• Journal of environmental and Sanitary engineering
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• v.10 no.1
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• pp.1-11
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• 1995

We had passed through a serious water pollution with a rapid urbanization and industrialization in the 1960's. Seoul Chunggyechun Sewage Disposal System set uP in 1966 and finished in 1976, as the first sewage disposal system in Korea, had covered only 4 percentage of the sewage disposal system per capita for 10 years. Through holding the Asian Games in 1986 and the Olympic Games in 1988, we expanded the sewage disposal system so that it became increased 18 percentage of the population in 1986. Finally, we have installed about 60 sewage disposal system by 1994 for a large environmental investment which was critically caused by "Phenol Accident in Nakdong River" . Now, the sewage disposal system per capita covers 42 percentage and the activity for water quality improvement is going on rapidly. The method of sewage disposal is mainly "activated sludge process" . However, the technical ability for the sewage disposal has largely developed since 1991 so the "extended aeration process" is used in Po$\v{u}$n, Tangyang, Mun$\v{u}$i, "rotating biological contact process" in Onch$\v{u}$ng, Pukok, and "oxidation ditch process" in K$\v{o}$ch'ana.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.113-123
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• 2009

A rank one matrix can be factored as $\mathbf{u}^t\mathbf{v}$ for vectors $\mathbf{u}$ and $\mathbf{v}$ of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in $\mathbf{u}$ plus the number of nonzero entries in $\mathbf{v}$. A matrix of rank k is the sum of k rank one matrices. The perimeter of a matrix of rank k is the minimum of the sums of perimeters of the rank one matrices. In this article we characterize the linear operators that preserve perimeters of matrices over semirings.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Journal of Digital Convergence
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• v.20 no.2
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• pp.345-351
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• 2022

For simple undirected graph G=(V,E), L(2,1)-coloring of G is a nonnegative real-valued function f : V → [0,1,…,k] such that whenever vertices x and y are adjacent in G then |f(x)-f(y)|≥ 2 and whenever the distance between x and y is 2, |f(x)-f(y)|≥ 1. For a given L(2,1)-coloring c of graph G, the c-span is λ(c) = max{|c(v)-c(v)||u,v∈V}. L(2,1)-coloring number λ(G) = min{λ(c)} where the minimum is taken over all L(2,1)-coloring c of graph G. In this paper, based on Harary's Theorem, we use Tabu Search to figure out the existence of Hamiltonian Path in a complementary graph and confirmed that if λ(G) is equal to n(=|V|).

• Journal of Broadcast Engineering
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• v.28 no.3
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• pp.267-274
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• 2023

There is a problem that the size of the dataset is insufficient due to the limitation of the collection of the medical image public data, so there is a possibility that the existing studies are overfitted to the public dataset. In this paper, we compare the performance of eight (Unet, X-Net, HarDNet, SegNet, PSPNet, SwinUnet, 3D-ResU-Net, UNETR) medical image semantic segmentation models to revalidate the superiority of existing models. Anatomical Tracings of Lesions After Stroke (ATLAS) V1.2, a public dataset for stroke diagnosis, is used to compare the performance of the models and the performance of the models in ATLAS V2.0. Experimental results show that most models have similar performance in V1.2 and V2.0, but X-net and 3D-ResU-Net have higher performance in V1.2 datasets. These results can be interpreted that the models may be overfitted to V1.2.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• East Asian mathematical journal
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• v.38 no.1
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• pp.13-20
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• 2022

We establish multiplicity results for positive solutions to the Schrödinger-type singular positone problem: -∆u + V (x)u = λf(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ^N, N > 2, λ is a positive parameter, V ∈ L^∞(Ω) and f : [0, ∞) → (0, ∞) is a continuous function. In particular, when f is sublinear at infinity we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub- and supersolution method.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.4
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• pp.157-164
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• 2023

This paper suggests O(n²) polynomial time heuristic algorithm for corporate tax structure optimization problem that has been classified as NP-complete problem. The proposed algorithm constructs tax tree levels that the target holding company is located at root node of Level 1, and the tax code categories(T_e) 1,4,3,2 are located in each level 2,3,4,5 sequentially. To find the maximum tax-relief path from source(S) to target(T), firstly we connect the minimum witholding tax rate _minr_w(u, v) arc of node u point of view for transfer the profit from u to v node. As a result we construct the spanning tree from all of the source nodes to a target node, and find the initial feasible solution. Nextly, we find the alternate path with minimum foreign tax rate _minr_fi(u, v) of v point of view. Finally we choose the minimum tax-relief path from of this two paths. The proposed heuristic algorithm performs better optimal results than linear programming and Tabu search method that is a kind of metaheuristic method.

• Journal of Arbitration Studies
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• v.24 no.3
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• pp.79-103
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• 2014

In light of increasing international trade in recent years, international arbitration has been more widely used by international parties to resolve their conflicts. Thus, the need for reliable and effective enforcement of foreign arbitral awards has amplified. To facilitate the enforcement of foreign arbitral awards, the New York Convention lists grounds for the refusal of recognition and enforcement in Article V. This paper examines prominent U.S. case law on Article V(1)(b), which is put in place to ensure that arbitration proceedings are conducted properly in accordance with due process requirements: proper notice to parties and an opportunity to a fundamentally fair hearing. This examination of case law conveys that U.S. courts refuse to enforce foreign arbitral awards pursuant to Article V(1)(b) only when due process rights of the party against whom the award is to be enforced are clearly violated by the arbitral tribunal. This paper also reveals that U.S. courts mainly defer to arbitral tribunals' discretion, especially as to evidentiary matters. Therefore, it is predicted that U.S. courts will likely continue to narrowly construe the grounds in Article V to facilitate reliable and effective enforcement of foreign arbitral awards in the U.S.