• Bulletin of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.479-484
• /
• 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
• /
• 2008.10a
• /
• pp.97-100
• /
• 2008

Mount Fuji is the focus of intense study because of its potential hazard signaled by seismic, geologic and historical activity. Based on extensive seismic data recorded in the vicinity of Mt. Fuji, coda quality factor ($Q_c^{-1}$) using a single scattering model hypothesis, and intrinsic and scattering quality factor $(Q_i^{-1}$ and $Q_s^{-1})$ using the Multiple Lapse Time Window Analysis (MLTW) method was measured. To focus the study on the magmatic structure below Mt. Fuji, to the data were separated into two groups: a near-Fuji region of rays traversing an area with radius 5 km around the summit (R < 5 km), and a far-Fuji region of rays beyond a radius of 20 km around the summit (R > 20 km). The results of the study have a small error range due to the large data sample, showing that all $Q^{-1}$ values in near-Fuji area are greater than those of far-Fuji area, and $Q_i^{-1}$ for both the near and far-Fuji area is higher than $Q_s^{-1}$ at high frequencies. The $Q_i^{-1}$ values of the near-Fuji area are lower than those of the other volcanic areas considered, while values of $Q_s^{-1}$ are not. The low $Q_i^{-1}$ for the volcanic region of near-Fuji suggests that the magmatic activity, or percent of partial melt, at Mt. Fuji is not as active as hot spot volcanoes such as Kilauea, Hawaii.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.983-991
• /
• 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
• /
• v.23 no.4
• /
• pp.571-590
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1441-1462
• /
• 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
• /
• v.34 no.1_2
• /
• pp.107-114
• /
• 2016

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

• Physical Therapy Korea
• /
• v.6 no.1
• /
• pp.1-14
• /
• 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.

• Korean Journal of Optics and Photonics
• /
• v.19 no.4
• /
• pp.320-326
• /
• 2008

The output characteristics of a laser-diode pumped electrooptic Q-switched Nd:YAG ceramic laser were investigated. The output energy of a Q-switched Nd:YAG ceramic laser was optimized under an output coupler reflectivity of 77%, a laser-diode pulse width of $1,000\;{\mu}s$, and a delay time of $985\;{\mu}s$. The output energy of the Q-switched pulse was measured to be 0.35 mJ with a pulse width of 4 ns under a pump energy of 17.9 mJ. The output efficiency and the peak power were 1.9% and 87.5 kW, respectively.

• Journal of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.391-410
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.20 no.4
• /
• pp.645-648
• /
• 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 $T/Q_1$.