• 제목/요약/키워드: Complex Calculations

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우리나라 초등학교 수학교육에 적용 가능한 계산기 활용 방안 연구 (A Study on How to Use Calculators in Elementary Mathematics Education in Korea)

  • 박교식
    • 대한수학교육학회지:수학교육학연구
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    • 제8권1호
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    • pp.237-249
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    • 1998
  • Calculators can be instructional instruments to be used specially in problem situations which need calculations through calculators. A calculator-calculations is one of the various calculation methods. As there are problem situations for each method, there are problem situations for a calculator-calculation, too. Basically, calculator-calculations can be admitted in any cases which need not paper-and-pencil calculations, estimations, mental calculations, and computer-calculations. In this paper, some basic knowledges on how to use calculators in elementary mathematics education are offered. Students learn concepts easier by doing complex and tedious calculations through calculators than through paper-and-pencil calculations. And, by doing complex and tedious calculations in problem solving, they can focus on understanding problems, planning, and looking back. Calculator can be used directly in phases of understanding and planning. Calculators can be used to practice guess and check strategies. Problems which contain calculations beyond students' paper-and-pencil calculations abilities. So, as a result, students' experiences on problem solving can be extended. Calculators experiences can affect students' persistences, confidences, enthusiasms, self-esteems positively.

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제일원리 계산을 활용한 전기화학 촉매 연구 (First-Principles Calculations for Design of Efficient Electrocatalysts)

  • 김동연
    • 한국전기전자재료학회논문지
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    • 제34권6호
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    • pp.393-400
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    • 2021
  • As the recent climate problems are getting worse year after year, the demands for clean energy materials have highly increased in modern society. However, the candidate material classes for clean energy expand rapidly and the outcomes are too complex to be interpreted at laboratory scale (e.g., multicomponent materials). In order to overcome these issues, the first-principles calculations are becoming attractive in the field of material science. The calculations can be performed rapidly using virtual environments without physical limitations in a vast candidate pool, and theory can address the origin of activity through the calculations of electronic structure of materials, even if the structure of material is too complex. Therefore, in terms of the latest trends, we report academic progress related to the first-principles calculations for design of efficient electrocatalysts. The basic background for theory and specific research examples are reported together with the perspective on the design of novel materials using first-principles calculations.

Molecular Orbital Study of Bonding and Stability on Rh(Ⅰ)-Alkyne Isomers

  • 강성권;송진수;문정현;윤석성
    • Bulletin of the Korean Chemical Society
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    • 제17권12호
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    • pp.1149-1153
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    • 1996
  • Ab initio and extended Huckel calculations were carried out on the isomers of trans-RhCl(η2-C2H2)(PH3)2 (1). Due to π-back donation in 1 complex, the rotational energy barrier of alkyne ligand is computed to be in the range of 18.6-25.2 kcal/mol at MP4 levels. The optimized hydrido-alkynyl complex (2) at ab initio level has the distorted trigonal bipyramidal structure. Vinylidene complex (3) is computed to be more stable than 1 complex by 17.1 kcal/mol at MP4//MP2 level. The stabilities of isomers show similar trend at the various level calculations, that is, EHT, MP4//HF, and MP4//MP2 levels. The optimized geometries at ab initio level are in reasonable agreement with experimental data. A detailed account of the bonding in each isomers (1-3) have been carried out in terms of orbital analyses.

Homogenized limit analysis of masonry structures with random input properties: polynomial Response Surface approximation and Monte Carlo simulations

  • Milani, G.;Benasciutti, D.
    • Structural Engineering and Mechanics
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    • 제34권4호
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    • pp.417-447
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    • 2010
  • The uncertainty often observed in experimental strengths of masonry constituents makes critical the selection of the appropriate inputs in finite element analysis of complex masonry buildings, as well as requires modelling the building ultimate load as a random variable. On the other hand, the utilization of expensive Monte Carlo simulations to estimate collapse load probability distributions may become computationally impractical when a single analysis of a complex building requires hours of computer calculations. To reduce the computational cost of Monte Carlo simulations, direct computer calculations can be replaced with inexpensive Response Surface (RS) models. This work investigates the use of RS models in Monte Carlo analysis of complex masonry buildings with random input parameters. The accuracy of the estimated RS models, as well as the good estimations of the collapse load cumulative distributions obtained via polynomial RS models, show how the proposed approach could be a useful tool in problems of technical interest.

Oxidative Addition Reaction of Mono(aryl)cyanoplatinum(Ⅱ) Complex with Two Amino Ligands with the Dihalogens

  • Ko Jaejung;Kim Moonsik;Kim Seho;Shin Yookil
    • Bulletin of the Korean Chemical Society
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    • 제13권2호
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    • pp.135-139
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    • 1992
  • The mono(aryl)cyanoplatinum(II) complex $[Pt(CN)(C_6H_3{CH_2NMe_2}_2-26)]$, reacts with the dihalogens to yield the mono(aryl)cyanoplatinum complexes $[PtX_2(CN)(C_6H_3{CH_2NMe_2}_2-26)]$, (X = Cl, Br, I). The structural configuration of the two halogen atoms for a square planar platinum complex was studied by 1H-NMR spectroscopy and led to a mixture of trans and cis orientation. The trans orientation was found to be more stable in energy (1.33 kcal/mol) than the cis orientation by means of Extended H ckel calculations. On the base of a combination of the analysis of $^1H-NMR$, $^{13}C-NMR spectra and computational calculations it is assumed that the intermediate consists of an initial attack in the linear transition state, leading to the $S_{N}2$ type mechanism.

Understanding DFT Calculations of Weak Interactions: Density-Corrected Density Functional Theory

  • Park, Hansol;Kim, Yeil;Sim, Eunji
    • 대한화학회지
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    • 제63권1호
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    • pp.24-28
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    • 2019
  • In this work, we discuss where the failure of Kohn-Sham Density Functional Theory (DFT) occurs in weak interactions. We have adopted density-corrected density functional calculations and dispersion correction separately to find out whether the failure is due to density-driven error or functional error. The results of Benzene Ar complex, one of the most common examples of van der Waals interactions, show that DFT calculations of van der Waals interaction suffer from functional error, rather than density-driven error. In addition, errors in DFT calculations of the S22 dataset, which contains small to relatively large (30 atoms) complexes with non-covalent interactions, are governed by functional errors.

CRX: A Characteristic Transport Theory Code for Cell and Assembly Calculations in Reactor Core Design

  • Cho, Nam-Zin;Hong, Ser-Gi
    • 한국원자력학회:학술대회논문집
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    • 한국원자력학회 1995년도 추계학술발표회논문집(1)
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    • pp.85-90
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    • 1995
  • A characteristic transport theory code CRX is developed and tested for cell and assembly calculations. Since the characteristic method treats explicitly (analytically) the streaming portion of the transport equation, CRX treats strong absorbers well and has no practical limitations placed on the geometry of the problem. To test the code, it was applied to three benchmark problems which consist of complex meshes and compared with other codes.

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Improvement of image processing speed of the 2D Fast Complex Hadamard Transform

  • Fujita, Yasuhito;Tanaka, Ken-Ichi
    • 한국방송∙미디어공학회:학술대회논문집
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    • 한국방송공학회 2009년도 IWAIT
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    • pp.498-503
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    • 2009
  • As for Hadamard Transform, because the calculation time of this transform is slower than Discrete Cosine Transform (DCT) and Fast Fourier Transform (FFT), the effectiveness and the practicality are insufficient. Then, the computational complexity can be decreased by using the butterfly operation as well as FFT. We composed calculation time of FFT with that of Fast Complex Hadamard Transform by constructing the algorithm of Fast Complex Hadamard Transform. They are indirect conversions using program of complex number calculation, and immediate calculations. We compared calculation time of them with that of FFT. As a result, the reducing the calculation time of the Complex Hadamard Transform is achieved. As for the computational complexity and calculation time, the result that quadrinomial Fast Complex Hadamard Transform that don't use program of complex number calculation decrease more than FFT was obtained.

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Theoretical Studies on Electronic Structure and Absorption Spectrum of Prototypical Technetium-Diphosphonate Complex 99mTc-MDP

  • Qiu, Ling;Lin, Jian-Guo;Gong, Xue-Dong;Ju, Xue-Hai;Luo, Shi-Neng
    • Bulletin of the Korean Chemical Society
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    • 제32권7호
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    • pp.2358-2368
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    • 2011
  • Density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations, employing the B3LYP method and the LANL2DZ, 6-31G$^*$(LANL2DZ for Tc), 6-31G$^*$(cc-pVDZ-pp for Tc) and DGDZVP basis sets, have been performed to investigate the electronic structures and absorption spectra of the technetium-99m-labeled methylenediphosphonate ($^{99m}Tc$-MDP) complex of the simplest diphosphonate ligand. The bonding situations and natural bond orbital compositions were studied by the Mulliken population analysis (MPA) and natural bond orbital (NBO) analysis. The results indicate that the ${\sigma}$ and ${\pi}$ contributions to the Tc-O bonds are strongly polarized towards the oxygen atoms and the ionic contribution to the Tc-O bonding is larger than the covalent contribution. The electronic transitions investigated by TDDFT calculations and molecular orbital analyses show that the origin of all absorption bands is ascribed to the ligand-to-metal charge transfer (LMCT) character. The solvent effect on the electronic structures and absorption spectra has also been studied by performing DFT and TDDFT calculations at the B3LYP/6-31G$^*$(cc-pVDZ-pp for Tc) level with the integral equation formalism polarized continuum model (IEFPCM) in different media. It is found that the absorption spectra display blue shift in different extents with the increase of solvent polarity.