• 대한수학회보
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• 제39권3호
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• pp.479-484
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction $Q=(a_1,a_2,...,a_d)$ generated by d elements in A and $G(I)=\bigoplus_{n\geq0}I^n/I^{n+1}$ of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a$_1$] and P = mS. In this paper, we show that the following conditions are equivalent. (1) $I^2$ = QI and I = Q:I. (2) $I^2S$ = $a_1$IS and IS = $a_1$S：sIS. (3) $I^2$Sp = $a_1$ISp and ISp = $a_1$Sp ：sp ISp. We denote by $X_A(Q)$ the set of good ideals I in $X_A(Q)$ such that I contains Q as a reduction. As a Corollary of this result, we show that $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.

• 한국지구물리탐사학회:학술대회논문집
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• 한국지구물리탐사학회 2008년도 공동학술대회
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• pp.97-100
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• 2008

일본 후지산은 역사적, 지질학적, 그리고 최근의 지진학적 징후로부터 화산활동의 재개에 의한 재해가능성이 있어 화산감시연구가 집중되고 있다. 후지산 감시활동의 일환으로 축적된 방대한 주변지역 지진자료를 바탕으로 단일산란모델에 의한 코다감쇠상수($Q_c^{-1}$)와 다중시간창분석에 의한 고유 및 산란감쇠상수 ($Q_i^{-1}$, $Q_s^{-1}$)를 측정하였다. 본 연구는 후지산 아래에 존재하는 것으로 여겨지고 있는 용암체의 감쇠구조에 초점을 맞추기 위해 정상에서 반경 5km 이내의 지대를 지진파가 통과하는 '후지산 근방', 지진파 통과지역이 모두 반경 20 km 바깥인 '먼 후지산'으로 자료를 분류하였다. 본 연구는 자료가 풍부하여 비교적 작은 오차범위를 나타내고 있는데, '후지산 근방'의 모든 감쇠상수 수 $Q^{-1}$는 '먼 후지산'에 비해 컸으며, 두 지대 공히 고주파 영역에서의 $Q_i^{-1}$값은 $Q_s^{-1}$ 값에 비해 높은 값이었다. 그러나, '후지산 근방'의 $Q_i^{-1}$ 값은 다른 화산지역에 비해 낮았는데, 이는 하와이화산과 같은 활동적인 화산에 비해 용융도의 비율이 낮거나 마그마활동이 덜한 것으로 해석된다.

• 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., ${\prod}_{j=0}^{-1}\;b_j=1$.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.571-590
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• 2015

Let a, b, q be integers with q > 0. The homogeneous Dedekind sum is dened by $$\Large S(a,b,q)={\sum_{r=1}^{q}}\(\({\frac{ar}{q}}\)\)\(\({\frac{br}{q}}\)\)$$, where $$\Large ((x))=\{x-[x]-{\frac{1}{2}},\text{ if x is not an integer},\\0,\hspace{75}\text{ if x is an integer.}$$ In this paper we study the mean value of S(a, b, q) by using mean value theorems of Dirichlet L-functions, and give some asymptotic formula.

• 대한수학회보
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• 제55권5호
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• pp.1441-1462
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• 2018

In this paper, we investigate the fractional p&q-Kirchhoff type system $$\{M_1([u]^p_{s,p})(-{\Delta})^s_pu+V_1(x){\mid}u{\mid}^{p-2}u\\{\hfill{10}}={\ell}k^{-1}F_u(x,\;u,\;v)+{\lambda}{\alpha}(x){\mid}u{\mid}^{m-2}u,\;x{\in}{\Omega}\\M_2([u]^q_{s,q})(-{\Delta})^s_qv+V_2(x){\mid}v{\mid}^{q-2}v\\{\hfill{10}}={\ell}k^{-1}F_v(x,u,v)+{\mu}{\alpha}(x){\mid}v{\mid}^{m-2}v,\;x{\in}{\Omega},\\u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}{\subset}{\mathbb{R}}^N$ is an unbounded domain with smooth boundary ${\partial}{\Omega}$, and $0<s<1<p{\leq}q$ and sq < N, ${\lambda},{\mu}>0$, $1<m{\leq}k<p^*_s$, ${\ell}{\in}R$, while $[u]^t_{s,t}$ denotes the Gagliardo semi-norm given in (1.2) below. $V_1(x)$, $V_2(x)$, $a(x):{\mathbb{R}}^N{\rightarrow}(0,\;{\infty})$ are three positive weights, $M_1$, $M_2$ are continuous and positive functions in ${\mathbb{R}}^+$. Using variational methods, we prove existence of infinitely many high-energy solutions for the above system.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.107-114
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• 2016

In this paper we give some symmetric property of the generalized twisted q-Euler zeta functions and q-Euler polynomials.

• 한국전문물리치료학회지
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• 제6권1호
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• pp.1-14
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• 1999

The quadriceps angle (Q angle) has been used to reflect the quadriceps muscle's force on the patella in the frontal plane. Previous investigations of the Q angle and it's relationship to knee disorders have yield equivocal results. The purpose of this study was to analyze the factors related to the Q angle and it's relation to other variables such as leg length, body weight, CTA (calcaneus to tibia angle), TOA (toe out angle), and pelvic width in normal subjects. The participants were 60 students (30 men and 30 women) who had no orthopedic and neurological impairments, aged from 20 to 29 years of age, with an average age of 22.1 years. Prior to participation, each subject was informed of the procedures of the experiment from a researcher and assistant researchers. The equipment used in this study were modified standard goniometer, ruler, marking pen, and Martin apparatus for pelvic width. In order to determine the statistical significance of the experiment, regression analysis, independent t-test, and Pearson correlation were used at the 0.05 level. The results were as follows: 1) It was found that the Q angle of women is greater than that of men's from both knees. 2) There was no significant difference between right and left quadriceps angle. 3) The Q angle decreased as the body weight (leg length) shifted from low to high. 4) It seems that factors related to the Q angle were body weight, CTA, and pelvic width, but there was no significant difference at the 0.05 level.

• 한국광학회지
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• 제19권4호
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• pp.320-326
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• 2008

광섬유 연결 반도체레이저 여기 세라믹 Nd:YAG 레이저의 전기광학 Q-스위칭 출력 특성에 대해 연구하였다. 세라믹 Nd:YAG 레이저의 Q-스위칭은 여기원의 펄스폭 $1,000\;{\mu}s$, 출력 거울의 반사율 77% 및 지연시간 $985\;{\mu}s$에서 최적화되었다. 여기 에너지 17.9 mJ에서 0.35 mJ의 Q-스위칭된 출력 에너지와 약 4 ns의 펄스폭이 측정되어 1.9%의 출력 효율과 87.5 kW의 첨두 출력을 나타내었다.

• 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.

• 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 $T/Q_1$.