• Journal of Korean Institute of Industrial Engineers
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• v.26 no.3
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• pp.220-226
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• 2000

The problem (P) of optimizing a linear function $d^Tx$ over the set of efficient points for a multiple objective linear program (M) is difficult because the efficient set is nonconvex. There are some interesting properties between the objective linear vector d and the matrix of multiple objectives C and those properties lead us to establish criteria to solve (P) with a linear program. In this paper we investigate a system of the linear equations $C^T{\alpha}$ = d and construct two linearly independent positive vectors u, v such that ${\alpha}$ = u - v. From those vectors u, v, solving an weighted sum linear program for finding an efficient extreme point for the (M) is a way of getting an optimal solution of the problem (P). Therefore the theorems presented in this paper provided us an easy way of solving nonconvex program (P) with a weighted sum linear program.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.165-169
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• 2009

The effect of the Dirichlet boundary condition for the redistance equation of level set method on the solutionof sloshing problem is investigated by adopting four Dirichlet boundary conditions. For the solution of the incompressible Navier-Stokes equations, P1P1 four-step fractional finite element method is employed and a least-square finite element method is used for the solutions of the two hyperbolic type equations of level set method; advection and redistance equation. ALE (Arbitrary Lagrangian Eulerian) method is used to deal with a moving computational domain. It has been shown that the free surface motion in a sloshing tank is strongly dependent on the type of the Dirichlet boundary condition and the results of broken dam and sloshing problems using various Dirichlet boundary conditions are discussed and compared with the existing experimental results.

• Journal of information and communication convergence engineering
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• v.9 no.1
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• pp.105-109
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• 2011

In this paper, we study the dominating-free sest which is defined as follows: k points called servers and n points called clients in the plane are given. For a point p in the plane is said to be dominated by a client c if for every server s, the distance between s and p is greater than the distance between s and c. The dominating-free set is the set of points in the plane which aren't dominated by any client. We present an O(nklogk+$n^2k$) time algorithm for computing the dominating-free set under the $L_1$-metric. Specially, we present an O(nlogn) time algorithm for the problem when k=2. The algorithm uses some variables and 1-dimensional arrays as its principle data structures, so it is easy to implement and runs fast.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.731-734
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• 1998

A scalable parallel algorithm is proposed for efficient image component labeling with local operatos on a mesh connected SIMD computer. In contrast to the conventional parallel labeling algorithms, where a single pixel is assigned to each PE, the algorithm presented here is scalable and can assign m$\times$m pixel set to each PE according to the input image size. The assigned pixel set is converted to a single pixel that has representative value, and the amount of the required memory and processing time can be highly reduced. For N$\times$N image, if m$\times$m pixel set is assigned to each PE of P$\times$P mesh, where P=N/m, the time complexity due to the communication of each PE and the computation complexity are reduced to O(PlogP) bit operations and O(P) bit operations, respectively, which is 1/m of each of the conventional method. This method also diminishes the amount of memory in each PE to O(P), and can decrease the number of PE to O(P2) =Θ(N2/m2) as compared to O(N2) of conventional method. Because the proposed parallel labeling algorithm is scalable, we can adapt to the increase of image size without the hardware change of the given mesh connected SIMD computer.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.83-96
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• 2013

Let K be a number field and fix a prime number $p$. For any set S of primes of K, we here say that an elliptic curve E over K has S-reduction if E has bad reduction only at the primes of S. There exists the set $B_{K,p}$ of primes of K satisfying that any elliptic curve over K with $B_{K,p}$-reduction has no $p$-torsion points under certain conditions. The first aim of this paper is to construct elliptic curves over K with $B_{K,p}$-reduction and a $p$-torsion point. The action of the absolute Galois group on the $p$-torsion subgroup of E gives its associated Galois representation $\bar{\rho}_{E,p}$ modulo $p$. We also study the irreducibility and surjectivity of $\bar{\rho}_{E,p}$ for semistable elliptic curves with $B_{K,p}$-reduction.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.2
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• pp.212-217
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• 2012

A fuzzy set $A$ defined on a probability space ${\Omega}$, $\mathfrak{F}$, $P$ is called a fuzzy event. Zadeh defines the probability of the fuzzy event $A$ using the probability $P$. We define the generalized triangular fuzzy set and apply the extended algebraic operations to these fuzzy sets. A generalized triangular fuzzy set is symmetric and may not have value 1. For two generalized triangular fuzzy sets $A$ and $B$, $A(+)B$ and $A(-)B$ become generalized trapezoidal fuzzy sets, but $A({\cdot})B$ and $A(/)B$ need not to be a generalized triangular fuzzy set or a generalized trapezoidal fuzzy set. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized triangular fuzzy sets.

• Journal of KIISE:Computer Systems and Theory
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• v.28 no.1_2
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• pp.73-79
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• 2001

단순 다각형 P에 대한 새로운 화량문제인 경비가능충분집합(Guard Sufficiency Set:GSS)에 대하여 소개하고 정의하였다. 집합 S P가 P의 경비가능집합이라는 의미는 P의 각 점들이 최소한 S에 있는 한 점으로부터 보인다는 것을 의미한다. 집합 G P가 P의 경비가능충분집합이라는 의미는 G를 경비 가능한 임의의 집합 S P가 P 역시 경비 가능하다는 것을 의미한다. 본 논문에서는 꼭지점에 대한 GSS가 다각형 전체에 대한 GSS가 되는 다각형 부류를 제시하고, 또한 에지에 대한 GSS가 다각형 전체에 대한 GSS가 되는 다각형 부류를 제시한다. 그리고, P의 꼭지점에 대한 GSS의 크기에 대한 하한과 상한을 제시하고, 기하학적 요소에 특정 제약조건을 주어 대체 GSS을 정의할 수 있음을 보인다. 이 외에도 다양한 GSS 문제들을 소개하고, 기하학적 요소에 제약을 가한 대체 GSS를 정의하고 그와 관련된 가설을 하나 제시한다.

• The Pure and Applied Mathematics
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• v.12 no.4 s.30
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• pp.253-274
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• 2005

An additive regular Semiring S is left inversive if the Set E+ (S) of all additive idempotents is left regular. The set LC(S) of all left inversive semiring congruences on an additive regular semiring S is a lattice. The relations $\theta$ and k (resp.), induced by tr. and ker (resp.), are congruences on LC(S) and each $\theta$-class p$\theta$ (resp. each k-class pk) is a complete modular sublattice with $p_{min}$ and $p_{max}$ (resp. With $p^{min}$ and $p^{max}$), as the least and greatest elements. $p_{min},\;p_{max},\;p^{min}$ and $p^{max}$, in particular ${\epsilon}_{max}$, the maximum additive idempotent separating congruence has been characterized explicitly. A semiring is quasi-inversive if and only if it is a subdirect product of a left inversive and a right inversive semiring.

• Journal of the military operations research society of Korea
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• v.8 no.1
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• pp.71-76
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• 1982

A procedure is established for combining a regression model and a time series model to fit to a set of autocorrelated data. This procedure is based on an iterative method to compute regression parameter estimates and time series parameter estimates simultaneously. The time series model which is discussed is basically AR(p) model, since MA(q) model or ARMA(p,q) model can be inverted to AR({$\infty$) model which can be approximated by AR(p) model. The procedure discussed in this articled is applied in general to any combination of regression model and time series model.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.669-677
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• 1996

Let $M_n$ be the $C^*$-algebra of all $n \times n$ matrices over the complex field, and $P[M_m, M_n]$ the convex cone of all positive linear maps from $M_m$ into $M_n$ that is, the maps which send the set of positive semidefinite matrices in $M_m$ into the set of positive semi-definite matrices in $M_n$. The convex structures of $P[M_m, M_n]$ are highly complicated even in low dimensions, and several authors [CL, KK, LW, O, R, S, W]have considered the possibility of decomposition of $P[M_m, M_n] into subcones.