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CHARACTERIZATION OF FUNCTIONS VIA COMMUTATORS OF BILINEAR FRACTIONAL INTEGRALS ON MORREY SPACES

  • Mao, Suzhen;Wu, Huoxiong
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1071-1085
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    • 2016
  • For $b{\in}L^1_{loc}({\mathbb{R}}^n)$, let ${\mathcal{I}}_{\alpha}$ be the bilinear fractional integral operator, and $[b,{\mathcal{I}}_{\alpha}]_i$ be the commutator of ${\mathcal{I}}_{\alpha}$ with pointwise multiplication b (i = 1, 2). This paper shows that if the commutator $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 is bounded from the product Morrey spaces $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to the Morrey space $L^{q,{\lambda}}({\mathbb{R}}^n)$ for some suitable indexes ${\lambda}$, ${\lambda}_1$, ${\lambda}_2$ and $p_1$, $p_2$, q, then $b{\in}BMO({\mathbb{R}}^n)$, as well as that the compactness of $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 from $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to $L^{q,{\lambda}}({\mathbb{R}}^n)$ implies that $b{\in}CMO({\mathbb{R}}^n)$ (the closure in $BMO({\mathbb{R}}^n)$of the space of $C^{\infty}({\mathbb{R}}^n)$ functions with compact support). These results together with some previous ones give a new characterization of $BMO({\mathbb{R}}^n)$ functions or $CMO({\mathbb{R}}^n)$ functions in essential ways.

Magnetic properties of $(Nd_{1-x}R_x)_2Fe_{14}B$ (R=Y, Pr) ($(Nd_{1-x}R_x)_2Fe_{14}B$ (R=Y, Pr)의 자기특성)

  • 김만중;김윤배;김희태;김택기
    • Journal of the Korean Magnetics Society
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    • v.8 no.5
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    • pp.271-274
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    • 1998
  • Spin reorientation and magnetocrystalline anisotropy of magnetically aligned $(Nd_{1-x}R_x)_2Fe_{14}B$ (R=Y, Pr) power were studied. The spin reorientation temperature $(T_{SR})$ of $(Nd_{1-x}R_x)_2Fe_{14}B$ decreases linearly by increasing Pr-substitution with the ratio of ${\Delta}T_{SR}=-1.35$ K/Pr at.% in composition range of 0$\leq$x$\leq$0.75. The spin reorientation temperature of $(Nd_{1-x}R_x)_2Fe_{14}B$ decreases by increasing Pr-substitution to 118 K (x=0.5) then increases to 122 K (x=0.75). The spin reorientation angle at 4.2 K decreases by increasing rare earth substitution with the ratio of $\Delta$SRA=-0.073$^{\circ}$/Y at.% and $\Delta$SRA=-0.258$^{\circ}$/Pr at.% in composition range of 0$\leq$x$\leq$0.5. The spin reorientation is expected to disappear at x$\geq$0.9 in case of $(Nd_{1-x}R_x)_2Fe_{14}B$ and at x$\geq$0.8 in case of $(Nd_{1-x}R_x)_2Fe_{14}B$.

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5.0 inch WVGA Top Emission AMOLED Display for PDA

  • Lee, Kwan-Hee;Ryu, Seoung-Yoon;Park, Sang-Il;Ryu, Do-Hyung;Kim, Hun;Song, Seung-Yong;Chung, Bo-Yong;Park, Yong-Sung;Kang, Tae-Wook;Kim, Sang-Chul;Cho, Yu-Sung;Park, Jin-Woo;Kwon, Jang-Hyuk;Chung, Ho-Kyoon
    • 한국정보디스플레이학회:학술대회논문집
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    • 2003.07a
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    • pp.7-10
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    • 2003
  • Samsung SDI has developed a full color 5.0" WVGA AMOLED display with top emission and a super fine pitch of 0.1365mm(l86ppi), the world's highest resolution OLED display ever reported to date. Scan driver circuits and demux circuit were integrated into the display panel, using low temperature poly-Si TFT CMOS technology, and data driver circuit were mounted using COG chips. Peak luminescence was greater than 300cd/ $m^2$ with power consumption of 500mW with 30% of the pixels on illuminated.

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Space Group $R\={3}c$ = $R\={3}2/c$(167) and the Crystal Structure of Tris(1,2,3,4-tetraphenylbuta-1,3-dienyl)cyclotriphosphazene (Space Group $R\={3}c$(167)과 Tris(1,2,3,4-tetraphenylbuta-1,3-dienyl)cyclotriphosphazene의 結晶構造)

  • Kim, Young-Sang;Ko, Jae-Jung;Kang, Sang-Ook;Lee, Young-Joo;Kang, Eu-Gene;Han, Won-Sik;Park, Young-Soo;Suh, Il-Hwan
    • Korean Journal of Crystallography
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    • v.15 no.1
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    • pp.9-17
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    • 2004
  • There are 25 space groups in the trigonal system. Eighteen out of them have a lattice letter P displaying only hexagonal axes, wherease the remaining seven rhombohedral space groups R3(146), $R\={3}$(148), R32(155), R3m(160), R3c(161), $R\={3}m$(166) and $R\={3}c$(167) are described with two corrdinate systems, first with hexagonal axes having three lattice points (0, 0, 0), (2/3, 1/3, 1/3), (1/3, 2/3, 2/3) and second with primitive rhombohedral axes. In this paper, the space group $R\={3}c$ is discussed and the crystal structure of a compound, tris(1,2,3,4-tetraphenylbuta-1,3-dienyl)cyclotriphosphazene, $C_{84}H_{60}N_3P_3$, belonging to the space group $R\={3}c$ is elucidated with both hexagonal and rhombohedral cells.

The Effect of waste Oyster Shell on Anaerobic Composting of Garbage (굴 패각이 음식쓰레기의 혐기성 퇴비화에 미치는 영향)

  • Kim, Nam-Chan;Han, Se-Hyun
    • Journal of the Korea Organic Resources Recycling Association
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    • v.8 no.3
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    • pp.89-96
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    • 2000
  • Waste oyster shell was used to study the applicability on anaerobic composting of garbage. Experiment was conducted with five anaerobic reactors. After garbage and compost for inoculation were mixed, waste oyster shell was added into mixed waste in mesophillic temperature for 60 days with 30%, 60% respectively. The amount of produced methane gas, gas composition, organic removal efficiency and pH were measured. Result showed that the amounts of produced gas were 0.62 l /g-VS in R-1, 0.63 l /g-VS in R-2, 0.16 l /g-VS in R-3, 0.75 l /g-VS in R-4, 0.21 l /g-VS in R-5 and the amounts of produced methane gas were 0.32 l /g-VS in R-1, 0.37 l /g-VS in R-2, 0.04 l /g-VS in R-3, 0.42 l /g-VS in R-4, 0.05 l /g-VS in R-5. Proportion of mathane gas which determines the efficiency of anaerobic composting was over 55%. pH were 6.0~8.0 in R-2 and R-4 which contained 30% of waste oyster shell and pH were increased over 8.5 in R-3 and R-5 which contained 60% of waste oyster shell. Since pH were so high and it had a negative effect on microbial growth, anaerobic reaction were not well operated in R-3 and R-5.

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An Analysis on the R&D Productivity and Efficiency of Korea: Focused on Comparison with the OECD Countries (우리나라의 R&D 생산성 및 효율성 분석: OECD 국가와의 비교를 중심으로)

  • Kim, Young-H.;Kim, Sun-G.
    • Journal of Technology Innovation
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    • v.19 no.1
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    • pp.1-27
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    • 2011
  • This paper aims to measure and analyze R&D productivities and efficiencies of 17 major OECD countries including Korea over the 1984-2008 period by using the Malmquist Productivity Index and Data Envelopment Analysis, classifying R&D performance into an output and outcome aspects. It also searches the Korea's current status and characteristics in each R&D stage to enhance Total Factor Productivity (TFP) compared with other developed countries. Our major findings are the followings: (i) Korea's productivity index of R&D input vis-a-vis R&D output is very high (13.39% annual growth rate) compared with those of major advanced countries, whereas the annual average of efficiency index is very low (0.33), i.e. Korea's technical efficiency index has risen to 0.83 at the last time series started at 0.10 point and come up to the level of major advanced countries. (ii) the Korea's productivity index of R&D output vis-a-vis R&D outcome is very low (14.02% annual reduction rate) compared with those of major advanced countries, whereas the annual average of efficiency index is very high (0.22), i.e. Korea's integrated frontier technical efficiency index has dropped to 0.057 at the last time series started at 1.00 point and coming up to the level of major advanced countries. (iii) The productivity of R&D input vis-a-vis R&D outcome is positively correlated with that of R&D output vis-a-vis R&D outcome and the growth of R&D input factors. In a nutshell, it implicates that the effort to take advantage of R&D outputs, namely establishing the diffusion and commercialization system of technical knowledge to the level of developed countries, should be strengthened over that on the growth of R&D investment and output for enhancing R&D productivity and efficiency in Korea.

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Comparison of shaping ability between various hybrid instrumentation methods with ProTaper (ProTaper를 사용한 다양한 hybrid instrumentation methods의 근관성형 효율 비교)

  • Hong, Eun-Sook;Park, Jeong-Kil;Hur, Bock;Kim, Hyeon-Cheol
    • Restorative Dentistry and Endodontics
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    • v.31 no.1
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    • pp.11-19
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    • 2006
  • The purpose of this study was to compare and evaluate the shaping abilities of various hybrid instrumentation method using constant tapered file systems with $ProTaper\^{(R)}$ S1 and the difference between experts and inexperienced clinicians in use of NiTi file. Three hybrid methods used in this study were composed of $ProTaper\^{(R)}\;S1\;and\;K-Flexofile\^{(R)}\;(group S),\;ProTaper\^{(R)}\;S1\;and\;HeroShaper\^{(R)}\;(group\;H),\;and\;ProTaper\^{(R)}\;S1\;and\;ProFile\^{(R)}\;(group\;P)$respectively. The $ProTaper\^{(R)}$-alone method (group C) was introduced as a control group. After canal preparation, the lapse of time was recorded. The images of pre- and post-operative canal were scanned and superimposed. Amounts of instrumented canal widths and centering ratio were measured at apical 1, 2 and 3 mm levels and statistical analysis was performed In this study. both of the group C and S took more time to prepare canals than other groups, Inexperienced operators required more time for the entire preparation with the groups C and H than the experienced (p<0.05). And the centering ratio of group P were preferable to $ProTaper\^{(R)}$-alone method or the hybrid technique using stainless steel files. As such, within experienced operators, group H also showed better results in addition to the group P. Under these condition, the hybrid methods of each the $ProFile^{(R)}$ system and $HeroShaper^{(R)}$ with ProTaper are recommendable comparative to $ProTaper\^{(R)}$-alone method. According to the results, the hybrid instrumentation method is a more appropriate method of canal preparation than single file system for narrow or curved canals.

On Semicommutative Modules and Rings

  • Agayev, Nazim;Harmanci, Abdullah
    • Kyungpook Mathematical Journal
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    • v.47 no.1
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    • pp.21-30
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    • 2007
  • We say a module $M_R$ a semicommutative module if for any $m{\in}M$ and any $a{\in}R$, $ma=0$ implies $mRa=0$. This paper gives various properties of reduced, Armendariz, Baer, Quasi-Baer, p.p. and p.q.-Baer rings to extend to modules. In addition we also prove, for a p.p.-ring R, R is semicommutative iff R is Armendariz. Let R be an abelian ring and $M_R$ be a p.p.-module, then $M_R$ is a semicommutative module iff $M_R$ is an Armendariz module. For any ring R, R is semicommutative iff A(R, ${\alpha}$) is semicommutative. Let R be a reduced ring, it is shown that for number $n{\geq}4$ and $k=[n=2]$, $T^k_n(R)$ is semicommutative ring but $T^{k-1}_n(R)$ is not.

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