• Title/Summary/Keyword: Basis sets

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A study on the comparison and analysis of school mathematics curriculum in England and Korea, focused on the 'shape, space, and measures' domain (영국과 우리나라의 수학과 교육과정 비교 분석 연구 - 도형과 측정 영역을 중심으로 -)

  • Shin, Hang-Kyun;Hwang, Hye-Jeang
    • The Mathematical Education
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    • v.45 no.4 s.115
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    • pp.407-438
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    • 2006
  • This study investigated school mathematics curriculum of England, newly revised in 1998, focused on the 'shape, space, and measures' domain among three major domains of the English curriculum. On the basis of its understanding, this domain was compared and analyzed with school mathematics curriculum of Korea. In doing so, this study explored its plans and procedures and established a frame of comparison for the curriculums between the two countries. The structure of the National Curriculum in England is composed of programmes of study and attainment targets. The former sets out what should be taught in mathematics at key stages 1, 2, 3, and 4 and provides the basis for planning schemes of work, and the latter sets out the knowledge, skills, and understanding that pupils of different abilities and matures are expected to have by the end of each key stage. Attainment targets are composed of eight levels and an additional level of increasing difficulty. According to the results of the present study, Korea focuses on the formal and systematic mathematical knowledge on the basis of sound understanding of certain mathematical terms or concepts. On the other hand, England curriculum tends to deal with the content which can be understood more intuitively, flexibly, and naturally through the experience and aquisition based on the concrete manipulation. Particularly, it emphasizes that mathematics be realistic and useful in solving a diverse problems confronted in everyday life.

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A Probabilistic Study on Seismic Response of Seismically Isolated Nuclear Power Plant Structures using Lead Rubber Bearing (LRB 면진장치를 적용한 원전구조물의 지진응답에 따른 확률론적 연구)

  • Kim, Hyeon-Jeong;Song, Jong-Keol;Moon, Ji-Ho
    • Journal of the Earthquake Engineering Society of Korea
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    • v.22 no.2
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    • pp.45-54
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    • 2018
  • The seismically isolated nuclear power plants shall be designed for design basis earthquake (DBE) and considered to ensure safety against beyond design basis earthquake (BDBE). In order to limit the excessive displacement of the seismic isolation system of the seismically isolated structure, the moat is installed at a certain distance from the upper mat supporting the superstructure. This certain distance is called clearance to stop (CS) and is calculated from the 90th percentile displacement of seismic isolation system subjected to BDBE. For design purposes, the CS can be obtained simply by multiplying the median displacement of the seismic isolation system against DBE by scale factor with a value of 3. The DBE and BDBE used in this study were generated by using 30 sets of artificial earthquakes corresponding to the nuclear standard design spectrum. In addition, latin hyper cube sampling was applied to generate 30 sets of artificial earthquakes corresponding to maximum - minimum spectra. For the DBE, the median displacement and the 99th percentile displacement of the seismic isolation system were calculated. For the BDBE, the suitability of the scale factor was assessed after calculating the 90th percentile displacement of the seismic isolation system.

The ab Initio Quantum Mechanical Investigation for the Weakly Bound $H^+_{2n+1}$(n=1-6) Complexes (약한 결합을 갖는 $H^+_{2n+1}$(n=1-6) complex들에 대한 순 이론 양자역학적 연구)

  • In, Eun Jeong;Seo, Hyeon Il;Kim, Seung Jun
    • Journal of the Korean Chemical Society
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    • v.45 no.5
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    • pp.401-412
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    • 2001
  • The geometrical parameters, vibrational frequencies, and dissociation energies for $H_{2n+1}^+$ (n=1~6) clusters have been investigated using high level ab initio quantum mechanical techniques with large basis sets. The equilibrium geometries have been optimized at the self-consistent field (SCF), the single and double excitation configuration interaction (CISD), the coupled cluster with single and double excitation (CCSD), and the CCSD with connected triple excitations [CCSD(T)] levels of theory. The highest levels of theory employed in this study are TZ2P+d CCSD(T) up to $H^+_g$ and TZ2P CCSD(T) for $H_{11}^+$ and $H_{13}^+$. Harmonic vibrational frequencies are also determined at the SCF level of theory with various basis sets and confirm that all the optimized geometries are true minima. The dissociation energies, $D_e$, for $H_{2n+1}^+$ (n=26) have been predicted using energy differences at each optimized geometry and zero-point vibrational energies(ZPVEs) have been considered to compare with experimental dissociation energies, $D_0$.

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Performance evaluation of principal component analysis for clustering problems

  • Kim, Jae-Hwan;Yang, Tae-Min;Kim, Jung-Tae
    • Journal of Advanced Marine Engineering and Technology
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    • v.40 no.8
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    • pp.726-732
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    • 2016
  • Clustering analysis is widely used in data mining to classify data into categories on the basis of their similarity. Through the decades, many clustering techniques have been developed, including hierarchical and non-hierarchical algorithms. In gene profiling problems, because of the large number of genes and the complexity of biological networks, dimensionality reduction techniques are critical exploratory tools for clustering analysis of gene expression data. Recently, clustering analysis of applying dimensionality reduction techniques was also proposed. PCA (principal component analysis) is a popular methd of dimensionality reduction techniques for clustering problems. However, previous studies analyzed the performance of PCA for only full data sets. In this paper, to specifically and robustly evaluate the performance of PCA for clustering analysis, we exploit an improved FCBF (fast correlation-based filter) of feature selection methods for supervised clustering data sets, and employ two well-known clustering algorithms: k-means and k-medoids. Computational results from supervised data sets show that the performance of PCA is very poor for large-scale features.

Mechanical behaviour of steel fibre reinforced SCC after being exposed to fire

  • Ponikiewski, Tomasz;Katzer, Jacek;Kilijanek, Adrian;Kuzminska, Elzbieta
    • Advances in concrete construction
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    • v.6 no.6
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    • pp.631-643
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    • 2018
  • The focus of this paper is given to the investigation of mechanical properties of steel fibre reinforced self-compacting concrete after being exposed to fire. The research programme covered tests of two sets of beams: specimens subjected to fire and specimens not subjected to fire. The fire test was conducted in an environment mirroring one of possible real fire situations where concrete surface for an extended period of time is directly exposed to flames. Micro-cracking of concrete surface after tests was digitally catalogued. Compressive strength was tested on cube specimens. Flexural strength and equivalent flexural strength were tested according to RILEM specifications. Damages of specimens caused by spalling were assessed on a volumetric basis. A comparison of results of both sets of specimens was performed. Significant differences of all tested properties between two sets of specimens were noted and analysed. It was proved that the limit of proportionality method should not be used for testing fire damaged beams. Flexural characteristics of steel fibre reinforced self-compacting concrete were significantly influenced by fire. The influence of fire on properties of steel fibre reinforced self-compacting concrete was discussed.

An hp-angular adaptivity with the discrete ordinates method for Boltzmann transport equation

  • Ni Dai;Bin Zhang;Xinyu Wang;Daogang Lu;Yixue Chen
    • Nuclear Engineering and Technology
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    • v.55 no.2
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    • pp.769-779
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    • 2023
  • This paper describes an hp-angular adaptivity algorithm in the discrete ordinates method for Boltzmann transport applications with strong angular effects. This adaptivity uses discontinuous finite element quadrature sets with different degrees, which updates both angular mesh and the degree of the underlying discontinuous finite element basis functions, allowing different angular local refinement to be applied in space. The regular and goal-based error metrics are considered in this algorithm to locate some regions to be refined. A mapping algorithm derived by moment conservation is developed to pass the angular solution between spatial regions with different quadrature sets. The proposed method is applied to some test problems that demonstrate the ability of this hp-angular adaptivity to resolve complex fluxes with relatively few angular unknowns. Results illustrate that a reduction to approximately 1/50 in quadrature ordinates for a given accuracy compared with uniform angular discretization. This method therefore offers a highly efficient angular adaptivity for investigating difficult particle transport problems.

On Some Teaching Problems Related to the Learning of Variable Concept in School Mathematics (학교 수학의 변수 개념 학습과 관련된 몇 가지 지도 문제에 대하여)

  • 김남희
    • School Mathematics
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    • v.1 no.1
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    • pp.19-37
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    • 1999
  • In this study, we examined some matters related to the learning of variable concept in school mathematics on the basis of the theoretical foundation from the previous studies(e.g. Davis, 1975; Rosnick, 1981; IK chemann, 1981; Wagner, 1983.) and practices on variable concept teaching by evaluating the current state of that. Matters be discussed are as follows; the use of symbol for place holders in elementary mathematics, the dealing with sets those elements are literals and operations of such sets, the teaching of dummy variable, the construction of literal expressions that contains variables, the labeling indeterminates as a constant, the change in the exact meaning of variable according to the function concept, the teaching of a generalization by means of variables. After considering on these matters that are connected with the teaching-learning of variable concept, we suggested the alternative proposal to the current state of variable concept teaching.

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The development of On-line Model for the Prediction of Effective Strain Distribution by Non-dimensionalization on FEM Basis (유한요소법 기반의 무차원화를 이용한 판 유효 변형률 분포 예측 온라인 모델 개발)

  • Kim S. H.;Lee J. H.;Hwang S. M.
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • 2004.08a
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    • pp.359-367
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    • 2004
  • In this research on-line model for the prediction of the effective strain distribution in strip on finishing mill process is presented. To describe the effective strain distribution in strip, three guide points and a distribution fitting variable are used. On-line models to get these points and fitting variable non-dimensionalization method and least square method were used with FEM simulation results. The model is developed using strip only FEM simulation as reference sets and compared with roll coupled FEM simulation results as perturbed sets. The on-line model to describe effective strain distribution shows good agreement with coupled FEM analysis results.

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An Adaptive Clustering Algorithm Based on Genetic Algorithm (유전자 알고리즘 기반 적응 군집화 알고리즘)

  • Park Namhyun;Ahn Chang Wook;Ramakrishna R.S.
    • Proceedings of the Korea Information Processing Society Conference
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    • 2004.11a
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    • pp.459-462
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    • 2004
  • This paper proposes a genetically inspired adaptive clustering algorithm. The algorithm automatically discovers the actual number of clusters and efficiently performs clustering without unduly compromising cluster purity. Chromosome encoding that ensures the correct number of clusters and cluster purity is discussed. The required fitness function is desisted on the basis of modified similarity criteria and genetic operators. These are incorporated into the proposed adaptive clustering algorithm. Experimental results show the efficiency of the clustering algorithm on synthetic data sets and real world data sets.

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Linguistic Modelling of the Theory of Indistinct Selections as the Basis of the Assessment of Quality of Education

  • Mixlievich, Yusupov Rabbim;Akbutayevich, Tavboyev Sirojiddin;Amonkulovich, Toshpulatov Mukhiddin;Raxmonberdiyevich, Axmedov Juraboy
    • Journal of Information Technology and Architecture
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    • v.11 no.2
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    • pp.125-130
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    • 2014
  • Today in different higher educational institutions there is the active on a structure of expert models of monitoring the quality of education in the higher educational institutions, assuming continuous tracking an education status as a whole and its separate components. In most cases creation of a monitoring system of quality of education relies on the intermediate results of activities.