• Title/Summary/Keyword: infinite matrix

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The Transport Phenomena of Some Solutes through the Copolymer Membranes of 2-hydroxyethylmethacrylate (HEMA) with Selected Hydrophobic Monomers

  • Kim, Whan-Gun;Jhon, Mu-Shik
    • Bulletin of the Korean Chemical Society
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    • v.6 no.3
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    • pp.128-131
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    • 1985
  • A series of copolymer membranes of 2-hydroxyethylmethacrylate (HEMA) with selected hydrophobic monomers were prepared without crosslinking agents. The equilibrium water content, the partition coefficient, and the permeability of the solutes such as urea, methylurea, 1,3-di-methylurea, and acetamide via these membranes were measured. The partition coefficient data show that as the hydrophobicity of solutes increased, the partition of solutes were dictated by hydrophobic interaction between solute and polymer matrix. Diffusion coefficients obtained in these experiments decrease as the water content of polymer membrane decreases. This decrease is blunt as the excess heat capacities, ${\phi}C^0_p$ (excess) in aqueous solution at infinite dilution of solute increases. To investigate the relationship between water content and diffusion coefficient, the results of the diffusion experiments were examined in light of a free-volume model of diffusive transport. The remarkable increase of urea mobility in the polymer network containing relatively larger bulk water can be considered as water structure breaking effect.

Application of Multichannel Quantum Defect Theory to the Triatomic van der Waals Predissociation Process II

  • 이천우
    • Bulletin of the Korean Chemical Society
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    • v.16 no.10
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    • pp.957-968
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    • 1995
  • Generalized Multichannel Quantum Defect theory (MQDT) was implemented to the vibrational predissociation of triatomic van der Waals molecules in the previous paper [Bull. Korean Chem. Soc, 12, 228 (1991)]. Implementation was limited to the calculation of the scattering matrix. It is now extended to the calculation of the predissociation spectra and the final rotational distribution of the photofragment. The comparison of the results with those obtained by other methods, such as Golden-rule type calculation, infinite order sudden approximation (IOS), and close-coupling method, shows that the implementation is successful despite the fact that transition dipole moments show more energy dependence than other quantum defect parameters. Examination of the short-range channel basis functions shows that they resemble angle-like functions and provide the validity of the IOS approximation. Besides the validity of the latter, only a few angles are found to play the major role in photodissociation. In addition to the implementation of MQDT, more progress in MQDT itself is made and reported here.

The finite element model of pre-twisted Euler beam based on general displacement solution

  • Huang, Ying;Chen, Changhong;Zou, Haoran;Yao, Yao
    • Structural Engineering and Mechanics
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    • v.69 no.5
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    • pp.479-486
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    • 2019
  • Based on the displacement general solution of a pre-twisted Euler-Bernoulli beam, the shape function and stiffness matrix are deduced, and a new finite element model is proposed. Comparison analyses are made between the new proposed numerical model based on displacement general solution and the ANSYS solution by Beam188 element based on infinite approach. The results show that developed numerical model is available for the pre-twisted Euler-Bernoulli beam, and that also provide an accuracy finite element model for the numerical analysis. The effects of pre-twisted angle and flexural stiffness ratio on the mechanical property are also investigated.

Thermo-mechanical response of size-dependent piezoelectric materials in thermo-viscoelasticity theory

  • Ezzat, Magdy A.;Al-Muhiameed, Zeid I.A.
    • Steel and Composite Structures
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    • v.45 no.4
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    • pp.535-546
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    • 2022
  • The memory response of nonlocal systematical formulation size-dependent coupling of viscoelastic deformation and thermal fields for piezoelectric materials with dual-phase lag heat conduction law is constructed. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern control theory, is applied to the non-dimensional equations. The resulting formulation together with the Laplace transform technique is applied to solve a problem of a semi-infinite piezoelectric rod subjected to a continuous heat flux with constant time rates. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons of the impacts of nonlocal parameters and time-delay constants for various forms of kernel functions on thermal spreads and thermo-viscoelastic response are illustrated graphically.

High-order Reduced Radial Zernike Polynomials for Modal Reconstruction of Wavefront Aberrations in Radial Shearing Interferometers

  • Tien Dung Vu;Quang Huy Vu;Joohyung Lee
    • Current Optics and Photonics
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    • v.7 no.6
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    • pp.692-700
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    • 2023
  • We present a method for improving the accuracy of the modal wavefront reconstruction in the radial shearing interferometers (RSIs). Our approach involves expanding the reduced radial terms of Zernike polynomials to high-order, which enables more precise reconstruction of the wavefront aberrations with high-spatial frequency. We expanded the reduced polynomials up to infinite order with symbolic variables of the radius, shearing amount, and transformation matrix elements. For the simulation of the modal wavefront reconstruction, we generated a target wavefront subsequently, magnified and measured wavefronts were generated. To validate the effectiveness of the high-order Zernike polynomials, we applied both low- and high-order polynomials to the wavefront reconstruction process. Consequently, the peak-to-valley (PV) and RMS errors notably decreased with values of 0.011λ and 0.001λ, respectively, as the order of the radial Zernike polynomial increased.

Electronic Structures of ANb2PS10 (A=Ag, Na) and AuNb4P2S20

  • Jung, Dong-Woon;Kim, Sung-Jin
    • Bulletin of the Korean Chemical Society
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    • v.24 no.6
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    • pp.739-743
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    • 2003
  • New quaternary compounds $ANb_2PS_{10}$ (A = Na, Ag) and $AuNb_4P_2S_{20}$ were synthesized and characterized. The structures of three compounds consist of one-dimensional infinite chains built by [$Nb_2S_{12}$] and [$PS_4$] units. Cation atoms are occupied within the van der Waals gap of sulfur atoms between infinite chains to make -S…$M^+$…S- contacts. There is only one Au atom site and so crystallographically a unit cell contains four equivalent Au atoms in $AuNb_4P_2S_{20}$. This is only the half of the numbers of Na or Ag atoms in $NaNb_2PS_{10}$ or $AgNb_2PS_{10}$. The ratio between $Nb_2PS_{10}$ matrix vs the cation is, therefore, 1 : 1 for Ag and Na, but it is 2 : 1 for Au. Mixed valency in Au or Nb was expected to balance the charge in the latter compound. The electronic structures calculated based on the extended Huckel tight-binding method show that $ANb_2PS_{10}$ (A = Ag, Na) are semiconducting, while $AuNb_4P_2S_{20}$ is metallic, which is not consistent with the experimental results of these three compounds that all exhibit semiconducting property. The result of calculation suggests that $AuNb_4P_2S_{20}$ might be a magnetic insulator. Magnetic measurement experiment exactly proved that the compound is a Slater antiferromagnetic material with the Neels' temperature of 45 K. It is recognized, therefore, that electronic structure analysis is very useful to understand the properties of compounds.

Numerical Calculation Method for Paraxial Zoom Loci of Complicated Zoom Lenses with Infinite Object Distance by Using Gaussian Bracket Method (가우스 괄호법을 이용한 무한 물점을 갖는 복잡한 줌 렌즈의 수치해석적인 근축광선 줌 궤적 추적법)

  • Yoo, Nam-Jun;Kim, Won-Seob;Jo, Jae-Heung;Ryu, Jae-Myung;Lee, Hae-Jin;Kang, Geon-Mo
    • Korean Journal of Optics and Photonics
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    • v.18 no.6
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    • pp.410-420
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    • 2007
  • We theoretically derive the set of utilizable paraxial zoom locus equations for all complicated zoom lens systems with infinite object distance, such as a camera zoom lens, by using the Gaussian bracket method and the matrix representation of paraxial ray tracing. And we make the zoom locus program according to these equations in Visual Basic. Since we have applied the paraxial ray tracing equations into Gaussian bracket representation, the resultant program systematically simplifies various constraints of the zoom loci of various N group types. Consequently, the solutions of this method can be consistently used in all types of zoom lens in the step of initial design about zoom loci. Finally, in order to verify the usefulness of this method, we show that one example among 4 groups and that among 5 groups, which are very complex zoom lens systems, can be rapidly and with versatility traced through various interpolations by using this program.

Introduction to the Indian Buffet Process: Theory and Applications (인도부페 프로세스의 소개: 이론과 응용)

  • Lee, Youngseon;Lee, Kyoungjae;Lee, Kwangmin;Lee, Jaeyong;Seo, Jinwook
    • The Korean Journal of Applied Statistics
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    • v.28 no.2
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    • pp.251-267
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    • 2015
  • The Indian Buffet Process is a stochastic process on equivalence classes of binary matrices having finite rows and infinite columns. The Indian Buffet Process can be imposed as the prior distribution on the binary matrix in an infinite feature model. We describe the derivation of the Indian buffet process from a finite feature model, and briefly explain the relation between the Indian buffet process and the beta process. Using a Gaussian linear model, we describe three algorithms: Gibbs sampling algorithm, Stick-breaking algorithm and variational method, with application for finding features in image data. We also illustrate the use of the Indian Buffet Process in various type of analysis such as dyadic data analysis, network data analysis and independent component analysis.

Experimental Study of Leaching Phenomena of Cs-137 From a Cement Matrix Generated at PWR Plant (가압 경수로에서 생성된 시멘트 고화체로부터 Cs-137의 용출 현상의 실험적 연구)

  • Doh, Jeong-Yeul;Lee, Kun-Jai
    • Journal of Radiation Protection and Research
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    • v.11 no.2
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    • pp.91-103
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    • 1986
  • Experimental study for the leaching behavior of Cs-137 was carried out using the simulated evaporator bottom product of PWR plant. The method of leach test proposed by the IAEA was partially modified using ANS method. The effect of various factors, i.e., sampling method, curing temperature, curing time, leachant temperature, vermiculite addition and volume-to-surface ratio, was considered in this experiment. Diffusion model in semi-infinite slab was in a good agreement with the data obtained from 4-weeks cured specimens. The effective diffusion coefficient of the specimens which were cured at the temperature of $24^{\circ}C$ for 4 weeks was found to be $1.20{\sim}1.47{\times}10^{-11}cm^2/sec$. With the experimentally obtained diffusion coefficient ($1.47{\times}10^{-11}cm^2/sec$), long-term prediction for the leaching of Cs-137 was carried out using finite-slab approximation. The estimated fraction of Cs-137 which remains in the environment is found to be less than 0.25 percent of initial amount after 100 years. About 25 years after the beginning of leaching, its fractional amount in the environment reachs the maximum value, 0.66 percent of initial amount.

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Crystal Structure of Penicillin V Potassium Salt

  • Kim, Whan-Chul;Yi, Seung-Ho;Shin, Jung-Mi;Yoon, Tae-Sung
    • Bulletin of the Korean Chemical Society
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    • v.14 no.6
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    • pp.713-717
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    • 1993
  • The crystal structure of the potassium salt of penicillin V has been studied by the X-ray crystallographic methods. Crystal data are as follows; potassium 3,3-dimethyl-7-oxo-6-phenoxyacetoamido-4-thia-1- azabicyclo[3.2.0]-heptane-2${\alpha}$-carboxylate, $K^+{\cdot}C_{16}H_{18}N_2O_5S^-$, $M_r$= 388.5, triclinic, Pl, a= 9.371 (1), b= 12.497 (2), c= 15.313 (2) ${\AA},\;{\alpha}= 93.74\;(2),\;{\beta}=99.32\;(1),\;{\gamma}=90.17\;(1)^{\circ},\;V=1765.7\;(2)\;{\AA}^3$, Z=4, $D_m=1.461\;gcm^{-1},\;{\lambda}(Cu\;K{\alpha})=1.5418\;{\AA},\;{\mu}=40.1\;cm^{-1}$, F(000)=808, T=296 K. The structure was solved by the heavy atom and difference Fourier methods with intensity data measured on an automated four-circle diffractometer. The structure was refined by the full-matrix least-squares method to a final R= 0.081 for 3563 observed $[I_0{\geq}2{\sigam}(I_0)]$ reflections. The four independent molecules assume different overall conformations with systematically different orientations of the phenyl groups although the penam moieties have the same closed conformations. There are intramolecular hydrogen bonds between the exocyclic amide nitrogen and phenoxy oxygen atoms. The penam moiety is conformationally very restricted although the carboxyl and exocyclic amide groups apparently have certain rotational degrees of freedom but the phenyl group is flexible about the ether bond despite the presence of the intramolecular N-H${\cdots}$O hydrogen bond. There are complicated pseudo symmetric relationships in the crystal lattice. The penam moieties are related by pseudo 20.5 screw axes and the phenyl groups by pseudo centers of symmetry. The potassium ions, related by both pseudo symmetries, form an infinite zigzag planar chain parallel to the b axis. Each potassium ion is coordinated to seven oxygen atoms in a severely distorted pentagonal bipyramid configuration, forming the infinite hydrophilic channels which in turn form the molecular stacks. Between these stacks, there are only lipophilic interactions involving the phenyl groups.