• The Korean Journal of Ecology
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• v.26 no.4
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• pp.155-163
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• 2003

In order to analyze the succession process from a pine forest to an oak forest, the tree growth of Pinus densiflora and Quercus mongolica ssp. crispula was monitored in a permanent quadrat for 23 years. The measurements were carried out for the stem diameter (DBH) of Pinus densiflora between 1977 and 1999 and for the height of Quercus mongolica ssp. crispula saplings between 1998 and 2000. The floristic composition and the locations of the individual P. densiflora and Q. mongolica ssp. crispula trees and saplings in the quadrat were recorded. P densiflora and Q. mongolica ssp. crispula individuals were randomly distributed within the quadrat. The relative growth rates (RGR) of DBH in P. densiflora were 0.085 $yr^{-1}$ for large trees and 0.056 $yr^{-1}$ for small trees in 1977. The RGR of height for Q. mongolica ssp. crispula was 0.122 $yr^{-1}$. The growth curve for DBH of P. densiflora was approximated by the logistic equation: $$DBH(t) = 30 {[1+1.16exp(-0.13 t)]}^{-1}$$ where DBH (t) the DBH (cm) in year t and t is the number of years since 1977. The growth in height of P. densiflora and Q. mongolica ssp. crispula was described by following equations: $$H (t) = 20.2 {[1+0.407exp(-0.137 t)]}^{-1} (P. densiflora)$$ $$H (t) = 30 {[1+20.7exp(-0.122 t)}^{-1} (Q. mongolica ssp. crispula)$$ Where H (t) is the tree height (m) in year t and t is the number of years since 1977 in P. densiflora and 1998 in Q. mongolica ssp. crispula. With these equations we predicted that the height of Q. mongolica ssp. crispula increases from 2 m in 1999 to 20 m in 2029. Therefore, Q. mongolica ssp. crispula and P. densiflora will be approximately the same height in 2029. The years required for succession from a pine forest to an oak forest are expected 33 with the range between 23 and 44 years.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.243-254
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• 1997

특정분포에 대한 P-P plot과 Q-Q plot의 특징을 분석하고 두 가지 그래프 사이의 관계를 비교해 보았다. NTV의 본질적인 특징을 알아보고 각 특정분포에 대한 NTV plot의 특징을 분석했다. 전형적인 bimodal 분포가 나타날 때 P-P 혹은 Q-Q plot은 뚜렷한 break-point를 갖는다는 것을 알아보고, 단지 skewed된 분포나 skewed된 것처럼 보이는 bimodal 분포 사이에서 발생하는 판단의 어려움에 대하여 여러 plot고찰해 보았다.

• Communications for Statistical Applications and Methods
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• v.5 no.1
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• pp.205-215
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• 1998

정규분포에 관한 검정에 있어서 P-P 플롯과 Q-Q 플롯의 가시적인 변동을 이용한 통계량을 제시하고 이 통계량들과 Shapiro-Wilk의 W 통계량과의 비교를 정확도(accuracy)의 측면을 고려하여 실시하였다. 또한, 의학이나 임상에서 척도의 우수성을 검정하기 위해 많이 사용하는 Receiver Operating Characteristic (ROC) 분석 기법을 이용하여 제시된 통계량들에 관한 Power와 Accuracy는 물론 Best Cut-Off 측면에서의 효율성을 검정하였다.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• Journal of the Korean earth science society
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• v.24 no.8
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• pp.684-690
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• 2003

Recently Choongchung provinces in the central part of South Korea have received increasing attention because of the newly Planned administrative capital construction. In this area, a seismic network of Korea National University of Education has been installed since September 1996, and analyzed Q$_P^{-1}$ and Q$_S^{-1}$ by the extended Coda normalization method based on 60 events recorded by 2 stations of the network. To compensate for insufficient data, we combined the data from 33 events observed at 1 of the stations of the network of Korea Institute of Geology, Mining & Materials. Estimated Q$_P^{-1}$ and Q$_S^{-1}$ showed frequency dependence that decrease from (1.9${\pm}$3.0)${\times}$10$^{-3}$ and (2.4${\pm}$1.4)${\times}$10$^{-3}$ at 3.0 Hz to (5.4${\pm}$1.5)${\times}$10$^{-4}$ and (6.3${\pm}$1.1)${\times}$10$^{-4}$ at 24 Hz, respectively. Using a power law dependent on frequency, the best fit of Q$_P^{-1}$ and Q$_S^{-1}$ are 0.003f$^{-0.62}$ and 0.006f$^{-0.71}$ respectively. These values correspond to those of seismically stable regions, and are slightly less dependent on frequency than those of the southeastern part of Korea due to high Q$^{-1}$ values in high frequencies. Further observations are required in the central part of S. Korea to evaluate the difference of Q$^{-1}$ between central and southeastern parts of S. Korea.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.467-485
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• 2005

Let p and q be odd primes with p=2q+1. We study the number of solutions of congruence equations $ax^i\;+\;by^j\;{\equiv}\;c$ (mod p) and a$ax^i\;+\;by^j\;+\;dz^t\;{\equiv}\;c(modp)$

• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.115-125
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• 2001

We consider the threshold autoregressive moving average(TARMA) process and find a sufficient condition for strict stationarity of the proces. Given region for stationarity of TARMA(p,q) model is the same as that of TAR(p) model given by Chan and Tong(1985), which shows that the moving average part of TARMA(p,q) process does not affect the stationarity of the process. We find also a sufficient condition for the existence of kth moments(k$\geq$1) of the process with respect to the stationary distribution.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.733-746
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• 2009

For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.

• 한국해양학회지
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• v.26 no.1
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• pp.59-66
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• 1991

Laboratory studies were carried out to measure the sound velocity (V/SUB p/) and quality factor (Q/SUB p/, inverse attenuation) in the horizontal (H) and vertical (V) direction on the core sampled sediment of deep-sea basin (1,850 meter water depth), East Sea of Korea (Sea of Japan). Sampled core was about 250 cm long and 500 kHz ultrasonic p-wave transducer was used for a sound soured. V/SUB p/ varies from 1,480 m/sec to 1,500 m/sec, it is not clear which direction is faster, V/SUB PH/ or V/SUB pv/, within${\pm}$ 1.0% anisotropy (A/SUB p/). It is thought because the core sediment facies is highly (or slightly) bioturbated homogeneous mud with very high porosity (more than 80%). The general trend of Q/SUB p/ is decreasing 10 to 5 with the buried depth, it is strongly affected by the variation of sediment texture (increasing silt, decreasing clay) with increasing of CaCO$_3$ and organic matter content, But Q/SUB PH/ is jumping up to 14.9 near the bottom of core sediment as including volcanic ash richly. The relationship between V/SUB PH/ and Q/SUB PH/ shows the mirror image nearly, it is interpreted that not only the geotechnical properties and texture but also sea-water characteristics (high Q/SUB p/, low V/SUB p/) according to rich water content affect strongly in the upper part of the unconsolidated deep-sea basin sediment.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.375-384
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• 2008

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.