• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제13권3호
• /
• pp.203-215
• /
• 2009

In this article, we study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive differential equation with nonlocal conditions u'(t) = Au(t) + f(t, u(t); Tu(t); Su(t)), $0{\leq}t{\leq}T_0$, $t{\neq}t_i$, u(0) + g(u) = $u_0$, ${\Delta}u(t_i)=I_i(u(t_i))$, i = 1,2,${\ldots}$p, 0<$t_1$<$t_2$<$\cdots$<$t_p$<$T_0$, in a Banach space X, where A is the infinitesimal generator of a $C_0$ semigroup, g constitutes a nonlocal conditions, and ${\Delta}u(t_i)=u(t_i^+)-u(t_i^-)$ represents an impulsive conditions.

• 대한수학회보
• /
• 제52권3호
• /
• pp.1007-1025
• /
• 2015

Let $\mathbb{N}_0$ be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., $P(n,l)=\{(x_1,x_2,{\cdots},x_l){\in}\mathbb{N}^l_0\;:\;x_1+x_2+{\cdots}+x_l=n\}$. For any element $u=(u_1,u_2,{\cdots},u_l){\in}P(n,l)$, denote its ith-coordinate by u(i), i.e., $u(i)=u_i$. A family $A{\subseteq}P(n,l)$ is said to be t-intersecting if ${\mid}\{i:u(i)=v(i)\}{\mid}{\geq}t$ for all $u,v{\epsilon}A$. A family $A{\subseteq}P(n,l)$ is said to be trivially t-intersecting if there is a t-set T of $[l]=\{1,2,{\cdots},l\}$ and elements $y_s{\in}\mathbb{N}_0(s{\in}T)$ such that $A=\{u{\in}P(n,l):u(j)=yj\;for\;all\;j{\in}T\}$. We prove that given any positive integers l, t with $l{\geq}2t+3$, there exists a constant $n_0(l,t)$ depending only on l and t, such that for all $n{\geq}n_0(l,t)$, if $A{\subseteq}P(n,l)$ is non-trivially t-intersecting, then $${\mid}A{\mid}{\leq}(^{n+l-t-l}_{l-t-1})-(^{n-1}_{l-t-1})+t$$. Moreover, equality holds if and only if there is a t-set T of [l] such that $$A=\bigcup_{s{\in}[l]{\backslash}T}\;A_s{\cup}\{q_i:i{\in}T\}$$, where $$A_s=\{u{\in}P(n,l):u(j)=0\;for\;all\;j{\in}T\;and\;u(s)=0\}$$ and $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• 음성과학
• /
• 제6권
• /
• pp.33-44
• /
• 1999

This paper aims to analyze whether the phenomenon of /u/$\rightarrow$/i/ is a hypercorrection or not in the North Korean dialects. Most North Koreans pronounce /i/(gold) as /kum/ because the vowel /i/ merges into the peripheral vowel space of /u/ in their dialects. The merger of back vowel is one of most distinctive characters in North Korean dialects. But some speakers pronounce /chubann/(exile) as /chiban/. This time /u/ in peripheral space moves to /i/ in central vowel space. It seems that the vowels /i/ and /u/ exchange places with each other when they uttered in North Korean. Though it was observed that the vowel movement of /i/$\rightarrow$/u/ was caused by the merger of back vowels, the reason why vowel /u/ moves in the opposite direction, that is, the central space of vowel /i/ has not been analyzed yet. This experiment starts with hypothesis that the movement of /u/$\rightarrow$/i/ might be caused by hypercorrection. The first step of this research is to analyze /u/$\rightarrow$/i/ pronunciation of North Koreans. The second step is to compare the results of North Korean pronunciation with those of South Korean pronunciation and observe whether tendency of /u/$\rightarrow$/i/pronunciation can also be found in the standard Seoul dialect and other South Korean dialects.

• Journal of applied mathematics & informatics
• /
• 제14권1_2호
• /
• pp.1-37
• /
• 2004

We consider the following system of discrete equations $u_i(\kappa)\;=\;{\Sigma{N}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;{\cdots}\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;,\;T\},\;1\;{\leq}\;i\;{\leq}\;n\;where\;T\;{\geq}\;N\;>\;0,\;1\;{\leq}i\;{\leq}\;n$. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on $\{0,\;1,\;{\cdots}\;\}\;u_i(\kappa)\;=\;{\Sigma{\infty}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;\cdots\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;\},\;1\;{\leq}\;i\;{\leq}\;n$ for which the existence of constant-sign solutions is investigated.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제11권2호
• /
• pp.9-14
• /
• 2007

A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with $U\;=\;\{u_1,\;u_2,\;{\cdots},\;u_p\},\;V\;=\;\{v_1,\;v_2,\;{\cdots},\;v_q\}\;and\;W\;=\;\{w_1,\;w_2,\;{\cdots},\;w_r\}$. Then, signed degree of $u_i(v_j\;and\;w_k)$ is $sdeg(u_i)\;=\;d_i\;=\;d^+_i\;-\;d^-_i,\;1\;{\leq}\;i\;{\leq}\;p\;(sdeg(v_j)\;=\;e_j\;=\;e^+_j\;-\;e^-_j,\;1\;{\leq}\;j\;{\leq}q$ and $sdeg(w_k)\;=\;f_k\;=\;f^+_k\;-\;f^-_k,\;1\;{\leq}\;k\;{\leq}\;r)$ where $d^+_i(e^+_j\;and\;f^+_k)$ is the number of positive edges incident with $u_i(v_j\;and\;w_k)$ and $d^-_i(e^-_j\;and\;f^-_k)$ is the number of negative edges incident with $u_i(v_j\;and\;w_k)$. The sequences ${\alpha}\;=\;[d_1,\;d_2,\;{\cdots},\;d_p],\;{\beta}\;=\;[e_1,\;e_2,\;{\cdots},\;e_q]$ and ${\gamma}\;=\;[f_1,\;f_2,\;{\cdots},\;f_r]$ are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.

• 대한수학회보
• /
• 제42권2호
• /
• pp.231-244
• /
• 2005

We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space H. $$Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,$$ $where\;Lu^i=\;\frac{\partial u^i}{\partial t}\;-\;Au^{i}$, A is a linear closed operator on Hand M(t, x) is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\beta^1\leq\beta^2\;then\;u^1{\leq}u^2$ under some conditions.

• Journal of Plant Biology
• /
• 제29권1호
• /
• pp.53-65
• /
• 1986

The montane forests of Ulreung Island, Korea, were investigated by the ZM school method. By comparing the montane forests of this island with those of Korean Peninsula and of Japan, a new order, F a g e t a l i a m u l t i n e r v i s, a new alliance, F a l g i o n m u l t i n e r v i s, a new association, H e p a t i c o-F a g e t u m m u l t i n e r v i s and Rhododendron brachycarpum-Pinus parviflora community were recognized. The H e p a t i c o - F a g e t u m m u l t i n e r v i s was further subdivided into four subassociations; Subass. of Sasa kurilensis, Subass. of Rumohra standishii, Subass. of Rhododendron brachycarpum and Subass. of typicum. Each community was described in terms of floristic, structural and environmental features.

• 대한수학회지
• /
• 제58권5호
• /
• pp.1109-1129
• /
• 2021

This paper considers an anisotropic polytropic infiltration equation with a source term $$u_t={\sum\limits_{i=1}^{N}}{\frac{{\partial}}{{\partial}x_i}}\(a_1(x){\mid}u{\mid}^{{\alpha}_i}{\mid}u_{x_i}{\mid}^{p_i-2}u_{x_i}\)+f(x,t,u)$$, where p_i > 1, α_i > 0, a_i(x) ≥ 0. The existence of weak solution is proved by parabolically regularized method. Based on local integrability $u_{x_i}{\in}W_{loc}^{1,p_i}(\Omega)$, the stability of weak solutions is proved without boundary value condition by the weak characteristic function method. One of the essential characteristics of an anisotropic equation different from an isotropic equation is found originally.

• 분석과학
• /
• 제6권5호
• /
• pp.489-499
• /
• 1993

Aresenazo I-XAD-2 킬레이수지를 합성하고 이 수지에 대한 U(VI) 이온의 흡착 거동을 조사 검토하였다. 킬레이트수지는 Arsenazo I 킬레이트제와 Amberlite XAD-2의 디아조늄 짝지움 반응에 의해서 합성하였으며 원소 분석법과 적외선 분광법으로 확인하였다. U(VI) 이온 흡착의 최적 조건을 찾기 위해서 pH, U(VI) 이온농도와 진탕 시간에 관해서 조사하였다. U(VI) 이온에 대한 킬레이트수지의 전체 흡착능은 pH 4.0~4.5 범위에서 0.39mmol U(VI)/g resin이었고, pH값이 증가함에 따라 흡착능이 증가하였다. Aresenazo I-XAD-2 킬레이트 수지에 대한 U(VI) 이온의 흡착 메카니즘은 U(VI) 이온과 $H^+$ 이온 사이의 경쟁반응임을 확인하였다. 컬럼법으로 구한 U(VI) 이온의 돌파점 부피와 전체 흡착능은 각각 600ml, 0.38mmol U(VI)/g resin이었다. 3M $HNO_3$와 3M $Na_2CO_3$의 탈착용액을 사용하여 구한 회수율은 90~96%였다. 따라서 본 연구에서는 합성한 Arsenaso I-XAD-2 킬레이트수지는 자연수 바닷물 중에 함유된 U(VI) 이온의 분리와 농축에 매우 유용함을 알았다.

• 대한한방내과학회지
• /
• 제29권4호
• /
• pp.856-870
• /
• 2008

Objectives : Consumption is a chronic wasting disease and major portion of Oriental Medicine's therapy. However, there is no standard diagnostic method for consumption that is $q{\grave{i}}-x{\bar{u}}$, $xu{\grave{e}}-x{\bar{u}}$, $yang-x{\bar{u}}$, $y{\bar{i}}n-x{\bar{u}}$. Methods : A questionnaire which includes symptoms and signs for diagnosis of $q{\grave{i}}-x{\bar{u}}$, $xu{\grave{e}}-x{\bar{u}}$, $yang-x{\bar{u}}$, $y{\bar{i}}n-x{\bar{u}}$ was evaluated by Delphi technique. Each question was valuated by interviewing 27 oriental medicine doctors. Then. we choose questions given over 5 points and reorganized some items according to the recommendations by interviewed-doctors. We then accessed the value of re-organized questions composing of the questionnaires. Conclusion : We finally chose each 9 items of $q{\grave{i}}-x{\bar{u}}$, $xu{\grave{e}}-x{\bar{u}}$, $yang-x{\bar{u}}$, $y{\bar{i}}n-x{\bar{u}}$'s questionnaire. Further study is necessary for modification of questionnaire by statistics and certification by clinical trial.