• Korea-Australia Rheology Journal
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• 제21권2호
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• pp.143-146
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• 2009

Breakthrough of high Weisenberg number problem is related with keeping the positive definiteness of the conformation tensor in numerical procedures. In this paper, we suggest a simple method to preserve the positive definiteness by use of vector decomposition of the conformation tensor which does not require eigenvalue problem. We also derive the constitutive equation of tensor-logarithmic transform in simpler way than that of Fattal and Kupferman and discuss the comparison between the vector decomposition and tensor-logarithmic transformation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권4호
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• pp.305-316
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• 2014

The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the $L^2$-orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be $O(h^{1.5})$ with step size h. In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.

• 충청수학회지
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• 제36권1호
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• pp.55-64
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• 2023

In this paper, we propose a two-level overlapping domain decomposition preconditioner for three dimensional vector field problems posed in H(div). We introduce a new coarse component, which reduces the computational complexity, associated with the coarse vertices. Numerical experiments are also presented.

• 대한수학회보
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• 제46권2호
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• pp.245-253
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• 2009

A new hard problem called the vector decomposition problem (VDP) was recently proposed by Yoshida et al., and it was asserted that the VDP is at least as hard as the computational Diffie-Hellman problem (CDHP) under certain conditions. Kwon and Lee showed that the VDP can be solved in polynomial time in the length of the input for a certain basis even if it satisfies Yoshida's conditions. Extending our previous result, we provide the general condition of the weak instance for the VDP in this paper. However, when the VDP is practically used in cryptographic protocols, a basis of the vector space ${\nu}$ is randomly chosen and publicly known assuming that the VDP with respect to the given basis is hard for a random vector. Thus we suggest the type of strong bases on which the VDP can serve as an intractable problem in cryptographic protocols, and prove that the VDP with respect to such bases is difficult for any random vector in ${\nu}$.

• ETRI Journal
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• 제33권4호
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• pp.652-655
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• 2011

In this letter, we propose a new compression method for a high dimensional support vector machine (SVM). We used singular value decomposition (SVD) to compress the norm part of a radial basis function SVM. By deleting the least significant vectors that are extracted from the decomposition, we can compress each vector with minimized energy loss. We select the compressed vector dimension according to the predefined threshold which can limit the energy loss to design criteria. We verified the proposed vector compressed SVM (VCSVM) for conventional datasets. Experimental results show that VCSVM can reduce computational complexity and memory by more than 40% without reduction in accuracy when classifying a 20,958 dimension dataset.

• 한국경영과학회지
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• 제10권1호
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• pp.9-13
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• 1985

This paper develops a decomposition method for stochastic programming with a block diagonal structure. Here we assume that the right-hand side random vector of each subproblem is differente each other. We first, transform this problem into a master problem, and subproblems in a similar way to Dantizig-Wolfe's Decomposition Princeple, and then solve this master problem by solving subproblems. When we solve a subproblem, we first transform this subproblem to a Deterministic Equivalent Programming (DEF). The form of DEF depends on the type of the random vector of the subproblem. We found the subproblem with finite discrete random vector can be transformed into alinear programming, that with continuous random vector into a convex quadratic programming, and that with random vector of unknown distribution and known mean and variance into a convex nonlinear programming, but the master problem is always a linear programming.

• 정보보호학회논문지
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• 제17권3호
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• pp.27-33
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• 2007

최근 M.Yoshida 등에 의해 2차원 벡터 공간상의 벡터 분해 문제 (vector decomposition problem 또는 VDP) 가 제안되었고, 그것은 어떤 특별한 조건하에서는 최소한 1차원 부분공간상의 계산적 Diffie-Hellman 문제 (CDHP) 보다 어렵다는 것이 증명되었다. 하지만 그들의 증명이, VDP를 암호학적 프로토콜 설계에 적용하려면 필요한 조건인 벡터 공간상의 주어진 기저에 관한 임의의 벡터의 벡터 분해 문제가 어렵다는 것을 보이는 것은 아니다. 본 논문에서는 비록 어떤 2차원 벡터 공간이 M.Yoshida 등이 제안한 특별한 조건을 만족한다 할지라도, 특정한 모양의 기저에 관해서는 벡터 분해 문제가 다항식 시간 안에 해결될 수 있다는 것을 보여준다. 또한 우리는 다른 구조를 갖는 어떠한 기저들에 대해서는 그 2차원 벡터 공간 상의 임의의 벡터에 대한 벡터 분해 문제가 적어도 CBHP 만큼 어렵다는 것을 증명한다. 그러므로 벡터 분해 문제를 기반이 되는 어려운 문제로 하는 암호학적인 프로토콜을 수행할 때는 기저를 주의하여 선택하여야 한다.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2007년도 추계학술대회 학술발표 논문집
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• pp.267-271
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• 2007

본 논문은 원본이미지와 은닉이미지의 좋은 압축률과 만족할만한 이미지의 질, 그리고 외부공격에 강인한 이미지은닉의 한 방법으로 특이치 분해와 퍼지 군집화를 이용한 벡터양자화를 이용한 워터마킹 방법을 소개하였다. 실험에서는 은닉된 이미지의 비가시성과 외부공격에 대한 강인성을 증명하였다.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2015년도 학술발표회
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• pp.475-478
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• 2015

The objective of this study is to apply a hybrid model for estimating solar radiation and investigate their accuracy. A hybrid model is wavelet-based support vector machines (WSVMs). Wavelet decomposition is employed to decompose the solar radiation time series into approximation and detail components. These decomposed time series are then used as inputs of support vector machines (SVMs) modules in the WSVMs model. Results obtained indicate that WSVMs can successfully be used for the estimation of daily global solar radiation at Champaign and Springfield stations in Illinois.

• East Asian mathematical journal
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• 제15권1호
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• pp.81-90
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• 1999