• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1007-1025
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• 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 $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• Speech Sciences
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• v.9 no.4
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• pp.59-75
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• 2002

Aerodynamic analysis study was performed on 14 normal subjects (2 males, 12 females) with nonsense syllables composed of Korean bilabial stops (/p, p', $p^{h}$) and their preceding and/or following vowels, /i, a, u/. That is, [pi, p'i, $p^{h}i$, pa, p'a, $p^{h}a$, pu, p'u, $p^{h}u$, ipi, apa, upu, $ip^{h}i$, $ap^{h}a$, $up^{h}u$, ip'i, ap'a, up'u]. All measures were taken and analysed using Aerophone II voice function analyzer and included peak air pressure, mean air pressure, maximum flow rate, volume, mean SPL and phonatory SPL. A t-test and one-way ANOVA were employed for analysis. A post-hoc analysis was performed with Scheffe and Bonferroni. The results were as follows: First, MSPL. and MAP of /p, p', $p^{h}$/ were significantly different in different positions (initial and medial position). In addition, different vowel environment also produced significantly different aerodynamic characteristics those consonants. Especially the lax consonant /p/ was significantly different /i, a, u/ vowel environments. The tense consonant /p'/ was significantly different only /i/ vowel environment.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1109-1129
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.999-1011
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• 2009

In this paper, we are concerned with the following eigenvalue problems of m-point boundary value problem for p-Laplacian dynamic equation on time scales $(\varphi_p(u^{\Delta}(t)))^\nabla+{\lambda}h(t)f(u(t))=0,\;t\in(0,T)$, $u(0)=0,\varphi_p(u^{\Delta}(T))=\sum\limits_{i=1}^{m-2}a_i\varphi_p(u^{\Delta}(\xi_i))$, where $\varphi_p(u)=|u|^{p-2}$u, p > 1 and $\lambda$ > 0 is a real parameter. Under certain assumptions, some new results on existence of one or two positive solution and nonexistence are obtained for $\lambda$ evaluated in different intervals. Our work develop and improve many known results in the literature even for the continual case. In doing so the usual restriction that $f_0=lim_{u{\rightarrow}0}+f(u)/\varphi_p(u)$ and $f_\infty = lim_{u{\rightarrow}{\infty}}f(u)/\varphi_p({u})$ exist is removed. As an applications, an example is given to illustrate the main results obtained.

• Analytical Science and Technology
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• v.6 no.5
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• pp.489-499
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• 1993

Some sorption behaviors of U(VI) ion on Arsenazo I-XAD-2 chelating resin were investigated. This chelating resin was synthesized by the diazonium coupling of Amberlite XAD-2 resin with Arsenzo I chelating reagent and characterized by elementary analysis method and IR spectrometry. The optimum conditions for the sorption of U(VI) ion were examined with respect to pH, U(VI) ion concentration and shaking time. Total sorption capacity of this chelating resin on U(VI) ion was 0.39mmol U(VI)/g resin in the pH range of 4.0~4.5. This chelating resin was showed increased sorption capacity on the increased pH value. It was confirmed that sorption mechanism of U(VI) ion on the Arsenazo I-XAD-2 chelating resin was competition reacting between U(VI) ion and $H^+$ ion. Breakthrough volume and overall capacity of U(VI) ion measured by column were was 600 ml and 0.38 mmol U(VI)/g resin, respectively. The desorption of U(VI) ion was showed recovery of 90~96% using 3M $HNO_3$ and 3M $Na_2CO_3$ as a desorption solution. The separation and concentration of U(VI) ion from natural water and sea water was performed successfully by Arsenazo I-XAD-2 chelating resin.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.9-14
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• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.203-215
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• 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.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1211-1220
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• 2009

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 2017.04a
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• pp.37-38
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• 2017

최근 방제 및 예찰과 같은 농작업에 단일 UAV(Unmanned Aerial Vehicle)시스템이 적용되고 있지만, 가반하중과 체공시간 등 기존시스템의 문제가 점차 대두되면서 작업 시간을 보다 단축시키고 작업 효율을 극대화 할 수 있는 농업용 멀티 UAV시스템의 필요성이 증대되고 있다. 본 논문에서는 작업자가 다수의 농업용 UAV를 효과적으로 제어할 수 있는 분산군집제어 알고리즘을 제안하며 알고리즘 검증 및 평가를 위한 시뮬레이터를 소개한다. 분산군집제어는 UAV 제어 계층, VP(Virtual Point) 제어 계층, 원격제어 계층으로 이루어진 3계층 제어구조를 가진다. UAV 제어 계층에서 각 UAV는 point mass로 모델링 되는 VP의 이상적인 경로를 추종하도록 제어한다. VP 제어 계층에서 각 VP는 입력 $p_i(t)=u^c_i+u^o_i+u^{co}_i+u^h_i$-(1)을 받아 제어되는데 여기서, $u^c_i{\in}{\mathbb{R}}^3$는 VP 사이의 충돌방지제어, $u^o_i{\in}{\mathbb{R}}^3$는 장애물과의 충돌방지제어, $u^{co}_i{\in}{\mathbb{R}}^3$는 UAV 상호간의 협조제어, $u^h_i{\in}{\mathbb{R}}^3$는 작업자로부터의 원격제어명령이다. (1)의 제어입력에서 충돌방지제어는 각 $u^i_c:=-{\sum\limits_{j{\in}{\eta}_i}}{\frac {{\partial}{\phi}_{ij}^c({\parallel}p_i-p_j{\parallel})^T}{{\partial}p_i}}$-(2), $u^o_c:=-{\sum\limits_{r{\in}O_i}}{\frac {{\partial}{\phi}_{ir}^o({\parallel}p_i-p^o_r{\parallel})^T}{{\partial}p_i}}$-(3)로 정의되면 ${\phi}^c_{ij}$와 ${\phi}^o_{ir}$는 포텐셜 함수를 나타낸다. 원격제어 계층에서 작업자는 햅틱 인터페이스를 통해 VP의 속도를 제어하게 된다. 이때 스케일변수 ${\lambda}$에 대하여 VP의 원격제어명령은 $u^t_i(t)={\lambda}q(t)$로 정의한다. UAV 시뮬레이터는 리눅스 환경에서 ROS(Robot Operating Systems)를 기반한 3차원 시뮬레이터인 Gazebo상에 구축하였으며, 마스터와 슬레이브 간의 제어 명령은 TCPROS를 통해 서로 주고받는다. UAV는 PX4 기반의 3DR Solo 모델을 사용하였으며 MAVROS를 통해 MAVLink 통신 프로토콜에 접속하여 UAV의 고도, 속도 및 가속도 등의 상태정보를 받을 수 있다. 현재 멀티 드론 시스템을 Gazebo 환경에 구축하였으며, 추후 시뮬레이터 상에 분산군집제어 알고리즘을 구현하여 검증 및 평가를 진행하고자 한다.

• Journal of Plant Biology
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• v.29 no.1
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• pp.53-65
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• 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.