• Korean Journal of Mathematics
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• 제6권2호
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• pp.221-229
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• 1998

Let $k$ be a real abelian field and $k_{\infty}$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $k_n$, the $nth$ layer of the $\mathbb{Z}_p$-extension. By using the main conjecture of Iwasawa theory, we have the following: If $p$ does not divide $\prod_{{{\chi}{\in}\hat{\Delta}_k},{\chi}{\neq}1}B_{1,{\chi}{\omega}^{-1}$, then $A_n$ = {0} for all $n{\geq}0$, where ${\Delta}_k=Gal(k/\mathbb{Q})$ and ${\omega}$ is the Teichm$\ddot{u}$ller character for $p$. The converse of this statement does not hold in general. However, we have the following when $k$ is of prime conductor $q$: Let $q$ be an odd prime different from $p$. and let $k$ be a real subfield of $\mathbb{Q}({\zeta}_q)$. If $p{\mid}{\prod}_{{\chi}{\in}\hat{\Delta}_{k,p},{\chi}{\neq}1}B_{1,{\chi}{\omega}}-1$, then $A_n{\neq}\{0\}$ for all $n{\geq}1$, where ${\Delta}_{k,p}$ is the $Gal(k_{(p)}/\mathbb{Q})$ and $k_{(p)}$ is the decomposition field of $k$ for $p$.

• Journal of Applied and Pure Mathematics
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• 제5권1_2호
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• pp.41-53
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• 2023

Let G = (V, E) be a (p, q) graph. Define $${\rho}=\{{\frac{2}{p}},\;{\text{{\qquad} if p is even}}\\{\frac{2}{p-1}},\;{{\text{if p is odd}}$$ and L = {±1, ±2, ±3, … , ±ρ} called the set of labels. Consider a mapping f : V ⟶ L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that ${\mid}{\Delta}_{f_1}-{\Delta}_{f^c_1}{\mid}{\leq}1$, where ${\Delta}_{f_1}$ and ${\Delta}_{f^c_1}$ respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behaviour of Petersen graphs P(n, k) like P(n, 2), P(n, 3), P(n, 4).

• Applied Biological Chemistry
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• 제47권1호
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• pp.33-40
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• 2004

Ubiquitin 폴딩 반응의 초기에 나타나는 transient 폴딩 intermediate 상태의 열역학적인 특성을 연구하였다. 온도와 화학변성제의 농도를 바꾸어주면서 측정한 폴딩 kinetics의 결과로부터 unfolded 상태와 intermediate 상태의 평형상수 및 자유에너지를 quantitative kinetic modeling을 통하여서 구하였으며 또한 온도에 따른 자유에너지의 변화로부터 unfolded 상태에서 intermediate 상태로 전환될 때의 열역학적 함수인 ${\Delta}H,\;{\Delta}S,\;{\Delta}C_p$를 구하였다. Ubiquitin이 unfolded 상태에서 intermediate 상태가 될 때의 ${\Delta}C_p$는 unfolded 상태에서 native 상태로 되는 과정의 ${\Delta}C_p$의 약 80% 정도 되었다. 이것은 intermediate가 native 상태에 가까운 매우 조밀한 구조를 이루고 있는 ensemble state임을 나타낸다. 상온에서의 ${\Delta}H$는 양의 값을 보였다. 이는 ubiquitin의 unfolded 상태에서 소수성 잔기 주위에 위치한 물 분자의 규칙적인 구조가 intermediate 상태가 될 때 와해되기 때문이라고 여겨진다. 이러한 양의 enthalpy는 자유로워진 물 분자에 의한 전체 계의 entropy의 증가에 의하여서 보상되어 unfolded 상태에서intermediate 상태로의 전환은 음의 자유에너지를 갖게 되며 폴딩 반응의 초기에 관찰되는 것으로 여겨진다.

• 대한화학회지
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• 제30권2호
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• pp.188-194
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• 1986

에탄올-물 혼합용매내에서 p-클로로 염화벤질의 가용매분해반응에 대한 속도상수를 압력 1~1,600bar, 온도를 30${\circ}$, 40${\circ}$C 에서 측정하였다. 반응속도들은 온도와 압력이 증가함에 따라 증가하고, 에탄올 몰 분율이 증가함에 따라 감소하였다. ln k대 압력의 플로트는 압력에 따라 이차함수꼴로 변함을 알았고, 이 플로트로부터 ${\Delta}V^{\neq}$와 ${\Delta}{\beta}^{\neq}$의 값을 얻었다. 그 결과 ${\Delta}V^{\neq}$와 ${\Delta}{\beta}^{\neq}$의 값은 약 0.20몰 분율에서 Extremum behavior가 나타남을 알았다. 이 현상을 용매구조 변화로 논의하였다. ln k대 용매파라미터, q 및 ln $C_w$의 플로트사이의 관계로부터 본 연구의 반응은 $S_N1(2)$메카니즘으로 진행됨을 추정할 수 있었다.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.421-426
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• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• 대한수학회보
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• 제49권6호
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• pp.1131-1145
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• 2012

The purpose of this paper is to use an appropriate variational framework to discuss the boundary value problem with p-Laplacian type operators $$\{({\alpha}(t,x^{\Delta}(t)))^{\Delta}-a(t){\phi}_p(x^{\sigma}(t))+f({\sigma}(t),x^{\sigma}(t))=0,\;{\Delta}-a.e.\;t{\in}I\\x^{\sigma}(0)=0,\\{\beta}_1x^{\sigma}(1)+{\beta}_2x^{\Delta}({\sigma}(1))=0,$$ where ${\beta}_1$, ${\beta}_2$ > 0, $I=[0,1]^{k^2}$, ${\alpha}({\cdot},x({\cdot}))$ is an operator of $p$-Laplacian type, $\mathbb{T}$ is a time scale. Some sufficient conditions for the existence of constant-sign solutions are obtained.

• Bulletin of the Korean Chemical Society
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• 제32권3호
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• pp.889-893
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• 2011

The energetics and transition state (TS) structures of the reactions of six substrates, $R_1R_2P$(=O or S)Cl-type where $R_1=R_2$=Me and/or MeO, with ammonia in acetonitrile are theoretically investigated at the level of CPCM-MP2/6-31+G(d) and CPCM-MP2/6-311+G(3df,2p). The degrees of distortion of TS from the ideal trigonal bipyramidal pentacoordinate, ${\Delta}{{\delta}}_{{\neq}b}$ for a backside and ${\Delta}{{\delta}}_{{\neq}f}$ for a frontside attack, are calculated. The results of calculation suggest that the feasibility of a frontside attack for P=S is greater than that for P=O system when the two ligands, $R_1$ and $R_2$, becomes larger. The experimental and calculated results of anilinolyses of $R_1R_2P$(=O or S)Cl-type show the consistent tendencies.

• Earthquakes and Structures
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• 제8권1호
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• pp.253-273
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• 2015

The current investigation has been conducted to examine the effect of gravity loads on the seismic responses of the doubly asymmetric, three-dimensional structures comprising walls and frames. The proposed model includes the P-${\Delta}$ effects induced by the building weight. Based on the variational approach, a 3D finite element with two nodes and six DOF per node including P-${\Delta}$ effects is formulated. Dynamic and static governing equations are derived for dynamic and buckling analyzes of buildings braced by wall-frame systems. The influences of P-${\Delta}$ effects and height of the building on tip displacements under Hachinohe earthquake record are investigated through many structural examples.

• 대한화학회지
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• 제32권5호
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• pp.464-475
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• 1988

Fe(Ⅲ) 및 Mn(Ⅱ)과 p-aminoazobenzene 및 그 유도체가 반응하여 형성된 착물들에 대하여 가시-자외선 및 적외선 분광광도법과 전기전도도방법을 이용하여 용매의 효과, donor의 염기도와 착물형성에 미치는 영향을 조사하였다. 그 결과 착물의 조성비, 안정도 상수 및 몰흡광계수를 구하여 van't Hoff식으로부터 ${\Delta}H^{\circ}$, ${\Delta}G^{\circ}$ 및 ${\Delta}S^{\circ}$를 계산하였으며 반응성과 등속도관계를 고려하여 반응속도와 평형조절인자를 알게 되었다.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.777-789
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• 2016

In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term $$(r(t)x^{\Delta}(t))^{\Delta}+q({\sigma}(t))x^{\Delta}(t)+p(t)f(x({\tau}(t)))=e(t)$$, and $$(r(t)x^{\Delta}(t))^{\Delta}+q(t)x^{\Delta}(t)+p(t)f(x({\sigma}(t)))=e(t)$$, on a time scale ${\mathbb{T}}$, where r(t), p(t) and q(t) are real-valued right-dense continuous (rd-continuous) functions [1] defined on ${\mathbb{T}}$ with p(t) < 0 and ${\tau}:{\mathbb{T}}{\rightarrow}{\mathbb{T}}$ is a strictly increasing differentiable function and ${\lim}_{t{\rightarrow}{\infty}}{\tau}(t)={\infty}$. No restriction is imposed on the forcing term e(t) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.