• 호남수학학술지
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• 제39권1호
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• pp.93-100
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• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• 대한두경부종양학회지
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• 제24권1호
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• pp.33-42
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• 2008

Head and neck squamous cell carcinoma(HNSCC) is notorious for its poor outcome and increasing incidence. But, the studies of cytogenetic analysis in HNSCC are relatively rare, because of difficulties in culturing solid tumor cells and complexity in chromosomal DNA abberations associated with the lesions. The purpose of this study is to evaluate the location of chromosomal aberrations in Korean HNSCC cell lines (SNU-1041, 1066, and 1076) with comparative genomic hybridization(CGH) and array based CGH(array-CGH). Chromosomal gains of 3q23-q27, 5p13-p15.3, 7p21-pter, 8q11.2-q12, 8q21.1-qter, 9q22-q34, 16q22-q24, and 20q11.2-qter, as well as chromosomal losses on 3p10-p14 were found in all 3 SNU cell lines. Losses on 3p15- p23, 4q22-q27, 4q31.3-qter, 6q14-q15, 7q31-q34, 8p12-pter, 18q21-q23, and 21q11.2-q12 were observed in 2 of 3 cell lines. In array-CGH, many genes were altered including gains of PIK3CA, MYC, EVI1, MAD1L1 genes and losses of SERPIN genes. These aberrations of gene and chromosome coincide with other results of study, generally. These data about the patterns of chromosomal aberrations could be a basic step for understanding more detailed genetic events in the carcinogenesis and also provide information for diagosis and treatment in HNSCC.

• 충청수학회지
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• 제1권1호
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• pp.27-32
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• 1988

In this paper, we study the multipliers of $A^p_q$ into $L^{p^{\prime}}$ when 0 < p' < p. For this purpose, we study the condition on the measure ${\mu}$ satisfying $A^p_q{\subset}A^{p^{\prime}}(d{\mu})$. It turns out that the quotient $k_q={\mu}/v_q$ over hyperbolic ball of radius less than 1 belongs to $L^s_q$, where $\frac{1}{s}+\frac{p^{\prime}}{p}=1$. For the proof, we replace the norm of $k_q$ by the Riemann sum, and then use a result of interpolation theory.

• 대한수학회보
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• 제50권3호
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• 충청수학회지
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• 제26권2호
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• 호남수학학술지
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• 제33권4호
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• pp.519-527
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• 2011

Recently, the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$. From those integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$.

• The Korean Journal of Ecology
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• 제21권3호
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• pp.283-290
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• 1998

The vegetation pattern of Mt. Odae based on the soil humidity gradient showed 3 types: (1) the forest of Pinus densiflora under the mesic or xeric conditions of the low altitudinal area, (2) the forest of Acer including A. mono, A. pseudo-sieboldianum and Tilia amurensis under the submesic or subxeric conditions and (3) the forest of Quercus including Q. mongolica of the higher elevational area and Q. variabilis of the lower elevational area under the xeric condition. Water content, organic matter and total nitrogen of soil were relatively low in Pinus densiflora and Quercus variabilis communities while they were relatively high in Betula platyphylla var. japonica and Quercus mongolica communities. According to the result of cluster analysis based on similarity indices of the communities, the proposed successional sere in the forest vegetation of Mt. Odae was as follows. P. densiflora community $\longrightarrow$ P. densiflore + Q. mongolica community $\longrightarrow$ Q. mongolica + A. pseudo-sieboldianum community. P. densiflora community $\longrightarrow$ P. densiflora + Q. variabilis community $\longrightarrow$ Q. variabilis community $\longrightarrow$ Q. mongolica + Q. variabilis community $\longrightarrow$ Q. mongolica + A. pseudo-sieboldianum community.

• 한국통신학회논문지
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• 제33권11C호
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• pp.874-879
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• 2008

[1]에서 LCZ 수열군의 2배 확장을 제안하였다. 본 논문에서는 [1]에서의 2배 확장방법을 일반화하는 새로운 확장방법을 제안한다. 이 생성방법을 사용하면 인수가 (N,M,L,${\epsilon}$)인 q진 LCZ 수열군은 인수가 (pN,pM,p[(L+1)/p]-1,p${\epsilon}$)인 q진 LCZ 수열군이 된다. 이 때, p는 소수이고 p는 q의 약수다. 특히 L${\equiv}$p-1modp일 때, 확장된 q진 LCZ 수열군의 인수는 (pN,pM,L,p${\epsilon}$)이 된다.

• 대한수학회논문집
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• 제20권4호
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Journal of Korean Neurosurgical Society
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• 제48권1호
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• pp.14-19
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• 2010

Objective : Allelic losses or loss of heterozygosity (LOH) at many chromosomal loci have been found in the cells of meningiomas. The objective of this study was to evaluate LOH at several loci of different chromosomes (1p32, 17p13, 7q21, 7q31, and 22q13) in different grades of meningiomas. Methods : Forty surgical specimens were obtained and classified as benign, atypical, and anaplastic meningiomas. After DNA extraction, ten polymorphic microsatellite markers were used to detect LOH. Medical and surgical records, as well as pathologic findings, were reviewed retrospectively. Results : LOH at 1p32 was detected in 24%, 60%, and 60% in benign, atypical, and anaplastic meningiomas, respectively. Whereas LOH at 7q21 was found in only one atypical meningioma. LOH at 7q31 was found in one benign meningioma and one atypical meningioma. LOH at 17p13 was detected in 4%, 40%, and 80% in benign, atypical, and anaplastic meningiomas, respectively. LOH at 22q13 was seen in 48%, 60%, and 60% in benign, atypical, and anaplastic meningiomas, respectively. LOH results at 1p32 and 17p13 showed statistically significant differences between benign and non-benign meningiomas. Conclusion : LOH at 1p32 and 17p13 showed a strong correlation with tumor progression. On the other hand, LOH at 7q21 and 7q31 may not contribute to the development of the meningiomas.