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SOLUTIONS TO M-POINT BOUNDARY VALUE PROBLEMS OF THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS AT RESONANCE

  • XUE CHUNYAN;DU ZENGJI;GE WEIGAO
    • Journal of applied mathematics & informatics
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    • 제17권1_2_3호
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    • pp.229-244
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    • 2005
  • In this paper, we study the third order ordinary differential equation : $$x'(t)=f(t,x(t),x'(t),x'(t)),t{\in}(0,1)$$ subject to the boundary value conditions: $$x'(0)=x'(\xi),x'(1)=^{m-3}{\Sigma}_{i=1}{{\beta}x'({\eta}i),x'(1)=0}$$. Here ${\beta}_{i}{\in}R,\;^{m-3}{\Sigma}_{i=1}\;{\beta}_{i}\;=\;1,\;0<{\eta}_1<{\eta}_2<{\cdots}<{\eta}_{m-3}<1,\;0<\xi<1$. This is the case dimKer L = 2. When the ${\beta}_i$ have different signs, we prove some existence results for the m-point boundary value problem at resonance by use of the coincidence degree theory of Mawhin [12, 13]. Since all the existence results obtained in previous papers are for the case dimKerL = 1, our work is new.

퍼지관계방정식의 해의 관계성 (On the solutions U$^+$ and U$_+$ of fuzzy relation equation)

  • Jeon, Jong-Duek;Kim, Hyun-Mee
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 1998년도 추계학술대회 학술발표 논문집
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    • pp.27-30
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    • 1998
  • The purpose of this paper is to investigate solutions U$_+$ and U$^+$ for the fuzzy relation equation R$\circ$U= T in cases of R < T, R $\leq$ T, and R = T, when R is irreflexive, U$_+$ ($\chi$$_i$, $\chi$$_k$)=$\bigwedge$[R($\chi$$_i$, $\chi$$_k$) << T($\chi$$_i$, $\chi$$_k$)], U$^+$ ($\chi$$_i$, $\chi$$_k$)=$\bigwedge$[R($\chi$$_i$, $\chi$$_k$)->T($\chi$$_i$, $\chi$$_k$)].

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EXISTENCE, MULTIPLICITY AND UNIQUENESS RESULTS FOR A SECOND ORDER M-POINT BOUNDARY VALUE PROBLEM

  • Feng, Yuqiang;Liu, Sang-Yang
    • 대한수학회보
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    • 제41권3호
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    • pp.483-492
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    • 2004
  • Let : [0, 1] $\times$ [0, $\infty$) $\longrightarrow$ [0, $\infty$) be continuous and a ${\in}$ C([0, 1], [0, $\infty$)),and let ${\xi}_{i}$ $\in$ (0, 1) with 0 < {\xi}$_1$ < ${\xi}_2$ < … < ${\xi}_{m-2}$ < 1, $a_{i}$, $b_{i}$ ${\in}$ [0, $\infty$) with 0 < $\Sigma_{i=1}$ /$^{m-2}$ $a_{i}$ < 1 and $\Sigma_{i=1}$$^{m-2}$ < l. This paper is concerned with the following m-point boundary value problem: $\chi$″(t)+a(t) (t.$\chi$(t))=0,t ${\in}$(0,1), $\chi$'(0)=$\Sigma_{i=1}$ $^{m-2}$ /$b_{i}$$\chi$'(${\xi}_{i}$),$\chi$(1)=$\Sigma_{i=1}$$^{m-2}$$a_{i}$$\chi$(${\xi}_{i}$). The existence, multiplicity and uniqueness of positive solutions of this problem are discussed with the help of two fixed point theorems in cones, respectively.

Population-Based Newborn Hearing Impairment Screening Test Using GJB2 Mutation Analysis

  • Lee, Kyung-Ok;Jeong, Su-Jin;Byun, Ji-Young;Kim, Jeong-Sook;Lee, Hye-Jung;Seong, Hye-Soon;Kim, Kyung-Tae
    • 대한임상검사과학회지
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    • 제39권2호
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    • pp.113-121
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    • 2007
  • 선천성난청은 비교적 흔한(1/1,000) 유전성질환으로 여러 유전자와 관련이 있으며, 최근에는 connexin 26 단백질내의 GJB2 유전자 돌연변이와의 관련성이 보고되고 있다. 유전질환을 예측하기 위한 유전자선별검사를 임상에 적용하기 위해서는 각 해당 국가별로 정상인에서 유전자돌연변이의 빈도를 구하고, 환자의 결과를 비교하여 활용성을 검토한 후 사용하여야 한다. 본 연구에서는 청력검사(TEOAE)가 정상인 신생아에서 GJB2 유전자 돌연변이 빈도를 구하여 screening test를 위한 한국인의 database를 수립하고자 하였다. 검체로는 437 명의 건강한 신생아의 발꿈치를 천자하여 얻은 혈액을 이용하였고, DNA는 Intron 사의 킷트를 사용하여 추출하였으며, GJB2 PCR을 실시한 후 증폭산물(783 bps)은 2% agarose gel로 전기영동을 실시하였고, DNA 자동염기서열분석기를 이용하여 분석을 실시하였다. 총 437명의 한국인 신생아에서 GJB2 유전자 중 8곳의 돌연변이(35delG, 167delT, 235delC, V27I, V37I, M34T, E114G, I203T)를 분석하였으며, 이 중 5곳에서 돌연변이가 발견되었다. 총 437명 중 301명(68.9%)에서 GJB2 유전자돌연변이가 발견되었는데, 그 중 154명이 단일돌연변이였다. V27I 변이가 271명으로 가장 많이 발견되었으며, 대부분의 V27I 변이는 E114G 변이와 함께 나타났다. E114G 변이는 총 146명, I203T 변이는 17명, V37I 변이는 14명, 235delC 변이는 1명의 순으로 나타났다. 이중돌연변이의 대부분은 V27I/E114G였으며, V27I/I203T는 3명에서 나타났고, 삼중돌연변이 V27I/E114G/I203T는 1명에서 발견되었다. 본 연구결과, PCR을 이용한 자동염기분석검사는 GJB2 유전자의 돌연변이 검출에 매우 유용하며, 본 결과는 향 후 신생아 난청선별검사를 위한 한국인의 database로 활용될 수 있을 것으로 사료된다.

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SUPERCYCLICITY OF JOINT ISOMETRIES

  • ANSARI, MOHAMMAD;HEDAYATIAN, KARIM;KHANI-ROBATI, BAHRAM;MORADI, ABBAS
    • 대한수학회보
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    • 제52권5호
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    • pp.1481-1487
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    • 2015
  • Let H be a separable complex Hilbert space. A commuting tuple $T=(T_1,{\cdots},T_n)$ of bounded linear operators on H is called a spherical isometry if $\sum_{i=1}^{n}T^*_iT_i=I$. The tuple T is called a toral isometry if each $T_i$ is an isometry. In this paper, we show that for each $n{\geq}1$ there is a supercyclic n-tuple of spherical isometries on $\mathbb{C}^n$ and there is no spherical or toral isometric tuple of operators on an infinite-dimensional Hilbert space.

A CLASS OF GRADE THREE DETERMINANTAL IDEALS

  • Kang, Oh-Jin;Kim, Joo-Hyung
    • 호남수학학술지
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    • 제34권2호
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    • pp.279-287
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    • 2012
  • Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

Cytoprotective Effect on Oxidative Stress and Inhibitory Effect on Cellular Aging of Terminalia chebula and Uncaria sinensis

  • Na, Min-Kyun;Hong, Nam-Doo;Kamiryo Yuko;Senoo, Yu-Ichiro;Yokoo Seiichi;Ito Shinobu;Miwa Nobuhiko
    • 대한약학회:학술대회논문집
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    • 대한약학회 2003년도 Proceedings of the Convention of the Pharmaceutical Society of Korea Vol.2-2
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    • pp.201.3-201.3
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    • 2003
  • The ethanol extract from the fruit of Terminalia chebula (Combretaceae) and the hook of Uncaria sinensis (Rubiaceae) exhibited significant inhibitory activity on oxidative stress and the age-dependent shortening of the telomeric DNA length. In the peroxidation model using t-BuOOH, human epidermal keratinocytes-neonatal foreskin (HEK-N/F) cells were treated with the T. chebula and U. sinensis extracts. The results showed a notable enhancing effect on the cell viability of 60.5 ${\pm}$ 3.8 and 65.0 ${\pm}$ 3.0%, respectively, by 50 $\mu\textrm{g}$/ml of the extracts. (omitted)

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석영 유리의 파괴 거동에 관한 연구(I) (A Study on the Fracture Behavior of Quartz Glass(I))

  • 최성대;정선환;정영관;김기만;홍영배
    • 한국산업융합학회 논문집
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    • 제10권3호
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    • pp.179-185
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    • 2007
  • Quartz glass are used in semiconductor industries as the reaction furnace, wafer carrier and accessaries. During the process the quartz glass received compression by direct contact with other quartz glass ware and metal as the form of weight itself and vacuum pressure and fatigue by vibrations caused by process. Even as the other ceramic materials quartz glass have high compressive strength but often there happened crack and breakage of quartz glass resulted in a great damage in the process. In this paper investigation will be carried out on fracture behavior of quartz glass under local load to give guideline to prevent unintended fracture of quartz glass.

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