• Korean Journal of Mathematics
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• v.26 no.4
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• pp.561-582
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• 2018

In this paper the growth properties of the composition of integer translated entire and meromorphic functions in terms of their (p, q)-th order are discussed and based upon that some new results are developed.

• 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.

• East Asian mathematical journal
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• v.16 no.1
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• pp.89-96
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• 2000

In this paper, a differential polynomial ring $R[x;\delta]$ of ring R with a derivation $\delta$ are investigated as follows: For a reduced ring R, a ring R is Baer(resp. quasi-Baer, p.q.-Baer, p.p.-ring) if and only if the differential polynomial ring $R[x;\delta]$ is Baer(resp. quasi-Baer, p.q.-Baer, p.p.-ring).

• The Korean Journal of Ecology
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• v.27 no.2
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• pp.115-120
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• 2004

Coarse woody debris (CWD, $\ge$ 5 cm in maximum diameter) is an important functional component, especially to nutrient cycling in forest ecosystems. To compare mass and nutrient dynamics of CWD in natural oak forests, a two-year study was conducted at Quercus serrata and Q. variabilis stands in Yangpyeong, Kyonggi Province. Total CWD (snag, stump, log and large branch) and annual decomposition mass (Mg/ha) were 1.9 and 0.4 for the Q. serrata stand and 7.5 and 0.5 for the Q. variabilis stand, respectively. Snags covered 72% of total CWD mass for the Q. variabilis stand and 42% for the Q. serrata stand. Most of CWD was classified into decay class 1 for both stands. CWD N and P concentrations for the Q. variabilis stand significantly increased along decay class and sampling time, except for P concentration in 2002. There were no differences in CWD N concentration for the Q. serrata stand along decay class and sampling time. However, CWD P concentration decreased along sampling time. CWD N and P contents (kg/ha) ranged from 3.5∼4.7 and 0.8∼1.3 for the Q. serrata stand to 22.8∼23.6 and 3.7∼4.7 for the Q. variabilis stand. Nitrogen and P inputs (kg/ha/yr) into mineral soil through the CWD decomposition were 0.7 and 0.3 for the Q. serrata stand and 1.6 and 0.3 for the Q. variabilis stand, respectively. The number of CWD and decay rate were main factors influencing the difference in CWD mass and nutrient dynamics between both stands.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

• Korean Journal of Environment and Ecology
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• v.26 no.1
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• pp.74-81
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• 2012

Decay rate and nutrient dynamics during leaf litter decomposition of deciduous Quercus acutissima and evergreen Quercus mysinaefolia were studied for 24 months from December 2008 to December 2010 in Gongju, Chungnam Province, Korea. Percent remaining weight of Q. acutissima and Q. mysinaefolia leaf litter after 24 months elapsed was $46.3{\pm}5.4%$ and $37.8{\pm}2.5%$, respectively. Decomposition of evergreen Q. mysinaefolia leaf litter was significantly faster than that of deciduous Quercus acutissima leaf litter. Decay constant(k) of Q. acutissima and Q. mysinaefolia leaf litter after 24 months elapsed was 0.38 and 0.49, respectively. Initial C/N and C/P ratio of Q. mysinaefolia leaf litter was significantly lower than those of Q. acutissima leaf litter. Initial C/N and C/P ratio of Q. acutissima leaf litter was 46.8 and 270.9, respectively. After 24 months elapsed, C/N and C/P ratio of decomposing Q. acutissima leaf litter decreased to 22.5 and 104.2, respectively. Initial C/N and C/P ratio of Q. mysinaefolia leaf litter was 22.4 and 41.7, respectively. After 24 months elapsed, C/N and C/P ratio of decomposing Q. mysinaefolia leaf litter decreased to 16.7 and 89.7, respectively. Initial concentration of N, P, K, Ca and Mg in leaf litter was 8.31, 0.44, 4.18, 9.38, 1.37 mg/g in Q. acutissima, and 19.88, 2.73, 7.06, 8.24, 2.61 mg/g in Q. mysinaefolia, respectively. Initial concentration of N and P in Q. mysinaefolia leaf litter was significantly higher than those in Q. acutissima. After 24 month elapsed, remaining N, P, K, Ca and Mg were 100.91, 114.75, 32.99, 50.63, 15.51% in Q. acutissima, and 43.22, 11.35, 12.98, 82.22, 44.23% in Q. mysinaefolia, respectively. N and P in decomposing leaf litter was immobilized in Q. acutissima, and mineralized in Q. mysinaefolia.

• 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).

• Honam Mathematical Journal
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• v.34 no.2
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• pp.183-190
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• 2012

The main purpose of this paper is to introduce a new type of $q$-Euler numbers and polynomials with weak weight (${\alpha}$,${\omega}$): $\tilde{E}^{({\alpha},{\omega})}_{n,q}$ and $\tilde{E}^{({\alpha},{\omega})}_{n,q}(x)$, respectively. By using the fermionic $p$-adic $q$-integral on $\mathbb{Z}_p$, we can obtain some results and derive some recurrence identities for the $q$-Euler numbers and polynomials with weak weight (${\alpha}$,${\omega}$).

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.413-421
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• 2017

In this paper, we study the generalizations of Euler numbers and polynomials by using the q-extension with p-adic integral on $\mathbb{Z}_p$. We call these: the generalized q-${\omega}$-Euler numbers $E^{({\alpha})}_{n,q,{{\omega}}(a)$ and polynomials $E^{({\alpha})}_{n,q,{\omega}}(x;a)$. We investigate some elementary properties and relations for $E^{({\alpha})}_{n,q,{{\omega}}(a)$ and $E^{({\alpha})}_{n,q,{\omega}}(x;a)$.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.243-252
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• 2010

In this paper we extend the projective properties of representations of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as left R-modules to the projective properties of representations of quiver $Q={\bullet}{\rightarrow}{\bullet}$ as left $R[x]$-modules. We show that if P is a projective left R-module then $0{\rightarrow}P[x]$ is a projective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as $R[x]$-modules. And we show $0{\rightarrow}L$ is a projective representation of $Q={\bullet}{\rightarrow}{\bullet}$ as R-module if and only if $0{\rightarrow}L[x]$ is a projective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as $R[x]$-modules. Then we show if P is a projective left R-module then $R[x]\longrightarrow^{id}P[x]$ is a projective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as $R[x]$-modules. We also show that if $L\longrightarrow^{id}L$ is a projective representation of $Q={\bullet}{\rightarrow}{\bullet}$ as R-module, then $L[x]\longrightarrow^{id}L[x]$ is a projective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as $R[x]$-modules.