• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.261-269
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• 2008

Let $B_1$ be a unit ball in $R^n(n{\geq}3)$, and $2^*=2n/(n-2)$ be the critical Sobolev exponent for the embedding $H_0^1(B_1){\hookrightarrow}L^{2^*}(B_1)$. By using a variant of Pohoz$\check{a}$aev's identity, we prove the nonexistence of nodal solutions for the Dirichlet problem $-{\Delta}u-{\mu}\frac{u}{{\mid}x{\mid}^2}={\lambda}u+{\mid}u{\mid}^{2^*-2}u$ in $B_1$, u=0 on ${\partial}B_1$ for suitable positive numbers ${\mu}$ and ${\nu}$.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.1-9
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• 1989

In 1980 and 1983, it was proved that P $D^{2}$-groups are surface groups ([2], [3]). Since then, topologists have been positively studying about P $D^{n}$ -groups (or $D^{n}$ -groups). For example, let a topological space X have a right .pi.-action, where .pi. is a multiplicative group. If each x.memX has an open neighborhood U such that for each u.mem..pi., u.neq.1, U.cap. $U_{u}$ =.phi., this right .pi.-action is said to be proper. In this case, if X/.pi. is compact then (1) .pi.$_{1}$(X/.pi).iden..pi.(X:connected, .pi.$_{1}$: fundamental group) ([4]), (2) if X is a differentiable orientable manifold with demension n and .rho.X (the boundary of X)=.phi. then $H^{k}$ (X;Z).iden. $H_{n-k}$(X;Z), ([6]), where Z is the set of all integers.s.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.349-361
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• 2022

In this paper, we study the following nonlinear problem: $$\{-\Delta_{p}^{3}(x)u\;=\;{\lambda}V_{1}(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u\;=\;{\Delta}u\;{\Delta}^{2}u\;=\;0\;on\;{\partial}\Omega, $$ under adequate conditions on the exponent functions p, q and the weight function V₁. We prove the existence and nonexistence of eigenvalues for p(x)-triharmonic problem with Navier boundary value conditions on a bounded domain in ℝ^N. Our technique is based on variational approaches and the theory of variable exponent Lebesgue spaces.

• 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.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.7 no.1
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• pp.45-49
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• 2014

In this paper, we propose a secure and efficient RFID-based patient authentication protocol to not only authenticate patients' authenticity but also protect patients' personal medical informations for u-Healthcare environments. Since the proposed RFID-based patient authentication protocol provides strong security and efficiency, it can be used practically for patient authentication and personal medical information protection on the high technology medical environments such as u-Hospital and u-Healthcare.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.911-926
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• 2022

Let u be a function on a locally finite graph G = (V, E) and Ω be a bounded subset of V. Let 𝜀 > 0, p > 2 and 0 ≤ λ < λ₁(Ω) be constants, where λ₁(Ω) is the first eigenvalue of the discrete Laplacian, and h : V → ℝ be a function satisfying h ≥ 0 and $h{\not\equiv}0$. We consider a perturbed Yamabe equation, say $$\{\begin{array}{lll}-{\Delta}u-{\lambda}u={\mid}u{\mid}^{p-2}u+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω and ∂Ω denote the interior and the boundary of Ω, respectively. Using variational methods, we prove that there exists some positive constant 𝜀₀ > 0 such that for all 𝜀 ∈ (0, 𝜀₀), the above equation has two distinct solutions. Moreover, we consider a more general nonlinear equation $$\{\begin{array}{lll}-{\Delta}u=f(u)+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ and prove similar result for certain nonlinear term f(u).

• Journal of Radiation Protection and Research
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• v.24 no.4
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• pp.187-193
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• 1999

The specific radioactivity concentrations in the coal fly ash obtained from heat producing stations in Korea were analyzed and its radiological hazard for reuse in construction purpose was evaluated. The concentrations of uranium isotopes in the real fly ash measured by TBP solvent extraction method and $\alpha$-spectrometer were found to be about 116.1 Bq $kg^{-1}$ for $^{238}U$, 5.01 Bq $kg^{-1}$ for $^{235}U$, and 121.2 Bq $kg^{-1}$ for $^{234}U$, respectively. The activity ratio of $^{234}U/^{238}U$, in the coal fly ash was in $1.04\;{\pm}\;0.03$, which is similar to that of uncontaminated Korean soil in natural conditions (1.14). The specific radioactivities of $^{226}Ra,\;^{232}Th,\;and\;^{40}K$ in the coal fly ash were also determined using $\gamma$-spectrometer with a HPGe detector The results showed that $^{226}Ra,\;^{232}Th,\;and\;^{40}K$ in the coal fly ash were in concentrations of $101.7{\sim}113.9$, $39.5{\sim}54.2\;and\;315.0{\sim}990.6$ Bq $kg^{-1}$, respectively. With the specific radioactivities obtained from $\gamma$-spectrometric measurements of the coal fly ash, its radiological hazard for reuse was evaluated. The result showed that the radioactivity of the coal fly ash was in permissible level.

• The Bulletin of The Korean Astronomical Society
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• v.20
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• pp.6.1-6.1
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• 1995

• Spatial Information Research
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• v.20 no.1
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• pp.19-26
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• 2012

Since $CO_2$ emissions are recognized as the biggest contribution to climate change, the needs and international efforts for $CO_2$ emissions reduction are increasing. The developed countries are driving strategies to boost green industry as a new growth engine. Following this global trend, based on the ongoing U-City project as a new city model, it is required to analyze the changes of $CO_2$ emissions in U-City to identify its potential for reducing carbon dioxide emissions. This study aims at identifying the potential and effects on $CO_2$ reduction by analyzing the level of $CO_2$ emissions before and after introducing U-City. Bundang-Gu, Seongnam-City & Ilsan-Gu, Goyang-City among Phase I new tow ns were selected as model cities before introducing U-City and Dongtan-Dong, Hwaseong-City as a model city after introducing U-City. The result showed 30% reduction of $CO_2$ emissions in the comparison of tw o models.