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RESEARCH ON NORMAL STRUCTURE IN A BANACH SPACE VIA SOME PARAMETERS IN ITS DUAL SPACE

  • Gao, Ji
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.465-475
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    • 2019
  • Let X be a Banach space and $X^*$ be its dual. In this paper, we give relationships among some parameters in $X^*$: ${\varepsilon}$-nonsquareness parameter, $J({\varepsilon},X^*)$; ${\varepsilon}$-boundary parameter, $Q({\varepsilon},X^*)$; the modulus of smoothness, ${\rho}_{X^*}({\varepsilon})$; and ${\varepsilon}$-Pythagorean parameter, $E({\varepsilon},X^*)$, and weak orthogonality parameter, ${\omega}(X)$ in X that imply uniform norm structure in X. Some existing results are extended or approved.

On the harris ergodicity of a class of markov processes

  • Lee, Chan-Ho
    • Journal of the Korean Mathematical Society
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    • v.32 no.1
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    • pp.85-92
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    • 1995
  • Supppose ${X_n}$ is a Markov process taking values in some arbitrary state space $(S, F)$ with temporarily homogeneous transition probabilities $p^n(x, A) = P(X_n \in $A\mid$X_0 = x), x \in S, A \in F$. Write $p(x, A) for p^1(x, A)$.

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Gottlieb groups of spherical orbit spaces and a fixed point theorem

  • Chun, Dae Shik;Choi, Kyu Hyuck;Pak, Jingyal
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.303-310
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    • 1996
  • The Gottlieb group of a compact connected ANR X, G(X), consists of all $\alpha \in \prod_{1}(X)$ such that there is an associated map $A : S^1 \times X \to X$ and a homotopy commutative diagram $$ S^1 \times X \longrightarrow^A X $$ $$incl \uparrow \nearrow \alpha \vee id $$ $$ S^1 \vee X $$.

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Structural properties of GeSi/Si heterojunction compound semiconductor films by using SPE (SPE법을 통해 형성된 $Ge_xSi_{1-x}/Si$이종접합 화합물 반도체의 결정분석)

  • 안병열;서정훈
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.4 no.3
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    • pp.713-719
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    • 2000
  • In order to Prepare the$Ge_xSi_{1-x}/Si$(111) heterosructure by solid phase epitaxy (SPE), about 1000A of Au and about 1000A Ge were sequentially deposited on the Si(111) substrate. The resulting Ge/Au/Si(111) samples were isochronically annealed in the high vacuum condition. The behaviors of Au and Ge during thermal annealing and the structural Properties of $Ge_xSi_{1-x}$ films were characterized by Auger electron spectroscopy (AES), X-ray diffraction (XRD) and high resolution transmission electron microscopy (TEM). The a-Ge/Au/Si(111) structure was converted to the Au/GeSi/Si(111) structure. Defects such as stacking faults, point defects and dislocations were found at the GeXSil-X(111) interface, but the film was grown epitaxially with the matching face relationship of $Ge_xSi_{1-x}/$(111)/Si(111). Twin crystals were also found in the $Ge_xSi_{1-x}/$(111) matrix.

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Effects of Ni Addition on the Microstructures and Magnetic Properties of Fe70-xPd30Nix High-Temperature Ferromagnetic Shape Memory Alloys

  • Lin, Chien-Feng;Yang, Jin-Bin
    • Journal of Magnetics
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    • v.17 no.2
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    • pp.86-95
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    • 2012
  • This study investigated the effects of adding a third alloying element, Ni, to create $Fe_{70-x}Pd_{30}Ni_x$ (x = 2, 4, 6, 8 at.% Ni) ferromagnetic shape memory alloys (FSMAs). The Ni replaced a portion of the Fe. The $Fe_{70-x}Pd_{30}Ni_x$ alloys were homogenized through hot and cold forging to gain a ~38% reduction in thickness, next they were solution-treated (ST) with annealing recrystallization at $1100^{\circ}C$ for 8 h and quenched in ice brine, and then aged at $500^{\circ}C$ for 100 h. Investigation of the microstructures and magnetostriction indicated that the greater Ni amount in the $Fe_{70-x}Pd_{30}Ni_x$ alloys reduced saturation magnetostriction at room temperature (RT). It was also observed that it was more difficult to generate annealed recrystallization. However, with greater Ni addition into the $Fe_{70-x}Pd_{30}Ni_x$ (x = 6, 8 at.% Ni) alloys, the $L1_0+L1_m$ twin phase decomposition into stoichiometric $L1_0+L1_m+{\alpha}_{bct}$ structures was suppressed after the $500^{\circ}C$/100 h aging treatment. The result was that the $Fe_{70-x}Pd_{30}Ni_x$ (x = 6, 8 at.% Ni) alloys maintained a high magnetostriction and magnetostrictive susceptibility (${\Delta}{\lambda}{_\parallel}{^s}/{\Delta}H$) after the alloys were aged at $500^{\circ}C$ for 100 h. This magnetic property of the $Fe_{70-x}Pd_{30}Ni_x$ (x = 6, 8 at.% Ni) alloys make it suitable for application in a high temperature (T > $500^{\circ}C$) and high frequency environments.

Empirical Analysis on Radio Communication Range and Vehicle Ratio in V2X Environment (무선 통신 가능 범위와 V2X 차량 비율에 관한 경험적 분석)

  • Park, Sang-Ung;Kim, Joo-Young;Na, Sung-Yong;Lee, Seung-Jae
    • The Journal of The Korea Institute of Intelligent Transport Systems
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    • v.15 no.5
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    • pp.29-41
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    • 2016
  • V2X environment is the most popular part of the C-ITS based on the high technologies. To evaluate V2X environment technologies, radio communication range and market penetration rate of V2X vehicle are used. This paper studies the V2X environment considering various traffic congestion level, radio communication range and market penetration rate of V2X vehicle using the microscopic simulation (VISSIM) based on proper parameters and algorithm. In conclusion, V2X environment can reduce the congestion in proper traffic volume. However, if traffic volume is almost near the capacity, even V2X environment can't relieve the road condition. Furthermore, increase of the radio communication range does not always mean the decrease of the congestion and even with the small market penetration rate, it can also have an impact on the V2X environment. This result will be the foundation for the V2X environment much better.

Crystallographic and Mossbauer Studies of Magnetic Garnet $Y_{3-x}Bi_xFe_5O_{12}$ by a Sol-Gel Method (Sol-gel 합성에 의한 자성 garnet $Y_{3-x}Bi_xFe_5O_{12}$의 결정학적 및 Mossbauer 분광학 연구)

  • 엄영란;김철성;이재광
    • Journal of the Korean Magnetics Society
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    • v.8 no.4
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    • pp.203-209
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    • 1998
  • Crystallographic and magnetic properties of single phase garnet $Y_{3-x}Bi_xFe_5O_{12}$ (x=0.0, 0.25, 0.5, 0.75, 1.0) were studied by using x-ray diffraction, Mossbauer spectroscopy and vibrating sample magnetometer (VSM). Ultra-fine polycrystalline cubic samples have been prepared by sol-gel method. The lattice constant increase linearly with increasing an amount of Bi. Annealing temperature was larger than 800 $^{\circ}C$ for the growth of a single-phase garnet powder. The second phase of garnet, $(BiFeO_3)$, was at 1000 $^{\circ}C$ for x=0.75, and 950 $^{\circ}C$ for x=1.00. From Mossbauer spectroscopy and VSM measurements, the magnetization and the coercivity were decreased and the Curie temperature $Y_{3-x}Bi_xFe_5O_{12}$(x=0.0, 0.25, 0.5, 0.75, 1.0) was slightly increased as increasing the Bi content.

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Electrical Transport Properties of LaNi1-xTixO3(x∼0.5) Ceramics (LaNi1-xTixO3(x∼0.5) 세라믹스의 전기전도 특성)

  • Jung, Woo-Hwan
    • Korean Journal of Materials Research
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    • v.19 no.4
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    • pp.186-191
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    • 2009
  • Thermoelectric power and resistivity are measured for the perovskite $LaNi_{1-x}Ti_xO_3$ ($x{\leq}0.5$) in the temperature range 77 K - 300 K. The measured thermoelectric power of $LaNi_{1-x}Ti_xO_3$ ($x{\leq}0.5$) increases linearly with temperature and is represented by A + BT. The x = 0.1 sample showed metallic behavior, the x = 0.3 showed metal and insulating transition around 150 K, and x = 0.5 showed insulating behavior the over the whole temperature range. The electrical resistivity of x = 0.1 shows linear temperature dependence over the whole temperature range and $T^2$ dependence. On the other hand, the electrical resistivity of x = 0.3 shows a linear relation between $ln{\rho}$ and $T^{-1/4}$ (variable range hopping mechanism) in the range of 77 K to 150 K. For x = 0.5, the temperature dependence of resistivity is characteristic of insulating materials; the resistivity data was fitted to an exponential law, such as ln(${\rho}/T$) and $T^{-1}$, which is usually attributed to a small polaron hopping mechanism. These experimental results are interpreted in terms of the spin polaron (x = 0.1) and variable range hopping (x = 0.3) or small polaron hopping (x = 0.5) of an almost localized $Ni^{3+}$ 3d polaron.

Gelatinization Properties of Starch Dough with Moisture Content, Heating Temperature and Heating Time (수분함량, 가열온도 및 가열시간에 따른 전분 반죽의 호화특성)

  • Lee, Boo-Yong;Lee, Chang-Ho;Lee, Cherl-Ho
    • Korean Journal of Food Science and Technology
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    • v.27 no.3
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    • pp.428-438
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    • 1995
  • The gelatinization properties of corn and waxy corn starch doughs were examined at various moisture contents, heating temperatures and heating times. The onset temperatures of gelatinization with 1% CMC using Brabender Amylograph were $64^{\circ}C$ for both corn and waxy corn starch. In the gelatinization properties using DSC, onset temperature$(T_o)$, maximum peak temperature$(T_p)$, completion temperature$(T_c)$ and enthalpy of the corn starch were $68.15^{\circ}C,\;74.01^{\circ}C,\;85.65^{\circ}C$ and $3.2\;cal/gram$ respectively. While those of the waxy corn starch were $68.24^{\circ}C,\;75.43^{\circ}C,\;93^{\circ}C$ and $4.2\;cal/gram$ respectively. In enzymatic analysis, when the moisture content increased from 36% to 52% and heating temperature from $60^{\circ}C$ to $100^{\circ}C$, the gelatinization degree of starch dough increased from about 10% to about 62%. The gelatinization degree of waxy corn starch dough was $15{\sim}20%$ higher than that of corn starch dough under the same gelatinization conditions. The regression equations of gelatinization degree (Y) of starch dough in the range of $36{\sim}52%$ moisture content $(X_1)\;60{\sim}100^{\circ}C$ heating temperature $(X_2)\;and\;0{\sim}2.0$ min heating time $(X_3)$ were examined using response surface analysis. The regression equation of corn starch dough was: $Y=28.659+8.638\;X_}+15.675\;X_2+7.770\;X_3-1.620\;{X_1}^2+10.790\;X_1X_2-4.220\;{X_2}^2+0.510\;X_1X_3+1.980\;X_2X_3-6.850\;{X_3}^2\;(R^2=0.9714)$ and that of waxy corn starch dough was: $Y=32.617+12.535\;X_1+20.470\;X_2+8.608\;X_3+4.093\;{X_1}^2+13.550\;X_1X_2-4.467\;{X_2}^2+1.560\;X_1X_3+2.160\;X_2X_3-9.527\;{X_3}^2$\;(R^2=0.9621)$. As the moisture content, heating temperature and heating time increased, the reaction rate constant(k) of gelatinization increased. The greatest reaction rate constant was observed at initial 0.5 min heating time of 1st gelatinization stage. At the heating temperature of $90^{\circ}C$, gelatinization of starch dough was completed almost in the initial 0.5 min heating time. The reaction rate constant of waxy corn starch dough was higher than that of corn starch dough under the same gelatinization conditions. At the 52% moisture content, the regression equation between reaction rate constant(k) and heating temperature(T) for corn starch dough was $log\;k=11.1140-4.1226{\times}10^3(1/T)$ (r=-0.9520) and that of waxy corn starch dough was $log\;k=10.1195-3.7090{\times}10^3(1/T)$ (r=-0.9064).

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The Measurement and Evaluation of X-ray Characteristics of Cadmium Sulfide as a Multi-function Dosimeter (다기능 선량계로서의 Cadmium sulfide의 X-선에 대한 특성 평가)

  • Park, Sung-Kwang;Park, Young-Min;Cho, Heung-Lae;Nam, Sang-Hee
    • Progress in Medical Physics
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    • v.14 no.3
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    • pp.161-166
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    • 2003
  • To evaluate the performance of cadmium sulfide as a multi-function X-ray dosimeter, we made an X-ray detector that was based on cadmium sulfide using evaporation technology, and measured its response to X-ray exposure. The voltages of cadmium sulfide were measured on the various X-ray tube potentials, X-ray tube currents and exposure times. The regression analysis of the voltage response of CdS on the tube-potential variation was y=0.0995x-0.1146 ($R^2$=0.9595, $\sigma$=0.08, standard error=2%) and the regression analysis of the voltage response of CdS on the tube-potential variation was y=0.0439x+1.1891 ($R^2$=0.9021, $\sigma$=0.04, standard error=1.8%) The regression analysis of the voltage response of CdS on the X-ray exposure time variation was y=8.2853+5.5878 ($R^2$=0.7287, $\sigma$=0.06, standard error=1.9%). In conclusion, cadmium sulfide responded linearly to the variation X-ray conditions, suggesting cadmium sulfide to be a feasible X-ray sensor of multi-function dosimeter related instruments.

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