• 한국전자통신학회논문지
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• 제3권4호
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• pp.254-259
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• 2008

이 논문에서는 주어진 패턴 집합을 두 개의 분할된 클래스로 분류하는 분류기로써 D1-MACA (Depth 1 Multiple Attractor Cellular Automata)를 제안한다. 이 때 메모리량을 최소화 할 수 있는 방법으로 attractor의 수가 2개 되게 D1-MACA를 구성할 수 있는 패턴 집합의 조건을 분석하고, 분류기로써의 D1-MACA를 구성하는 방법을 부분공간의 개념을 이용하여 효율적으로 구성한다.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.307-316
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• 2006

Incomplete LU factorization preconditioning techniques often have difficulty on indefinite sparse matrices. We present hybrid reordering strategies to deal with such matrices, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm. We first use the diagonal reorderings to efficiently search for entries of single element rows and columns and/or the maximum absolute value to be placed on the diagonal for computing a nonsymmetric permutation. To augment the effectiveness of the diagonal reorderings, a nondecreasing degree algorithm is applied to reduce the amount of fill-in during the ILU factorization. With the reordered matrices, we achieve a noticeable improvement in enhancing the stability of incomplete LU factorizations. Consequently, we reduce the convergence cost of the preconditioned Krylov subspace methods on solving the reordered indefinite matrices.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.447-452
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• 2005

Given operators X and Y on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. Let L be a subspace lattice acting on a separable complex Hilbert space H and Alg L be a tridiagonal algebra. Let X = $(x_{ij})\;and\;Y\;=\;(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a compact operator A = $(x_{ij})$ in AlgL such that AX = Y. (2) There is a sequence {$\alpha_n$} in $\mathbb{C}$ such that {$\alpha_n$} converges to zero and $$y_1\;_j=\alpha_1x_1\;_j+\alpha_2x_2\;_j\;y_{2k}\;_j=\alpha_{4k-1}x_{2k\;j}\;y_{2k+1\;j}=\alpha_{4k}x_{2k\;j}+\alpha_{4k+1}x_{2k+1\;j}+\alpha_{4k+2}x_{2k+2\;j\;for\;all\;k\;\epsilon\;\mathbb{N}$$.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.459-474
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• 2018

Cao et al. in (Numer. Linear. Algebra Appl. 18 (2011) 875-895) proposed a splitting method for saddle point problems which unconditionally converges to the solution of the system. It was shown that a Krylov subspace method like GMRES in conjunction with the induced preconditioner is very effective for the saddle point problems. In this paper we first modify the iterative method, discuss its convergence properties and apply the induced preconditioner to the problem. Numerical experiments of the corresponding preconditioner are compared to the primitive one to show the superiority of our method.

• 대한기계학회논문집A
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• 제30권3호
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• pp.310-317
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• 2006

Currently most practical vibration and structural problems in automotive suspensions require the use of the finite element method to obtain their structural responses. When the finite element model has a very large number of degrees of freedom the harmonic and dynamic analyses are computationally too expensive to repeat within a feasible design process time. To alleviate the computational difficulty, this paper presents a moment-matching based model order reduction (MOR) which reduces the number of degrees of freedom of the original finite element model and speeds up the necessary simulations with the reduced-size models. The moment-matching model reduction via the Arnoldi process is performed directly to ANSYS finite element models by software mor4ansys. Among automotive suspension components, a knuckle is taken as an example to demonstrate the advantages of this approach for vibration simulation. The frequency and transient dynamic responses by the MOR are compared with those by the mode superposition method.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.517-524
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• 2012

In this paper, we first show that for any space X, there is a Boolean subalgebra $\mathcal{G}(z_X)$ of R(X) containg $\mathcal{G}(X)$. Let X be a strongly zero-dimensional space such that $z_{\beta}^{-1}(X)$ is the minimal cloz-coevr of X, where ($E_{cc}({\beta}X)$, $z_{\beta}$) is the minimal cloz-cover of ${\beta}X$. We show that the minimal cloz-cover $E_{cc}(X)$ of X is a subspace of the Stone space $S(\mathcal{G}(z_X))$ of $\mathcal{G}(z_X)$ and that $E_{cc}(X)$ is a strongly zero-dimensional space if and only if ${\beta}E_{cc}(X)$ and $S(\mathcal{G}(z_X))$ are homeomorphic. Using these, we show that $E_{cc}(X)$ is a strongly zero-dimensional space and $\mathcal{G}(z_X)=\mathcal{G}(X)$ if and only if ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• 대한수학회지
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• 제31권3호
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• pp.467-475
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• 1994

In 1983 Harmand and Lima [5] proved that if X is a Banach space for which K(X), the space of compact linear operators on X, is an M-ideal in L(X), the space of bounded linear operators on X, then it has the metric compact approximation property. A strong converse of the above result holds if X is a closed subspace of either $\elll_p(1 < p < \infty) or c_0 [2,15]$. In 1979 J. Johnson [7] actually proved that if X is a Banach space with the metric compact approximation property, then the annihilator K(X)^\bot$ of K(X) in $L(X)^*$ is the kernel of a norm-one projection in $L(X)^*$, which is the case if K(X) is an M-ideal in L(X).

• 대한수학회논문집
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• 제27권1호
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• pp.201-205
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• 2012

A space X is cs-starcompact if for every open cover $\mathcal{U}$ of X, there exists a convergent sequence S of X such that St(S, $\mathcal{U}$) = X, where $St(S,\mathcal{U})\;=\; \cup\{U{\in}\mathcal{U}:U{\cap}S{\neq}\phi\}$. In this paper, we prove the following statements: (1) There exists a Tychonoff cs-starcompact space having a regular-closed subset which is not cs-starcompact; (2) There exists a Hausdorff cs-starcompact space with arbitrary large extent; (3) Every Hausdorff centered-Lindel$\ddot{o}$f space can be embedded in a Hausdorff cs-starcompact space as a closed subspace.

• 대한수학회보
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• 제47권5호
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• pp.915-932
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• 2010

The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set $X\;{\subset}\;Z^n$ take a subspace (X, $T_n^X$) induced from the Khalimsky nD space ($Z^n$, $T^n$). Considering (X, $T_n^X$) with one of the k-adjacency relations of $Z^n$, we call it a computer topological space (or a space if not confused) denoted by $X_{n,k}$. In addition, we introduce several kinds of k-retracts of $X_{n,k}$, investigate their properties related to several continuities and homeomorphisms in computer topology and study extension problems of these continuities in relation with these k-retracts.

• 대한수학회지
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• 제45권2호
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• pp.575-585
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• 2008

Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).