• 대한수학회지
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• 제46권3호
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• pp.493-511
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• 2009

Let $q\;{\geq}\;3$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;\(N(a,\;q)\;-\;\frac{{\phi}(q)}{8}\)^2$ and obtain a sharp asymptotic formula.

• 대한수학회지
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• 제34권4호
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• pp.1049-1064
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• 1997

We study the existence and uniqueness of nonnegative singular solution u(x,t) of the semilinear parabolic equation $$ u_t = \Delta u - a \cdot \nabla(u^q) = u^p, $$ defined in the whole space $R^N$ for t > 0, with initial data $M\delta(x)$, a Dirac mass, with M > 0. The exponents p,q are larger than 1 and the direction vector a is assumed to be constant. We here show that a unique singular solution exists for every M > 0 if and only if 1 < q < (N + 1)/(N - 1) and 1 < p < 1 + $(2q^*)$/(N + 1), where $q^* = max{q, (N + 1)/N}$. This result agrees with the earlier one for N = 1. In the proof of this result, we also show that a unique singular solution of a diffusion-convection equation without absorption, $$ u_t = \Delta u - a \cdot \nabla(u^q), $$ exists if and only if 1 < q < (N + 1)/(N - 1).

• Journal of Genetic Medicine
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• 제8권2호
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• pp.119-124
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• 2011

목적: 표지염색체(supernumerary marker chromosome, SMC)는 유래한 염색체에 따라서 임상 증상이 다양하다. 본 연구는 염색체 마이크로어레이를 이용하여 SMC의 기원을 밝히고 각 증례마다 분자세포유전학적 특성과 임상 표현형을 분석하고자 하였다. 대상 및 방법: 염색체 검사에서 SMC가 검출된 환자들 중에서 15번 염색체 유래를 제외한 4명의 환자에서 CGH 기법의 올리고 뉴클레오티드 염색체 마이크로어레이를 시행하였다. 결과: 3명의 환자에서 유래된 염색체 부위를 확인할 수 있었다. 증례1은 1q21.1-q23.3에서 16.1 Mb의 SMC를 가졌고, 증례2는 19p13.11-q13.12에서 21 Mb, 증례3은 22q11.1-q11.21과 22q11.22-q11.23의 두 구간에서 각각 2.5Mb와 2.0Mb로 재배열된 4.5 Mb의 SMC를 나타내었다. 결론: 증례1은 1q21.1 중복증후군을 포함하여 광범위한 임상표 현형을 나타내었다. 증례2는 아스퍼거 증후군과 유사한 정신행동 이상 소견은 19p12-q13.11, 청력장애와 사시는 19p13.11, 그 외 증상은 19q13.12의 유전자와 연관 가능성이 높다. 증례３은 묘안 증후군 type I 및 22q11.2 미세중복증후군과 비교했을 때 항문폐쇄는 22q11.1-q11.21, 그 외 증상들은 22q11.22-q11.23과 연관성을 시사하였다. 고해상도 염색체 마이크로어레이 분석은 SMC의 유래를 확인할 수 있고 유전형-표현형 상관성을 이해함으로써 유전상담에 도움이 된다.

• 한국식품영양학회지
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• 제22권4호
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• pp.577-586
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• 2009

Aging is associated with decreased energy expenditure, thermogenesis and energy requirements. Maintenance of physical fitness of the elderly has been reported to reduce the rate at which the basal metabolic rate, muscle strength, skeletal muscle mass and bone density deteriorate. Skeletal muscle disease is known to increase the risk of physical disability and psychological problems. This study was conducted to investigate changes in disability, emotional problems, body compositions, obesity indices and nutrient intake levels according to physical fitness with the elderly in rural areas. According to the results, physical fitness was negatively related with Activities of Daily Living(ADL, p<0.05), Instrumental Activities of Daily Living(IADL, p<0.001), Body Mass Index(BMI, p<0.001) and abdominal obesity(p<0.05), while it showed a positive correlation with the General Self Efficacy Scale(GSES)(p<0.001) and nutrient intake(p<0.05). When changes in these factors were compared according to the range of quartile of the Fullerton Advanced Balance Scale(FAB Scale), GSES(Q1=35.3, Q2=43.5, Q3=53.2, Q4=51.9, p<0.001), BMI(Q1=36.1%, Q2=34.7%, Q3=33.2%, Q4=28.6%, p<0.01), abdominal obesity(Q1=1.02, Q2=0.99, Q3=0.97, Q4=0.94, p<0.001) and nutrient intake(Q1=71.1%, Q2=75.4%, Q3=80.6%, Q4=80.2%, p<0.05) differed significantly. Taken together, these results suggested that better physical fitness would lead to a reduction in negative factors including physical disability and obesity indices, but to an increase in positive factors such as GSES and nutrient intake. The results of this study are expected to be used as basic data for the development of programs to promote the health of the elderly in a local society.

• Childhood Kidney Diseases
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• 제16권1호
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• pp.46-50
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• 2012

C1q 신병증은 1985년 Jennett와 Hipp에 의해 발표된 이래 어린 영아에서부터 청 장년층에 까지 발표되어 왔으나 아직 임상병리학적으로 논란이 많은 질환이다. 저자들은 어린 남매에서 스테로이드 저항성의 콩팥증후군의 임상 양상을 보이며 병리 조직학적으로 국소분절사구체경화증과 메산지움에 C1q의 현저한 침착을 보인, C1q 신증을 발표하는 바이다.

• 대한수학회논문집
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• 제38권1호
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• 대한수학회보
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• 제48권6호
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• pp.1303-1314
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• 2011

We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.

• 정보보호학회논문지
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• 제12권1호
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• pp.21-32
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• 2002

본 논문에서는 소수 p의 멱승인 q에 대해서 주기 $q_n$-1인 q진 시퀸스(d-동차함수)로부터 Singer 파라미터 equation omitted를 갖는 새로운 순회차집합을 생성하였다. q가 3의 멱승일 때, Helleseth, Kumar, Martinsen의 주기가 $q_n$-1이고, 이상적인 자기상관성질을 갖는 3진 시퀸스로부터 Singer 파라미터 equation omitted를 갖는 새로운 순회 차집합을 생성시킨다.

• 지구물리
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• 제5권3호
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• pp.211-218
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• 2002

$Q_{Lg}^{-1}$를 구하는 방법 중에서 Chun et al. (1987)이 고안한 Reversed two station method (RSTM)는 진앙거리 90 km 이상의 Lg파에 대하여 시행되고 있다. 진앙거리 95 km 에서 381 km에 이르는 중부지역 지진자료에 대하여 RSTM에 의한 $Q_{Lg}^{-1}$를 구한 결과, 비슷한 진앙거리에 대한 동일한 방법으로부터 얻어진 남한 남동부지역의 값과 비슷한 높은 값이 도출되었다. 남한 남동부 및 중부지방의 높은 $Q_{Lg}^{-1}$는 실제와 다른 것으로, RSTM이 본 연구 진앙거리 구간에서는 감쇠율이 표면파 감쇠율 0.5 보다 크기 때문인 것으로 해석된다.

• 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.