• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1491-1499
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• 2020

We give a strong fundamental domain for the quotient of PGL₂(𝔽_q((t^-1))) by PGL₂(𝔽_q[t]) as a subset of distinct ordered triple points of ℙ¹(𝔽_q((t^-1))).

• Journal of Korean Society of Forest Science
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• v.85 no.1
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• pp.76-83
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• 1996

Four natural Quercus stands in Kwangju, Kyonggi-Do, of which ages ranging from 32 to 38 years old, were studied to compare their growth, biomass and net production. Ten $10m{\times}10m$ quadrats were set up and ten sample trees were harvested for dimension analysis in each stand. The largest mean DBH and height were shown by Q. acutissima stand, and followed by Q. variabilis stand, Q. mongolica stand, and Q. dentata stand in descending order. Tree density was the highest at Q. variabilis stand, and followed by Q. dentata stand, Q. mongolica stand, and Q. acutissima stand in descending order. Biomass was the largest at Q. acutissima stand(122.73t/ha), and followed by Q. variabilis stand(87.03t/ha), Q. mongolica stand(72.14t/ha), and Q. dentata stand(38.56t/ha) in descending order. Net production was the greatest at Q. mongolica stand(7.49t/ha/yr.), and followed by Q. variabilis stand(6.47t/ha/yr.), Q. acutissima stand(6.06t/ha/yr.), and Q. dentata stand(3.52t/ha/yr.) in descending order. The highest net assimilation ratio was exhibited by Q. acutissima stand (3.275), and followed by Q. variabilis stand(2.898), Q. mongolica stand(2.888), and Q. dentata stand (1.840) in descending order. The difference in net assimilation ratio and net production among four stands was caused by differences in their leaf biomass. The difference in net production and biomass among four stands was due to that in the distribution of net production among stems, branches and leaves.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.15 no.4
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• pp.312-316
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• 1982

With an object to obtain an indication on the efficiency of the saury baits for tuna longline, frequencies of the saury heads found in the tuna stomachs were analysed by the equations developed from tile binomial distribution. Four factors were introduced into the equations : The hooking rate, p; rate of not being hooked q; rate of the effective baits retained in the stomachs of the captured tuna r; and the rate of tile previously taken baits retained in the tuna stomachs, t. The best estimates of $\frac{p}{p+q^t}$ and r are empirically obtained as follows. Yellowfin tuna: $\frac{p}{p+q^t}$=0.789, r=0.598 Bigeye tuna: $\frac{p}{p+q^t}$=0.810 r=0.608, Albacore tun : $\frac{p}{p+q^t}$=0.838, r=0.621.

• The Korean Journal of Physiology
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• v.16 no.1
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• pp.41-50
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• 1982

The effects of $NaHCO_3$ on the electrocardiogram of rats were studied in the induced hyperkalemia. The subjects were divided into 4 groups: the group 1 was normal control and the data on this normal control had teen obtained from the following three groups before administration of KCl or $NaHCO_3$, the group 2 (KCl) was administered 40 ml per kg body weight of the 10 per cent KCl solution, the group 3 $(NaHCO_3)$ was administered 40 ml per kg body weight of the 10 per cent $NaHCO_3$ solution, and the group 4 $(KCl+NaHCO_3)$ was received 10 per cent KCl, which was followed by administration of 10 per cent $NaHCO_3$ at one and half hours later. In KCl, the heart rate was decreased rapidly, and then maintained its level, later rapid decreasing heart rate was followed by the cardiac stand still. The mean electrical axis of QRS complex became progressively deviated to the left. The amplitude of T wave was increased transiently but was not changed thereafter. There was prolongation of the P-Q interval and the Q-T interval at the beginning and then they were shortened. In $NaHCO_3$, the heart rate was decreased rapidly at the beginning, later showed a tendency of recovery. The mean electrical axis of QRS was not changed initially, but later became deviated to the left. The amplitude of T wave was not changed. There was prolongation of the P-Q interval and the Q-T interval at the beginning and then they were shortened. In $KCl+NaHCO_3$, there were a tendency of recovery of both the amplitude of the T wave and the electrical axis of the QRS complex after administration of $NaHCO_3$ but the heart rate was not recovered. There was prolonged P-Q interval, but the Q-T interval was relatively unchanged.

• Journal of Korean Tunnelling and Underground Space Association
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• v.10 no.4
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• pp.383-395
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• 2008

The grouting is one of the improved techniques which is aim to decrease the permeability and to strengthen the soft ground. But The grouting method has many problems about a suitability of grouting procedure and an effectiveness of grouting after grouting work because of a technical characteristic operated inside the soil. The grouting $p{\sim}q{\sim}t$ chart of a typical index about grouting rate and time alteration of grouting pressure is one method to estimate the suitability of grouting factor with monitoring during grouting procedure. This study is automatic grouting system (AGS) which can control the testing and grouting procedures. It can make the detailed $p{\sim}q{\sim}t$ chart and analyze the grouting characters of the ground by comparing the detailed pattern of $p{\sim}q{\sim}t$ chart with standard pattern. If using the $p{\sim}q{\sim}t$ chart derived from AGS in the grouting work, it is an objective standard estimating the suitability of grouting factor with grouting materials, grouting method, grouting rate and grouting pressure, as results it expects successfully to improve reliability of the grouting work.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.641-645
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• 2013

In this article, we show that the modular equation ${\Phi}_p^{T_q}(X,Y)$ of Thompson series $T_q$ corresponding to ${\Gamma}_0(q)+q$ gives an affine model of a modular curve $X_0(pq)+q$.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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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 applied mathematics & informatics
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• v.28 no.5_6
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• pp.1285-1304
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• 2010

The purpose of this paper is to establish some sufficient conditions for oscillation of solutions of the second-order functional dynamic equation of Emden-Fowler type $\[a(t)x^{\Delta}(t)\]^{\Delta}+p(t)|x^{\gamma}(\tau(t))|\|x^{\Delta}(t)\|^{1-\gamma}$ $sgnx(\tau(t))=0$, $t\;{\geq}\;t_0$, on a time scale $\mathbb{T}$, where ${\gamma}\;{\in}\;(0,\;1]$, a, p and $\tau$ are positive rd-continuous functions defined on $\mathbb{T}$, and $lim_{t{\rightarrow}{\infty}}\;{\tau}(t)\;=\;\infty$. Our results include some previously obtained results for differential equations when $\mathbb{T}=\mathbb{R}$. When $\mathbb{T}=\mathbb{N}$ and $\mathbb{T}=q^{\mathbb{N}_0}=\{q^t\;:\;t\;{\in}\;\mathbb{N}_0\}$ where q > 1, the results are essentially new for difference and q-difference equations and can be applied on different types of time scales. Some examples are worked out to demonstrate the main results.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.941-947
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• 2009

Let q be a power of 16. Every polynomial $P\in\mathbb{F}_q$[t] is a strict sum $P=A^2+A+B^3+C^3+D^3+E^3$. The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial $Q\in\mathbb{F}_q$[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: $Q=F^2+F+tG^2$. This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation $Q=F^2$+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.