• East Asian mathematical journal
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• 제39권3호
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• pp.271-278
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• 2023

We consider a 1-dimensional reaction diffusion equation with the following boundary conditions arising in a theory of the thermal explosion {-u"(t) = λf(u(t)), t ∈ (0, l), -u'(0) + C(0)u(0) = 0, u'(l) + C(l)u(l) = 0, where C : [0, ∞) → (0, ∞) is a continuous and nondecreasing function, λ > 0 is a parameter and f : [0, ∞) → (0, ∞) is a continuous function. We establish the extension of Quadrature method introduced in [8]. Using this extension, we provide numerical results for models with a typical function of f and C in a thermal explosion theory, which verify the existence, uniqueness and multiplicity results proved in [6].

• East Asian mathematical journal
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• 제1권
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• pp.89-100
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• 1985

A mapping f: X$\rightarrow$Y is introduced to be weakly irresolute if, for each x $\varepsilon$ X and each semi-neighborhood V of f(x), there exists a semi-neighborhood U of x in X such that $f(U){\subset}scl(V)$. It will be shown that a mapping f: X$\rightarrow$Y is weakly irresolute iff(if and only if) $f^{-1}(V){\subset}sint(f^{_1}(scl(V)))$ for each semiopen subset V of Y. The relationship between mappings described in [3,5, 6,8] and a weakly irresolute mapping. will be investigated and it will be shown that every irresolute retract of a $T_2$-space is semiclosed.

• 의료법학
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• 제10권2호
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• pp.183-201
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• 2009

Im Allgemeinen auch psychische Patienten k$\ddot{o}$nnen sich daruber selbst entscheiden, $\ddot{a}$rztliche Behandlung zu nehmen und ins Krankenhaus aufgenommen zu werden. Im S$\ddot{u}$dkorea bei der zwangsweisen Unterbringung wird kein KBGB des privatlichen Rechts, sondern Gesetz $\ddot{u}$ber psychisch Gesundheitspflege des $\ddot{o}$ffentlichen Rechts vorz$\ddot{u}$glich verwandt. Aber das noch kann ein selbst Bestimmungsrecht von der psychischen Patient verletzen. Im Deutschland regelt BGB $\S$ 1906 Zwangsunterbringung der psychische Patienten, die Gef$\ddot{a}$hr des Selbstmord oder der Eigengef$\ddot{a}$hrdung haben. Au$\ss$erdemhat jedes Land eigen Gesetz $\ddot{u}$ber psychischen Kranken, das $\ddot{o}$ffentliche Vorschrift f$\ddot{u}$r Zwangsunterbringung regelt. Im Fall der Zwangsunterbringung im Deutschland BGB $\S$ 1906 wird prim$\ddot{a}$rer als $\ddot{o}$ffentlich Rechts verwandt, um die Selbstbestimmungsrecht der Patienten zu unterstutzen. Auch im Korea KBGB (koreanisches B$\ddot{u}$rgerliches Gesetzbuch) Ver$\ddot{a}$nderungen f$\ddot{u}$r die Einf$\ddot{u}$hrung des Betreuungsrechts, die sich mit der Zwangsunterbringung befassen, sollten diskutiert werden, damit die Selbstbestimmung sch$\ddot{a}$tzen.

• 대한수학회보
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• 제55권5호
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• pp.1441-1462
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• 2018

In this paper, we investigate the fractional p&q-Kirchhoff type system $$\{M_1([u]^p_{s,p})(-{\Delta})^s_pu+V_1(x){\mid}u{\mid}^{p-2}u\\{\hfill{10}}={\ell}k^{-1}F_u(x,\;u,\;v)+{\lambda}{\alpha}(x){\mid}u{\mid}^{m-2}u,\;x{\in}{\Omega}\\M_2([u]^q_{s,q})(-{\Delta})^s_qv+V_2(x){\mid}v{\mid}^{q-2}v\\{\hfill{10}}={\ell}k^{-1}F_v(x,u,v)+{\mu}{\alpha}(x){\mid}v{\mid}^{m-2}v,\;x{\in}{\Omega},\\u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}{\subset}{\mathbb{R}}^N$ is an unbounded domain with smooth boundary ${\partial}{\Omega}$, and $0<s<1<p{\leq}q$ and sq < N, ${\lambda},{\mu}>0$, $1<m{\leq}k<p^*_s$, ${\ell}{\in}R$, while $[u]^t_{s,t}$ denotes the Gagliardo semi-norm given in (1.2) below. $V_1(x)$, $V_2(x)$, $a(x):{\mathbb{R}}^N{\rightarrow}(0,\;{\infty})$ are three positive weights, $M_1$, $M_2$ are continuous and positive functions in ${\mathbb{R}}^+$. Using variational methods, we prove existence of infinitely many high-energy solutions for the above system.

• 대한수학회지
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• 제58권5호
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• pp.1181-1209
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• 2021

In the present paper, we are concerned with the existence of ground state sign-changing solutions for the following Schrödinger-Poisson-Kirchhoff system $$\;\{\begin{array}{lll}-(1+b{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+k(x){\phi}u={\lambda}f(x)u+{\mid}u{\mid}^4u,&&\text{in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=k(x)u^2,&&\text{in }{\mathbb{R}}^3,\end{array}$$ where b > 0, V (x), k(x) and f(x) are positive continuous smooth functions; 0 < λ < λ₁ and λ₁ is the first eigenvalue of the problem -∆u + V(x)u = λf(x)u in H. With the help of the constraint variational method, we obtain that the Schrödinger-Poisson-Kirchhoff type system possesses at least one ground state sign-changing solution for all b > 0 and 0 < λ < λ₁. Moreover, we prove that its energy is strictly larger than twice that of the ground state solutions of Nehari type.

• 대한수학회지
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• 제60권3호
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• pp.565-586
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• 2023

We study the Dirichlet problem for the degenerate nonlocal parabolic equation u_t - a(||∇u||²_L²(Ω))∆u = C_b ||u||^β_L²(Ω) |u|^q(x,t)-2 u log |u| + f in Q_T, where Q_T := Ω × (0, T), T > 0, Ω ⊂ ℝ^N, N ≥ 2, is a bounded domain with a sufficiently smooth boundary, q(x, t) is a measurable function in Q_T with values in an interval [q^-, q⁺] ⊂ (1, ∞) and the diffusion coefficient a(·) is a continuous function defined on ℝ₊. It is assumed that a(s) → 0 or a(s) → ∞ as s → 0⁺, therefore the equation degenerates or becomes singular as ||∇u(t)||2 → 0. For both cases, we show that under appropriate conditions on a, β, q, f the problem has a global in time strong solution which possesses the following global regularity property: ∆u ∈ L²(Q_T) and a(||∇u||²_L²(Ω))∆u ∈ L²(Q_T ).

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• 통상정보연구
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• 제12권2호
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• pp.59-83
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• 2010

The purposes of the study is to evaluate the discrepancy between user's expectation and satisfaction degree in the service of uTradeHub. In this regard, this study infers general solutions in order to induce the intersection area using IPA technique. Then this paper will present directions to improve the service of uTradeHub. In terms of methodology, this article disclosed that IPA model approach is greatly useful to evaluate user's attribute. First, variables like the link of different works(f1), trust of system(f4), information connection(f7) are located on the first quadrant. This means that importance and satisfaction are all high variables for user. So, this is very important variables that need continuous administration in order to maintain present state. Second, variables such as the speed of information acquisition(f2), improvement of use(f3), stability of system(f5) are located on the second quadrant. This means that user's importance is high but user's satisfaction is low. Therefore, this area needs an active improvement strategy and quick maintenance for e-Trade application. Third, variables like the appropriateness of information usage fees(f8), easy subscription(f9), customer support service(f10) are located on the third quadrant. Because these variables are all low for user's importance and satisfaction, we have to arrange strong and radical remedy for e-Trade service. Finally, variables like information offer(f6) are located on the fourth quadrant. This means that user's satisfaction is high but user's importance is low. The research result suggests that e-Trade service development would be re-organised as much as user feels the importance of process innovation.

• 국방과기술
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• 8호통권174호
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• pp.44-51
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• 1993

F-5 성능개량의 근본적인 배경은 경제성입니다. F-16 한대 도입할 가격이면 대략 10대의 F-5 성능개량이 가능하므로 비용 대 효과 측면에서 많은 국가들이 매력을 느끼고 있습니다 또한 선도 훈련기로서의 필요성이 전투기.성능이 급격히 높아짐에 따라, 성능개량되는 F-5 수준의 항공기로 예비훈련을 함으로써, 고성능 전투기의 비전력화 훈련소요를 상당부분 대체할수 있습니다

• Journal of the Korean Wood Science and Technology
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• 제48권2호
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• pp.136-153
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• 2020

In this paper, the influence of initial formaldehyde/urea (F/U) molar ratios on the performance of low molar ratio (1.0) urea-formaldehyde (UF) resin adhesives has been investigated. Two initial F/U molar ratios, i.e., the first and second initial molar ratios were used for the alkaline addition reaction. Three levels of the first initial F/U molar ratios (2.0, 3.0, and 4.0) and two levels of the second initial molar ratios (2.0 and 1.7) were employed to prepare a total of six UF resins with an identical final molar ratio (1.0). The basis properties, functional groups, molecular weight, crystallinity, and thermal curing properties of the UF resins were characterized in detail. Higher levels (3.0 and 4.0) of the first initial F/U molar ratio provided the UF resins with better properties (non-volatile solids content, viscosity, gelation time, pH, and specific gravity) than those of the resins prepared with the conventional level F/U molar ratio of 2.0. Statistical analysis suggested that combining the first and second initial molar ratio of 4.0 with 1.7 would result in UF resins with greater adhesion strength and lower formaldehyde emission than those of the resins prepared with other molar ratios. The results showed that higher levels of the first initial molar ratio resulted in a more branched structure, as indicated by GPC, FTIR, DSC, XRD, and greater adhesion strength than those of the other UF resins with an identical final molar ratio of 1.0.