In addition, treating barley grain with alum and sugar beet pulp extract could change the site and extend digestion of protein and starch.

Analysis of the Differences Among Core Competency of Collegiate and Career Preparation Behavior, Career Decision-Making Self-Efficacy, Career Barriers (대학생 핵심역량에 따른 진로준비행동 및 진로결정 자기효능감, 진로장벽의 차이 분석)

  • Ha, Jungyoun;Kim, Jeongmin;Kang, Jiyeon;Cha, Jicheol
    • The Journal of the Korea Contents Association
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    • v.17 no.5
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    • pp.80-89
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    • 2017
  • This study aims to get necessary information for designing the systematic and practical career preparation education program by checking the differences among core competency of collegiate and career variables. In order to do that, the core competence of collegiate was identified through Korea collegiate essential skills assessment(K-CESA), and the survey results about career preparation behavior, career decision-making self efficacy and career barriers were collected. And then the data were compared and analyzed to differentiate relationships among core competency of collegiate and career variables, based on the university types and the locations. The data were analyzed by ANOVAs and t-tests using the SPSS 21.0 program. According to the analysis, firstly, there is a difference in the level of collegiate essential skills depending on the characteristics of schools. Secondly, the students at metropolitan four-year universities feel more difficulties primarily in the variable of career barriers than the students at local universities and students at colleges. Thirdly, the students of high rank at core competence showed higher career decision-making self-efficacy and career preparation behavior than the students of low rank, and they feel less difficulties in the matter of career barrier. This study shows that in order to support students' career efficiently, it is necessary for each college and university to design career program by considering the core competency and the level of career development of students, instead of providing them with a unified and fractional program.

Application of Multispectral Remotely Sensed Imagery for the Characterization of Complex Coastal Wetland Ecosystems of southern India: A Special Emphasis on Comparing Soft and Hard Classification Methods

  • Shanmugam, Palanisamy;Ahn, Yu-Hwan;Sanjeevi , Shanmugam
    • Korean Journal of Remote Sensing
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    • v.21 no.3
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    • pp.189-211
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    • 2005
  • This paper makes an effort to compare the recently evolved soft classification method based on Linear Spectral Mixture Modeling (LSMM) with the traditional hard classification methods based on Iterative Self-Organizing Data Analysis (ISODATA) and Maximum Likelihood Classification (MLC) algorithms in order to achieve appropriate results for mapping, monitoring and preserving valuable coastal wetland ecosystems of southern India using Indian Remote Sensing Satellite (IRS) 1C/1D LISS-III and Landsat-5 Thematic Mapper image data. ISODATA and MLC methods were attempted on these satellite image data to produce maps of 5, 10, 15 and 20 wetland classes for each of three contrast coastal wetland sites, Pitchavaram, Vedaranniyam and Rameswaram. The accuracy of the derived classes was assessed with the simplest descriptive statistic technique called overall accuracy and a discrete multivariate technique called KAPPA accuracy. ISODATA classification resulted in maps with poor accuracy compared to MLC classification that produced maps with improved accuracy. However, there was a systematic decrease in overall accuracy and KAPPA accuracy, when more number of classes was derived from IRS-1C/1D and Landsat-5 TM imagery by ISODATA and MLC. There were two principal factors for the decreased classification accuracy, namely spectral overlapping/confusion and inadequate spatial resolution of the sensors. Compared to the former, the limited instantaneous field of view (IFOV) of these sensors caused occurrence of number of mixture pixels (mixels) in the image and its effect on the classification process was a major problem to deriving accurate wetland cover types, in spite of the increasing spatial resolution of new generation Earth Observation Sensors (EOS). In order to improve the classification accuracy, a soft classification method based on Linear Spectral Mixture Modeling (LSMM) was described to calculate the spectral mixture and classify IRS-1C/1D LISS-III and Landsat-5 TM Imagery. This method considered number of reflectance end-members that form the scene spectra, followed by the determination of their nature and finally the decomposition of the spectra into their endmembers. To evaluate the LSMM areal estimates, resulted fractional end-members were compared with normalized difference vegetation index (NDVI), ground truth data, as well as those estimates derived from the traditional hard classifier (MLC). The findings revealed that NDVI values and vegetation fractions were positively correlated ($r^2$= 0.96, 0.95 and 0.92 for Rameswaram, Vedaranniyam and Pitchavaram respectively) and NDVI and soil fraction values were negatively correlated ($r^2$ =0.53, 0.39 and 0.13), indicating the reliability of the sub-pixel classification. Comparing with ground truth data, the precision of LSMM for deriving moisture fraction was 92% and 96% for soil fraction. The LSMM in general would seem well suited to locating small wetland habitats which occurred as sub-pixel inclusions, and to representing continuous gradations between different habitat types.