• East Asian mathematical journal
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• 제16권1호
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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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• 제27권2호
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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.

• 한국수학사학회지
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• 제20권4호
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• pp.71-84
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• 2007

베르누이가 처음으로 자연수 k에 대하여 합 $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$에 관한 공식들을 유도하는 방법을 발견하였다([4]). 그 이후, 리만 제타함수와 관련된 베르누이 수와 오일러 수에 관한 성질들이 연구되어왔다. 최근에 김태균은 $\mathbb{Z}_p$상에서 p-진 q-적분과 관련된 확장된 q-베르누이 수와 q-오일러 수, 연속된 q-정수의 멱수의 합에 관한 성질들을 밝혔다. 본 논문에서는 연속된 q-정수의 멱수의 합에 관한 역사적 배경과 발달과정을 고찰하고, 오일러 및 베르누이 수와 관련된 리만 제타함수가 해석적 함수로써 값을 가지는 문제를 q-확장된 부분의 이론으로 연구되어온 q-오일러 제타함수에 대해 체계적으로 논의한다.

• 대한수학회지
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• 제34권4호
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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).

• 호남수학학술지
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• 제34권2호
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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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• 제35권3_4호
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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 $E^{({\alpha})}_{n,q,{\omega}}(x;a)$.

• 한국환경생태학회지
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• 제26권1호
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• pp.74-81
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• 2012

상록활엽수인 가시나무와 낙엽활엽수인 상수리나무 낙엽의 분해율 및 분해과정에 따른 영양염류의 함량 변화를 파악하기 위해 2008년 12월 공주의 상수리나무군락에 낙엽주머니를 설치하고 2009년 3월부터 2010년 12월까지 3개월 간격으로 낙엽주머니를 수거하여 분해율, 분해상수(k), 그리고 분해과정에 따른 C/N비, C/P비의 변화와 영양염류의 동태를 조사하였다. 24개월경과 후 상수리나무 낙엽과 가시나무 낙엽의 잔존률은 각각 $46.3{\pm}5.4%$와 $37.8{\pm}2.5%$로 가시나무 낙엽의 분해가 상수리나무 낙엽의 분해보다 빠르게 진행되는 것으로 나타났다. 24개월경과 후 상수리나무 낙엽과 가시나무 낙엽의 분해상수(k)는 각각 0.38과 0.49로 가시나무 낙엽의 분해상수가 높게 나타났다. 상수리나무 낙엽의 분해과정에 따른 C/N. C/P 비율은 초기에 각각 46.8, 270.9 이었으나 24개월경과 후에는 각각 22.5와 104.2로 점차 감소하였으며, 가시나무 낙엽의 경우 초기 C/N, C/P 비율은 각각 22.4와 41.7로 나타났고, 24개월경과 후에는 각각 16.7와 89.9로 나타났다. 낙엽의 초기 N, P, K, Ca, Mg 함량은 상수리나무 낙엽에서 각각 8.31, 0.44, 4.18, 9.38, 1.37 mg/g, 가시나무 낙엽에서 각각 19.88, 2.73, 7.06, 8.24, 2.61 mg/g으로 가시나무 낙엽의 질소와 인의 함량이 상수리나무 낙엽에 비해 현저히 높았다. 24개월경과 후 N, P, K, Ca, Mg의 잔존률은 상수리나무 낙엽에서 각각 100.91, 114.75, 32.99, 50.63, 15.51% 이었고, 가시나무 낙엽에서 각각 43.22, 11.35, 12.98, 82.22, 44.23% 로 조사기간 동안에 상수리나무 낙엽에서는 질소와 인의 부동화가, 가시나무 낙엽에서는 질소와 인의 무기화가 진행되었다.

• Korean Journal of Mathematics
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• 제18권3호
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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.

• Molecules and Cells
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• 제24권1호
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• pp.105-112
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• 2007

Most neuroblastoma cells have chromosomal aberrations such as gains, losses, amplifications and deletions of DNA. Conventional approaches like fluorescence in situ hybridization (FISH) or metaphase comparative genomic hybridization (CGH) can detect chromosomal aberrations, but their resolution is low. In this study we used array-based comparative genomic hybridization to identify the chromosomal aberrations in human neuroblastoma SH-SY5Y cells. The DNA microarray consisting of 4000 bacterial artificial chromosome (BAC) clones was able to detect chromosomal regions with aberrations. The SH-SY5Y cells showed chromosomal gains in 1q12~ q44 (Chr1:142188905-246084832), 7 (over the whole chro-mosome), 2p25.3~p16.3 (Chr2:18179-47899074), and 17q 21.32~q25.3 (Chr17:42153031-78607159), while chromosomal losses detected were the distal deletion of 1p36.33 (Chr1:552910-563807), 14q21.1~q21.3 (Chr14:37666271-47282550), and 22q13.1~q13.2 (Chr22:36885764-4190 7123). Except for the gain in 17q21 and the loss in 1p36, the other regions of gain or loss in SH-SY5Y cells were newly identified.

• 대한수학회지
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• 제59권2호
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• pp.235-254
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• 2022

Let ℍⁿ be the Heisenberg group and Q = 2n + 2 be its homogeneous dimension. Let 𝓛 = -∆_ℍⁿ + V be the Schrödinger operator on ℍⁿ, where ∆_ℍⁿ is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class $B_{q_1}$ for q₁ ≥ Q/2. Let H^p_𝓛(ℍⁿ) be the Hardy space associated with the Schrödinger operator 𝓛 for Q/(Q+𝛿₀) < p ≤ 1, where 𝛿₀ = min{1, 2 - Q/q₁}. In this paper, we consider the Hardy type estimates for the operator T_𝛼 = V^𝛼(-∆_ℍⁿ + V )^-𝛼, and the commutator [b, T_𝛼], where 0 < 𝛼 < Q/2. We prove that T_𝛼 is bounded from H^p_𝓛(ℍⁿ) into L^p(ℍⁿ). Suppose that b ∈ BMO^𝜃_𝓛(ℍⁿ), which is larger than BMO(ℍⁿ). We show that the commutator [b, T_𝛼] is bounded from H¹_𝓛(ℍⁿ) into weak L¹(ℍⁿ).