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DISTRIBUTIONAL SOLUTIONS OF WILSON'S FUNCTIONAL EQUATIONS WITH INVOLUTION AND THEIR ERDÖS' PROBLEM

  • Chung, Jaeyoung
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1157-1169
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    • 2016
  • We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

Thermal Phenomenon of $BaMgAl_{10}O_{17}$:$Eu^{2+}$ Blue Phosphor by XANES and Rietveld Method

  • Kim, Kwang-Bok;Koo, Kyung-Wan;Chun, Hui-Gon
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2002.07a
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    • pp.210-213
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    • 2002
  • The blue phosphor, $BaMgAl_{10}O_{17}$:$Eu^{2+}$, showing a blue emission band at about 450 nm were prepared by solid state reaction of BaC $O_3$, A $l_2$ $O_3$, MgO and E $u_2$ $O_3$ with Al $F_3$ as a flux. The thermal quenching of BaMgAl $O_{17}$:E $u^{2+}$ phosphor significantly reduces the intensity of the blue emission. It is reduced by an amount of 50% after heating at around 800$^{\circ}C$ for 1 hr. The red emission in the 580∼720 nm region of $^{5}$ $D_{0}$\longrightarro $w^{7}$ $F_1$ and $^{5}$ $D_{0}$\longrightarro $w^{7}$ $F_2$ transition of $Eu^{3+}$ is produced from the phosphor heated above 1,100$^{\circ}C$. The EPR spectrum also reveals that some part of E $u^{2+}$ ions are oxidized to trivalent ions above 1,100$^{\circ}C$ at around 90 and 140mT. This oxidation evidence is also detected from XANES absorption spectra for $L_{III}$ shell of Eu ions: an absorption peak is at 6,977eV of E $u^{2+}$ and 6,984eV of $Eu^{3+}$. The combined X-ray and neutron data suggests that the new phase of EuMgA $l_{11}$ $O_{19}$ magnetoplumbite structure may be formed by heat treatment.eat treatment.tment.eat treatment.tment.t.

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Path Algorithm for Maximum Tax-Relief in Maximum Profit Tax Problem of Multinational Corporation (다국적기업 최대이익 세금트리 문제의 최대 세금경감 경로 알고리즘)

  • Sang-Un Lee
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.23 no.4
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    • pp.157-164
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    • 2023
  • This paper suggests O(n2) polynomial time heuristic algorithm for corporate tax structure optimization problem that has been classified as NP-complete problem. The proposed algorithm constructs tax tree levels that the target holding company is located at root node of Level 1, and the tax code categories(Te) 1,4,3,2 are located in each level 2,3,4,5 sequentially. To find the maximum tax-relief path from source(S) to target(T), firstly we connect the minimum witholding tax rate minrw(u, v) arc of node u point of view for transfer the profit from u to v node. As a result we construct the spanning tree from all of the source nodes to a target node, and find the initial feasible solution. Nextly, we find the alternate path with minimum foreign tax rate minrfi(u, v) of v point of view. Finally we choose the minimum tax-relief path from of this two paths. The proposed heuristic algorithm performs better optimal results than linear programming and Tabu search method that is a kind of metaheuristic method.

Quantitative Determination of $UO2^{2+}$ with Modified $[Ru(v-bpy)_3]^{2+}$ Polymer Film Electrode (수식된 $[Ru(v-bpy)_3]^{2+}$ 고분자 피막전극을 이용한 U(VI)의 정량)

  • Cha, Seong-Keuck
    • Journal of the Korean Chemical Society
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    • v.44 no.1
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    • pp.17-23
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    • 2000
  • Electrodes of the polycationic film with electropolymerized $[Ru(v-bpy)_3]^{2+}$ having about 1:1 ratio of $PF6^-/ClO_4^-$as the doped counter ions, were modified with xylenol orange and diethylditbiocarbamate by ion exchange which had stability constant as 38.6 and 17.5 respectively. These electrodes were employed in the quantitative multiple determination of U(W) in solution. The working electrode of electrochemical cell for the analytical signal was Pt/p-$[Ru(v-bpy)_3]^{2+}$, ligand, U(VI) with Ag/AgCl reference elecrode. In the stripping voltammetry. electrode process was electron transfer controlled one and calibration curves at the ranges of $1.0{\times}10^{-3}{\sim}1.0{\times}10^{-7}$ M had excellent relationship as 0.99 and relative standard deviation as 5${\sim}$8%.

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Characteristics of Vibrio anguillarum Isolated from Seawater Cultured Rainbow Trout Oncorhynchus mykiss in Korea (해수 사육 무지개송어(Oncorhynchus mykiss)에서 분리된 Vibrio anguillarum의 특성 분석)

  • Chun, Hye-Jin;Kim, Wi-Sik;Cho, Mi-Young;Jung, Sung-Hee;Han, Hyun-Ja
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.51 no.3
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    • pp.254-261
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    • 2018
  • From 2014 to 2017, mortalities of seawater-cultured rainbow trout Oncorhynchus mykiss, were observed in the Goheung and Jeju areas of Korea, with Vibrio anguillarum (seven strains: RT1, 2, 3, 4, 5, 6, and 7) identified as the etiological agent. The phenotypic (based on API 20NE, API ZYM, and E-test kits), serotypic (slide agglutination tests with O1, O2, O3, O4, and O7 antisera), and genotypic (16S rRNA and ompU sequencing) characteristics of the seven RT strains were analyzed and compared to those of seven additional V. anguillarum stains (SF, isolated from sweet fish; FM, isolated from flathead mullet; ATCC43305; ATCC43311; ATCC43307; ATCC43308; and KCTC2711). The phenotypes of the RT strains showed variance, while the slide agglutination tests of the RT1-7, SF, and FM strains all showed positive reactions with serotype O1 antiserum. The 16S rRNA and ompU sequences of the RT1-7, SF, and FM strains were affiliated with V. anguillarum ATCC43305 (Serotype O1), but the ompU sequence of the SF strain differed from those of the RT1-7, FM, and ATCC43311 strains, including one amino acid substitution. We thus confirmed that serotype O1 V. anguillarum, with multiple phenotypes, continues to infect seawater-cultured rainbow trout in Korea.

Sewage disposal system management policy in Korea (우리나라의 하수도사업현황 및 시책방향)

  • 류지영
    • Journal of environmental and Sanitary engineering
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    • v.10 no.1
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    • pp.1-11
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    • 1995
  • We had passed through a serious water pollution with a rapid urbanization and industrialization in the 1960's. Seoul Chunggyechun Sewage Disposal System set uP in 1966 and finished in 1976, as the first sewage disposal system in Korea, had covered only 4 percentage of the sewage disposal system per capita for 10 years. Through holding the Asian Games in 1986 and the Olympic Games in 1988, we expanded the sewage disposal system so that it became increased 18 percentage of the population in 1986. Finally, we have installed about 60 sewage disposal system by 1994 for a large environmental investment which was critically caused by "Phenol Accident in Nakdong River" . Now, the sewage disposal system per capita covers 42 percentage and the activity for water quality improvement is going on rapidly. The method of sewage disposal is mainly "activated sludge process" . However, the technical ability for the sewage disposal has largely developed since 1991 so the "extended aeration process" is used in Po$\v{u}$n, Tangyang, Mun$\v{u}$i, "rotating biological contact process" in Onch$\v{u}$ng, Pukok, and "oxidation ditch process" in K$\v{o}$ch'ana.

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Charge/discharge Properties of $Li_xV_3O_8$ Composite Cathode for Lithium Polymer Batteries (리튬 폴리머 전지용 $Li_xV_3O_8$ Composite Cathode의 충방전 특성)

  • Park, B.G.;Kim, J.U.;Park, G.C.;Gu, H.B.
    • Proceedings of the KIEE Conference
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    • 1997.07d
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    • pp.1591-1593
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    • 1997
  • The purpose of this study is to research and develop $Li_xV_3O_8$ composite cathode for lithium polymer battery. We investigated electrochemical, interfacial properties and charge/discharge cycling of $Li_xV_3O_8$/SPE/Li cell. The radius of semicircle associated with the interfacial resistance of $Li_xV_3O_8$/SPE/Li cell increased very slowly during discharge process from 100% SOC to 90% SOC. And then the cell resistance was increased at discharge process from 10% SOC to 0% SOC. The discharge capacity based on $Li_xV_3O_8$ was 212mAh/g at 15th cycle. The $Li_xV_3O_8$/SPE/Li cell has a good properties.

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Low operating voltage and long lifetime organic light-emitting diodes with vanadium oxide $(V_2O_5)$ doped hole transport layer

  • Yun, J.Y.;Noh, S.U.;Shin, Y.C.;Baek, H.I.;Lee, C.H.
    • 한국정보디스플레이학회:학술대회논문집
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    • 2006.08a
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    • pp.1038-1041
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    • 2006
  • We report low operating voltage and long lifetime organic light-emitting diodes (OLEDs) with a vanadium oxide $(V_2O_5)-doped$ N,N'-di(1-naphthyl)- N,N'-diphenylbenzidine $({\alpha}-NPD)$ layer between indium tin oxide and ${\alpha}-NPD$. At a luminance of $1000\;cd/m^2$, $V_2O_5$ doped ${\alpha}-NPD$ device shows a operation voltage of 5.1V, while the device without $V_2O_5$ shows 5.8V. The $V_2O_5$ doped $({\alpha}-NPD)$ device also shows a longer lifetime and smaller operation voltage variation over time. It is suggested that the improved device performance can be attributed to the higher hole-injection efficiency and stability of the $V_2O_5$ doped $({\alpha}-NPD)$ layer.

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TIME VARIATION OF SiO (v=1, J=2-1) MASERS OF LONG PERIOD VARIABLES

  • LEE SANG GAK;KIM EUNHYEUK;LEE HYUNG MOK
    • Journal of The Korean Astronomical Society
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    • v.27 no.2
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    • pp.133-146
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    • 1994
  • We have detected a SiO maser line (v=1, J=2- 1) for 15 stars out of about 80 long period variables in the wide range of period. No new sources are detected; all detected sources are variables with period longer than 300 days; no evidence is found that the dust grains in the outer envelope have influenced on this line. The time variation of this maser line for 7 stars, T Cep, ${\mu} Cep$, U Her, R Leo, R Lmi, U Ori, and R Ser is observed and compared with optical light curve at the same epoch of maser observation. No universial relation between the time variation and the optical light curve is found. It implies that the radiation from a central star does not much play an important role for the direct pumping of the SiO maser line.

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n-ZnO/p-GaN 이종접합 LED의 전기.광학적 특성

  • Kim, Jun;Song, Chang-Ho;Sin, Dong-Hwi;Jo, Yeong-Beom;Bae, Nam-Ho;Byeon, Chang-Seop;Kim, Seon-Tae
    • Proceedings of the Materials Research Society of Korea Conference
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    • 2011.10a
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    • pp.41.1-41.1
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    • 2011
  • 본 연구에서는 MOCVD법으로 사파이어 기판위에 u-GaN를 성장한 후 Mg을 도핑시켜 p-GaN를 성장하고, RF 스퍼터를 이용하여 n-ZnO를 도포하여 n-ZnO/p-GaN 이종접합을 형성한 후 진공증착기를 이용하여 Au/Ni를 증착시켜 발광다이오드(LED)를 제작하고 전기 광학적 특성을 조사하였다. 두께가 500 nm인 u-GaN 위에 성장된 p-GaN의 운반자 농도는 $1.68{\times}10^{17}\;cm^{-3}$ 이었다. 그리고 150, 300 nm 두께의 p-GaN에 대하여 측정된 DXRD 반치폭은 각각 450 arcsec, 396 arcsec 이었고, 상온에서 2.8~3.0 eV 영역에서 Mg 억셉터와 관련된 광루미네센스가 검출되었다. RF 스퍼터링에 의해 0.7 nm/min의 속도로 증착된 n-ZnO 박막은 증착 두께에 따라 비저항이 27.7 $m{\Omega}{\cdot}cm$ 에서 6.85 $m{\Omega}{\cdot}cm$ 까지 감소하였다. 그리고 n-ZnO 박막은 (0002)면으로 우선 배향되었으며, 상온에서 에너지갭 관련된 광루미네센스가 3.25 eV 부근에서 주되게 검출되었다. n-ZnO/p-GaN 이종접합 LED의 전류전압 특성곡선은 다이오드 방정식에 만족하는 특성을 나타내었다. 다이오드 지수는 3 V 이하 영역에서 1.64, 3~5 V 영역에서 0.85이었다. 그리고 5 V 이상 영역에서 공간전하의 제한을 받았으며, 다이오드 지수는 3.36이었다. 한편, 역방향 전류전압 특성은 p-GaN 박막의 두께에 영향을 받았으며, p-GaN 박막의 두께가 150, 300 nm 일 때 각각의 누설 전류는 $1.3{\times}10^{-3}$ mA와 $8.6{\times}10^{-5}$ mA 이었다. 상온에서 측정된 EL 스펙트럼의 주된 발광피크는 430 nm이었고, 반치폭은 49.5 nm이었다.

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