• Asian Pacific Journal of Cancer Prevention
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• 제13권1호
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• pp.225-229
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• 2012

Background: Males have a higher prevalence of hepatocellular carcinoma (HCC) than females in general, but the reasons for the sex disparity are still obscure. DNA copy number alteration (CNA) is a major feature of solid tumors including HCC, but whether CNA plays a role in sex-related differences in HCC development has never been evaluated. Methods: High-resolution array comparative genomic hybridization (CGH) was used to examine 17 female and 46 male HCC patients with chronic hepatitis B virus (HBV) infection in Shanghai, China. Two-tailed Fisher's exact or ${\chi}^2$ tests was used to compare CNAs between females and males. Results: The overall frequencies and patterns of CNAs in female and male cases were similar. However, female HCC tumors presented more copy number gains compared to those in males on 1q21.3-q22 (76.5% vs. 37.0%, P = 0.009), 11q11 (35.3% vs. 0.0%, P = 0.0002) and 19q13.31-q13.32 (23.5% vs. 0.0%, P = 0.004), and loss on 16p11.2 (35.3% vs. 6.5%, P = 0.009). Relative to females, male cases had greater copy number loss on 11q11 (63.0% vs. 17.6%, P = 0.002). Further analyses showed that 11q11 gain correlated with 19q13.31-q13.32 gain (P = 0.042), 11q11 loss (P = 0.011) and 16p11.2 loss (P = 0.033), while 1q21.3-q22 gain correlated with 19q13.31-q13.32 gain (P = 0.046). Conclusions: These findings suggest that CNAs may play a role in sex-related differences in HBVassociated HCC development.

• 대한수학회보
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• 제26권2호
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• 제26권3호
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• pp.245-253
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• 2000

The development and progression of oral cancer is associated with an accumulation of multiple genetic alterations through the multistep processes. Comparative genomic hybridization(CGH), newly developed cytogenetic and molecular biologic technique, has been widely accepted as a useful method to allow the detection of genetic imbalance in solid tumors and the screening for chromosome sites frequently affected by gains or losses in DNA copy number. The authors examined 19 primary oral squamous cell carcinomas using CGH to identify altered chromosome regions that might contain novel oncogenes and tumor suppressor genes. Interrelationship between these genetic aberrations detected and major oncogenes and tumor suppressor genes previously recognized in carcinogenesis of oral cancers was studied. 1. Changes in DNA copy number were detected in 14 of 19 oral cancers (78.9%, mean: 5.58, range: $3{\sim}13$). High level amplification was present in 4 cases at 9p23, $12p21.1{\sim}q13.1$, 3q and $8q24{\sim}24.3$. Fourteen cases(78.9%, mean: 3.00, range: $1{\sim}8$) showed gains of DNA copy number and 12 cases(70.5%, mean: 2.58, range: $1{\sim}9$) revealed losses of DNA copy number. 2. The most common gains were detected on 3q(52.6%), 5p(21.0%), 8q(21.0%), 9p(21.0%), and 11q(21.0%). The losses of DNA copy number were frequently occurred at 9p(36.8%), 17q(36.8%), 13q(26.3%), 4p(21.0%) and 9p(21.0%). 3. The minimal common regions of gains were repeatedly observed at $3q24{\sim}26.7$, $3q27{\sim}29$, $1q22{\sim}31$, $5p12{\sim}13.3$, $8q23{\sim}24$, and 11q13.1-13.3. The minimal common regions of losses were detected at $9q11{\sim}21.3$, 17p31, $13q22{\sim}34$, and 14p16. 4. In comparison of CGH results with tumor stages, the lower stage group showed more frequent gain at 3q, 5q, 9p, and 14q, whereas gains at 1q($1q22{\sim}31$) and 11q($11q13.1{\sim}13.3$) were mainly detected in higher stage group. The loss at $13q22{\sim}34$ was exclusively detected in higher stage. The results indicate that the most frequent genetic alterations in the development of oral cancers were gains at $3q24{\sim}26.3$, $1q22{\sim}31$, and $5p12{\sim}13.3$ and losses at $9q11{\sim}21.3$, 17p31, and 13q. It is suggested that genetic alterations manifested as gains at $3q24{\sim}26.3$, $3q27{\sim}29$, $5p12{\sim}13.3$ and 5p are associated with the early progression of oral cancer. Gains at $1q22{\sim}31$ and $11q13.1{\sim}13.3$ and loss at 13q22-34 could be involved in the late progression of oral cancers.

• 대한수학회논문집
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• 제24권3호
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• pp.367-379
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• 2009

For a prime number p, let $\mathbb{Q}_p$ denote the p-adic field and let $\mathbb{Q}_p^d$ denote a vector space over $\mathbb{Q}_p$ which consists of all d-tuples of $\mathbb{Q}_p$. For a function f ${\in}L_{loc}^1(\mathbb{Q}_p^d)$, we define the Hardy-Littlewood maximal function of f on $\mathbb{Q}_p^d$ by $$M_pf(x)=sup\frac{1}{\gamma{\in}\mathbb{Z}|B_{\gamma}(x)|H}{\int}_{B\gamma(x)}|f(y)|dy$$, where |E|$_H$ denotes the Haar measure of a measurable subset E of $\mathbb{Q}_p^d$ and $B_\gamma(x)$ denotes the p-adic ball with center x ${\in}\;\mathbb{Q}_p^d$ and radius $p^\gamma$. If 1 < q $\leq\;\infty$, then we prove that $M_p$ is a bounded operator of $L^q(\mathbb{Q}_p^d)$ into $L^q(\mathbb{Q}_p^d)$; moreover, $M_p$ is of weak type (1, 1) on $L^1(\mathbb{Q}_p^d)$, that is to say, |{$x{\in}\mathbb{Q}_p^d:|M_pf(x)|$>$\lambda$}|$_H{\leq}\frac{p^d}{\lambda}||f||_{L^1(\mathbb{Q}_p^d)},\;\lambda$ > 0 for any f ${\in}L^1(\mathbb{Q}_p^d)$.

• East Asian mathematical journal
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• 제35권3호
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• pp.285-288
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• 2019

Let $F_n$, $n{\in}{\mathbb{N}}$ be the n - th Fibonacci number, and let (p, q) be one of ordered pairs ($F_{n+2}$, $F_n$) or ($F_{n+1}$, $F_n$). Then we show that the multiplicative inverse of q mod p as well as that of p mod q are again Fibonacci numbers. For proof of our claim we make use of well-known Cassini, Catlan and dOcagne identities. As an application, we determine the number $N_{p,q}$ of nonzero term of a polynomial ${\Delta}_{p,q}(t)=\frac{(t^{pq}-1)(t-1)}{(t^p-1)(t^q-1)}$ through the Carlitz's formula.

• 한국인터넷방송통신학회논문지
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• 제13권6호
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• pp.221-228
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• 2013

큰 반소수 n=pq의 소인수 p,q를 나눗셈 시행법으로 직접 찾는 것은 현실적으로 거의 불가능하다. 따라서 대부분의 소인수분해 알고리즘은$a^2{\equiv}b^2$ (mod n)의 제곱합동을 찾아 p=GCD(a-b, n), q=GCD(a+b, n)의 소인수를 찾는 간접 방법을 적용하고 있다. n = pq에 대해 p와 q를 선택한 영역은 $l(p)=l(q)=l(\sqrt{n})=0.5l(n)$의 [$10{\cdots}01$, $99{\cdots}9$] 범위에서 $\sqrt{n}$을 기준으로 $10{\cdots}00$ < p < $\sqrt{n}$과 $\sqrt{n}$ < q < $99{\cdots}9$에 존재한다는 사실만이 밝혀졌다. 본 논문은 n으로 부터 획득한 정보를 이용하여 p의 범위를 보다 축소시키는 방법을 제안한다. 제안 방법은 $n=n_{LR}+n_{RL}$, $l(n_{LR})=l(n_{RL})=l(\sqrt{n})$으로 분할하여 $p_{min}=n_{LR}$, $q_{min}=n_{RL}$로 설정하는 방법을 적용하였다. 본 논문에서 제안한 n의 정보로 p의 범위를 축소하는 방법은 $\sqrt{n}$의 정보로 p의 범위 축소 방법에 비해 최소 17.79%에서 최대 90.17%의 범위 축소 효과를 얻었다.

• 대한수학회보
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• 제33권1호
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• pp.39-44
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• 1996

Throughout this paper $Z^p, Q_p$ and C_p$ will denote the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of $Q_p$, respectively. Let $v_p$ be the normalized exponential valuation of $C_p$ with $$\mid$p$\mid$_p = p^{-v_p (p)} = p^{-1}$. We set $p^* = p$ for any prime p > 2 $p^* = 4 for p = 2$.

• 지능정보연구
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• 제12권1호
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• pp.107-123
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• 2006

이 논문은 정규문법과 동등한 의미를 가지는 일반적인 이진 이차 재귀 신경망(Generalized Binary Second-order Recurrent Neural Networks: GBSRNN)의 구조 및 학습 방법을 제안하며 이를 이용하여 정규언어를 인식하는 어휘분석기 구현을 소개한다. GSBRNN는 성분들의 이진값 표현으로 정규문법과 동치인 모든 표현에 대하여 하드웨어로 표현할 수 있는 방법을 제공하며 정규 문법과의 구조적 관련성을 보여준다. 정규문법에서 심볼들의 개수 m, 비단말 심볼의 개수 p, 단말 심볼의 개수 q, k인 문자열이 입력된다고 할 때, GBSRNN의 크기는 $O(m(p+q)^2)$ 이고 병렬처리 시간은 O(k)이며 순차처리 시간은 $O(k(p+q)^2)$이다.

• 대한수학회지
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• 제37권3호
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• pp.391-410
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• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• 한국조경학회지
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• 제21권2호
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• pp.107-119
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• 1993

This study was conducted to increase to increase the plant species diversity, which was based on the analysis of plant community structure and the survey of human's disturbance degree in Mt. Yongma and Mt. Acha urban nature park, Seoul. The plant community were divided into four groups by TWINSPAN and DCA. These groups were Pinus rigida-P. densiflora community, Quercus mongolica-Q.aliena-Q.accutissima community, Robinia pseudoacaia-Q.accutissima-Poplus${\times}$albaglandulosa community and R.pseudoacacia community. The successional trends of tree species seems to be from P.densiflora, P.rigida, Sorbus alniflora to Q.mongolica, Q.aliena and from P.${\times}$albaglandulosa, R.pseudoacacia, through Q.accutissima, to Q. mongolica, Q.aliena. The species diversity of plant community was high in natual plant community but was low in artificial planting community respectively. Number of species, number of species individuals, indices of species diversity was lowered and soil hardness was increased by the user's trampling, undercutting work and planting P.koraiensis after thinning. In the basis of study results, we proposed the management plan for the urban forest.