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A Historical Study on the Continuity of Function - Focusing on Aristotle's Concept of Continuity and the Arithmetization of Analysis - (함수의 연속성에 대한 역사적 고찰 - 아리스토텔레스의 연속 개념과 해석학의 산술화 과정을 중심으로 -)

  • Baek, Seung Ju;Choi, Younggi
    • Journal of Educational Research in Mathematics
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    • v.27 no.4
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    • pp.727-745
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    • 2017
  • This study investigated the Aristotle's continuity and the historical development of continuity of function to explore the differences between the concepts of mathematics and students' thinking about continuity of functions. Aristotle, who sought the essence of continuity, characterized continuity as an 'indivisible unit as a whole.' Before the nineteenth century, mathematicians considered the continuity of functions based on space, and after the arithmetization of nineteenth century modern ${\epsilon}-{\delta}$ definition appeared. Some scholars thought the process was revolutionary. Students tended to think of the continuity of functions similar to that of Aristotle and mathematicians before the arithmetization, and it is inappropriate to regard students' conceptions simply as errors. This study on the continuity of functions examined that some conceptions which have been perceived as misconceptions of students could be viewed as paradigmatic thoughts rather than as errors.

Performance Evaluation of Selective Coatings for Solar Thermal Collectors (태양열 집열기에 사용될 선택흡수막의 성능 평가)

  • Lee, Kil-Dong
    • Journal of the Korean Solar Energy Society
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    • v.32 no.4
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    • pp.43-50
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    • 2012
  • Metal-metal oxide (M-M oxide) cermet solar selective coatings with a double cermet layer film structure were deposited on the Al-deposited glass substrate by using a directed current (DC) magnetron sputtering technology. M oxide (CrO and ZrO) was used as the ceramic component in the cermets, and Cr and Zr used as the metallic components. In addition, black Cr (Cr-$Cr_2O_3$ cermet) solar selective coatings were deposited on the Ni-plated Cu substrate by using a electroplating method for comparison. The thermal stability tests were carried out for performance evaluation of solar coatings. Reflectance measurements were used to evaluate both solar absorptance(${\alpha}$) and thermal emittance (${\epsilon}$) of the solar coatings before and after thermal testing by using a spectrometer. Optical properties of optimized cermet solar coatings were ${\alpha}{\simeq}0.94-0.96$ and ${\epsilon}{\simeq}0.1$ ($100^{\circ}C$). The results of thermal stability test of M-M oxide solar coatings showed that the Cr-CrO cermet solar selective coatings were more stable than the Zr-ZrO cermet selective coatings at temperature of both $400^{\circ}C$ in air and $450^{\circ}C$ in vacuum. The black Cr solar selective coatings were degraded in air at temperature of $400^{\circ}C$. The main optical degradation modes of these coatings were diffusion of metal atoms, and oxidation.

Thermo-Hydrodynamic Behaviors of Open Channel Flow Inside A Multi-Stage Flash Evaporator (다단 후래시 증발장치내 개수로 유동의 열.수력학적 거동)

  • 설광원;이상용
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.14 no.3
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    • pp.702-715
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    • 1990
  • This paper describes behaviors of two-phase open channel flow inside the flash chamber of a horizontal Multi-Stage-Flash evaporator numerically along with the experimental observations. Bubble trajectories and the velocity and temperature distributions of the liquid phase were predicted by using the particle-source-in-cell(PSI-Cell) method with the appropriate bubble motion/growth equations. Size and number of bubble nuclei embedded in the incoming liquid(brine) were taken into account as important parameters in addition to the conventional ones such as the velocity, degree of inlet superheat, inlet opening height, and the liquid level. Bubble motions, which are unsteady, appeared to be mostly determined by the buoyancy and the drag forces. The calculations, though a number of simplifying assumptions were made, reasonably simulated the hydrodynamic behaviors of the two-phase horizontal stream observed in the experiments. The simulated temperature distributions also agreed fairly well with the other's measurements. Non-equilibrium allownaces, evaluated from the simulated temperature distributions, were within the range of those obtained from the existing correlations, and reduced with the increases of the number and size of incoming bubble nuclei due to vigorous flashing.

Ultra-wideband Antipodal Vivaldi Antenna with H-shaped Parasitic Patches (에이치(H)자 형태의 기생패치를 가진 초광대역 안티포달 비발디 안테나)

  • Jung, Dongkeun
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.21 no.9
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    • pp.1642-1648
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    • 2017
  • Ultra-wideband antennas are desired for several applications including satellite communications, radars, remote sensing system, telescopes, and microwave imaging systems. There are many types of wideband antenna structures, but the tapered slot Vivaldi antenna is advantageous in terms of cost, weight, scan angle capabilities, end-fire radiation, and ease of feeding and system integration. In this paper, a modified antipodal Vivaldi antenna is presented. A novel AVA with H-shaped parasitic patches has the capacity to improve the radiation characteristics in the whole operation frequencies. A prototype of the modified antenna with RT/duroid 5880 substrate of a relative dielectric constant (${\epsilon}_r$) of 2.2, and a thickness of 31mil is fabricated and experimentally studied as well. It measures a ${\mid}S_{11}{\mid}$ of less than -10dB and gain of 9-12dBi over 7.8-52.5GHz which shows reasonable agreement with the simulated one.

No Evidence of Association of Interleukin 1A (-889) Genetic Polymorphism with Alzheimer's Disease in Koreans

  • Jhoo, Jin Hyeong;Park, Woong Yang;Kim, Ki Woong;Lee, Kwang Hyuk;Lee, Dong Young;Youn, Jong Chul;Suh, Young Ju;Seo, Jeong-Sun;Woo, Jong Inn
    • Genomics & Informatics
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    • v.2 no.2
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    • pp.81-85
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    • 2004
  • To examine whether the IL-1A (-889) polymorphism associates with a risk for Alzheimer's disease (AD) and acts interactively with the apolipoprotein (APOE) $\epsilon$4 in the development of AD, we performed genotype analyses of the IL-1A and the APOE of the 102 Korean AD patients and 200 Korean non-demented controls. We failed to detect a significant difference in genotypic and allelic frequencies of IL-1A between the AD group and control group. No overexpression of the IL-1A C/T genotype and IL-1A T allele was found when we analyzed the late-onset and early-onset patients, separately. There was no significant genetic interaction between IL-1A polymorphism and the APOE polymorphism. I n conclusion, the IL-1A polymorphism did not contribute to the development of AD independently or interactively with the APOE $\epsilon$4 allele in Koreans.

Propagation Constant and Material constants of Metamaterials (Metamaterial의 전파 상수 및 물질 상수)

  • Lee, Dong-Hyun;Kim, Jae-Hee;Park, Wee-Sang
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.45 no.8
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    • pp.69-74
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    • 2008
  • The propagation constant, which is defined for a double-positive (DPS) material of positive permittivity (${\varepsilon}'$) and permeability (${\mu}'$), is extended and derived for an epsilon-negative (ENG) material (${\varepsilon}'<0,\;{\mu}'>0$), a mu-negative (MNG) material (${\varepsilon}'>0,\;{\mu}'<0$), and a double-negative (DNG) material (${\varepsilon}'<0,\;{\mu}'<0$). By investigating how the permittivity loss (${\varepsilon}"$) and permeability loss (${\mu}"$) terms affect the propagation constant, we determine that the wave in the materials propagates as a right-handed (RH) triad or a left-handed (LH) triad. Regardless of the magnitudes of ${\varepsilon}"$ and ${\mu}"$, DPS and DNG materials become RH and LH media, respectively. However, ENG and MNG materials possess unusual characteristics that both materials become a RH medium when the sign of (${\varepsilon}'{\mu}"+{\varepsilon}"{\mu}'$) is positive and they become a LH medium when the sign is negative.

Interpretation of Geological Samples Based on Ce and Nd Isotopic Ratio (Ce 및 Nd 동위원소비에 의한 지질 시료의 해석법)

  • 이승구;증전창정;청수양;조진화
    • The Journal of the Petrological Society of Korea
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    • v.5 no.2
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    • pp.135-141
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    • 1996
  • La-Ce method is one of new geochronological methods developed recently. La and Ce are one of the rare earth elements, and, with Sm-Nd system. La-Ce system is very useful in understanding the evolution processes of crust and mantle. In this paper, I introduce the basic concept of the La-Ce method, and apply it in clarifying LREE pattern of source material of leuco-granitic gneisses from the Imweon area, Kangwon-do, and K-rich granite from the Anshan area in Liaoning Province, NE China. Sm-Nd data on the Anshan K-rich granites give an age of $3.16{\pm}0.06$ Ga($2{\sigma}$), with initial $^{143}Nd/^{144}Nd$=$0.50846{\pm}0.00005$ (${\epsilon}_{Nd}$=-1.5). On the basis of Ce and Nd isotopic ratio, leucogranitic gneiss and K-rich granite has been fractionated from the source material which had had similar to CHUR (chundritic uniform reservoir). And the initial ${\epsilon}_{Nd}$ value suggest that the crustal formation age of the Liaoning Province area, NE China was early Archean.

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Free Surface Flow in a Trench Channel Using 3-D Finite Volume Method

  • Lee, Kil-Seong;Park, Ki-Doo;Oh, Jin-Ho
    • Journal of Korea Water Resources Association
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    • v.44 no.6
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    • pp.429-438
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    • 2011
  • In order to simulate a free surface flow in a trench channel, a three-dimensional incompressible unsteady Reynolds-averaged Navier-Stokes (RANS) equations are closed with the ${\kappa}-{\epsilon}$ model. The artificial compressibility (AC) method is used. Because the pressure fields can be coupled directly with the velocity fields, the incompressible Navier-Stokes (INS) equations can be solved for the unknown variables such as velocity components and pressure. The governing equations are discretized in a conservation form using a second order accurate finite volume method on non-staggered grids. In order to prevent the oscillatory behavior of computed solutions known as odd-even decoupling, an artificial dissipation using the flux-difference splitting upwind scheme is applied. To enhance the efficiency and robustness of the numerical algorithm, the implicit method of the Beam and Warming method is employed. The treatment of the free surface, so-called interface-tracking method, is proposed using the free surface evolution equation and the kinematic free surface boundary conditions at the free surface instead of the dynamic free surface boundary condition. AC method in this paper can be applied only to the hydrodynamic pressure using the decomposition into hydrostatic pressure and hydrodynamic pressure components. In this study, the boundary-fitted grids are used and advanced each time the free surface moved. The accuracy of our RANS solver is compared with the laboratory experimental and numerical data for a fully turbulent shallow-water trench flow. The algorithm yields practically identical velocity profiles that are in good overall agreement with the laboratory experimental measurement for the turbulent flow.

Phylogenetic analysis of procaryote by uridylate kinase (Uridylate kinase를 이용한 원핵생물의 분류)

  • 이동근;김철민;김상진;하배진;하종명;이상현;이재화
    • Journal of Life Science
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    • v.13 no.6
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    • pp.856-864
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    • 2003
  • The 16S rRNA gene is the most common gene in the phylogenetic analysis of procaryotes. However very high conservative of 16S rRNA has limitation in the discrimination of highly related organisms, hence other molecule was applied in this study and the result was compared with that of 16S rRNA. Three COGs (Clusters of Orthologous of protein) were only detected in 42 procaryotes ; transcription elongation facto. (COG0195), bacterial DNA primase (COG0358) and uridylate kinase (COG0528). Uridylate kinase gene was selected because of the similarity and one single copy number in each genome. Bacteria, belong to same genus, and Archaebacteria were same position with high bootstrap value in phylogenetic tree like the tree of 16S rRNA. However, alpha and epsilon Proteobcteria showed different position and Spirochaetales of Eubarteria was grouped together with Archaebacteria unlike the result of 16S rRNA. Uridylate kinase may compensate the problem of very high conservative of 16S rRNA gene and it would help to access more accurate discrimination and phylogenetic analysis of bacteria.

Microwave Dielectric Properties of Ca(Li1/4Nb3/4)O3-CaTiO3 Ceramics added with Zinc-borosilicate Glass Frit (Zinc-borosilicate Glass Frit 첨가에 따른 Ca(Li1/4Nb3/4)O3-CaTiO3 세라믹스의 마이크로파 유전 특성)

  • Yoon Sang-Ok;Kim Kwan-Soo;Jo Tae-Hyun;Shim Sang-Heung;Park Jong-Guk
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.19 no.6
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    • pp.524-530
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    • 2006
  • $xCa(Li_{1/4}Nb_{3/4})O_{3}-(1-x)CaTiO_{3}$ ceramics were sintered under the presence of zinc-borosilicate(ZBS) glass and resultant microwave dielectric properties were investigated with a view to applying the composition to low-temperature co-fired ceramic(LTCC) technology. The addition of $5{\sim}15wt%$ ZBS glass ensured successful sintering below $900\;^{\circ}C$. In general, increased addition of ZBS glass increased sinterability but it decreased the quality factor($Q{\times}f_{0}$) significantly due to the formation of an excessive liquid and second phases. As for the addition of $CaTiO_3$, the dielectric constant(${\epsilon}_r$) and temperature coefficient of resonant frequency(${\tau}_f$) increased, while the quality factor($Q{\times}f_{0}$) did not show an apparent change. The sintered $0.9Ca(Li_{1/4}Nb_{3/4})O_{3}-0.1CaTiO_{3}$ specimen at $900\;^{\circ}C$ with 10 wt% ZBS glass demonstrated 39.6 in dielectric constant(${\epsilon}_r$), 4,400 in quality factor$(Q{\times}f_{0}),\;and\;-11ppm/^{\circ}C$ in temperature coefficient of resonant frequency(${\tau}_f$).