• 대한수학회보
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• 제52권3호
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• pp.907-914
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• 2015

In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.147-163
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• 2014

In this paper, we study the existence of positive solutions for singular impulsive differential equations with integral boundary conditions $$\{u^{{\prime}{\prime}}(t)+q(t)f(t,u(t),u^{\prime}(t))=0,\;t{\in}\mathbb{J}^{\prime},\\{\Delta}u(t_k)=I_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\{\Delta}u^{\prime}(t_k)=-L_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\u=(0)={\int}_{0}^{1}g(t)u(t)dt,\;u^{\prime}=0,$$) where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based on the theory of Leray-Schauder degree, together with a truncation technique. Some recent results in the literature are generalized and improved.

• 한국지반공학회논문집
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• 제29권9호
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• pp.43-54
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• 2013

본 연구는 연약지반현장의 사면활동에 관한 계측자료를 분석하여, p-q 응력경로에서 얻은 안정관리지수(Stability Control Index, SCI)를 이용한 새로운 성토체의 안정관리기법을 제안하고자 한다. 여기서는 이와 같은 새로운 기법을 검증하기 위하여 삼축압축시험(CU)을 실시하여 현장 계측자료와 상호 비교 검토하였다. 안정관리지수(SCI)는 응력경로에서 전응력경로점 $p_{max}$ 와 $k_f$선상의 점 $p_f$사이의 상대적인 위치를 이용하여 현재의 유효응력경로점 ($p^{\prime}=p-{\Delta}u$)으로부터 얻은 값이다. 이와 같은 결과로 유효응력점 $p^{\prime}(=p-{\Delta}u)$ 는 간극수압이 발생될 때는 $k_f$선상의 점인 $p_f$, 간극수압이 소산될 때는 전응력점인 $p^{\prime}_{max}$에 접근할 것이다. 따라서 안정관리지수(SCI)는 유효응력경로점의 상대적인 위치로부터 성토체의 안정상태를 정량적으로 평가할 수 있다.

• 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 $p$.

• 대한수학회논문집
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• 제32권1호
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• pp.193-200
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• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.

• 접착 및 계면
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• 제10권2호
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• pp.84-89
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• 2009

The objective of this research was to investigate the curing behavior and adhesion performance of urea-melamine-formaldehyde (UMF) resin for the four types of UMF-1, UMF-2, UMF-3, and UMF-4 which synthesized by the staged addition of melamine. Also, various network structures of these resin types were discussed based on their different curing behavior and adhesion performance. The curing behavior was evaluated by DMTA and thermal stability was checked by TGA. Adhesion performance was evaluated by dry and wet shear strengths and the pH value of each cured resin was checked to see its effect on the adhesion performance. The results indicated that the UMF-1 resin type by the addition of melamine initially with the urea and formaldehyde at the same F/(U+M) rate showed the lowest thermal stability, rigidity (${\Delta}E^{\prime}$), temperature of tan ${\delta}$ maximum ($T_{tan}\;_{\delta}$), and wet shear strength, and pH value of cured resin. In wet shear strength, however, the UMF-4 resin type appears to be slightly higher than UMF-1 resin type.

• 대한토목학회논문집
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• 제29권6C호
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• pp.277-285
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• 2009

실트함유량 변화에 따른 낙동강 모래의 반복전단강도 특성을 살펴보고자 낙동강 유역에 분포하는 모래와 실트를 채취하여 실트함유량 0~50%의 범위로 실내에서 재성형된 실트질 모래시료에 대하여 일련의 비배수 반복삼축실험을 실시하였다. 실험 결과, 실트함유량 변화에 따른 반복횟수(N) 10에서의 반복전단응력비(CSR)는 모든 상대밀도에서 실트함유량 5%에서 최대였고, 20%에서 최소를 보였다. 반복비($N/N_L$)에 따른 간극수압비(${\Delta}u/p^{\prime}$) 관계로 부터 분석된 간극수압의 발달 경향은 실트함유량에 따른 CSR 크기변화와는 무관하였다. 압밀 후 간극비(e)와 skeleton 간극비($e_s$)를 비교해 본 결과, 전반적으로 실트함유량에 따른 CSR의 변화 경향과 일치하여 실트함유량에 따른 CSR은 실트질 모래의 전단거동에 영향을 미치는 모래만의 간극비인 skeleton 간극비($e_{s}$)에 큰 영향을 받는 것으로 나타났다.