• 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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 하계학술대회 논문집 B
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• pp.967-969
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• 2003

It is difficult to realize the complicate SUM which is applied vector control system, but widely used in AC motor vector motor control system or servo control system because of its high performance in current control. In this paper, we use the dynamic characteristic analyzing methode that can calculate efficiently the end effect by using equivalent circuit methode in the operating SLIM system modeling and doing simulation of output characteristics of vector controller.

• International Journal of Contents
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• 제1권2호
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• pp.26-30
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• 2005

According to the fast growth of information on the Internet, it is becoming increasingly difficult to find and organize useful information. To reduce information overload, it needs to exploit automatic text classification for handling enormous documents. Support Vector Machine (SVM) is a model that is calculated as a weighted sum of kernel function outputs. This paper describes a document classifier for web documents in the fields of Information Technology and uses SVM to learn a model, which is constructed from the training sets and its representative terms. The basic idea is to exploit the representative terms meaning distribution in coherent thematic texts of each category by simple statistics methods. Vector-space model is applied to represent documents in the categories by using feature selection scheme based on TFiDF. We apply a category factor which represents effects in category of any term to the feature selection. Experiments show the results of categorization and the correlation of vector length.

• Communications for Statistical Applications and Methods
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• 제26권4호
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• pp.337-346
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• 2019

This paper discusses a method for obtaining nonnegative estimates for variance components in a random effects model. A variance component should be positive by definition. Nevertheless, estimates of variance components are sometimes given as negative values, which is not desirable. The proposed method is based on two basic ideas. One is the identification of the orthogonal vector subspaces according to factors and the other is to ascertain the projection in each orthogonal vector subspace. Hence, an observation vector can be denoted by the sum of projections. The method suggested here always produces nonnegative estimates using projections. Hartley's synthesis is used for the calculation of expected values of quadratic forms. It also discusses how to set up a residual model for each projection.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.119-121
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• 2000

A functional central limit theorem is obtained for a stationary multivariate linear process of the form $X_t=\sum\limits_{u=0}^\infty{A}_{u}Z_{t-u}$, where {$Z_t$} is a sequence of strictly stationary m-dimensional linearly positive quadrant dependent random vectors with $E Z_t = 0$ and $E{\parallel}Z_t{\parallel}^2 <{\infty}$ and {$A_u$} is a sequence of coefficient matrices with $\sum\limits_{u=0}^\infty{\parallel}A_u{\parallel}<{\infty}$ and $\sum\limits_{u=0}^\infty{A}_u{\neq}0_{m{\times}m}$. AMS 2000 subject classifications : 60F17, 60G10.

• Journal of electromagnetic engineering and science
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• 제14권4호
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• pp.405-410
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• 2014

In this paper, we compare the quality of images reconstructed by a conventional delayed-sum (DS) algorithm and radiation pattern-based DS algorithm. In order to evaluate the quality of images, we apply the target-to-clutter ratio (TCR), which is commonly used in synthetic aperture radar (SAR) image assessment. The radiation pattern-based DS algorithm enhances the TCR of the image by focusing the target signals and preventing contamination of the radar scene. We first consider synthetic data obtained through GprMax2D/3D, a finite-difference time-domain (FDTD) forward solver. Experimental data of a 2-GHz bandwidth stepped-frequency signal are collected using a vector network analyzer (VNA) in an anechoic chamber setup. The radiation pattern-based DS algorithm shows a 6.7-dB higher TCR compared to the conventional DS algorithm.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권3호
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• pp.37-41
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• 2007

The semi-convexity for planar shapes has been recently introduced in [2]. As a generalization of the convextiy, semi-convexity is closed under the Minkowski sum. But the definition of semi-convexity requires that the shape boundary should satifisfy a differentiability condition $C^{1:1}$, which means that it should be possible to take the normal vector field along the domain's extended boundary. In view of the fact that the semi-convextiy is a most natural generalization of the convexity in many respects, this is a severe restriction for the semi-convexity, since the convexity requires no such a priori differentiability condition. In this paper, we generalize the semi-convexity to the closure of the class of semi-convex $\mathcal{M}$-domains for any Minkowski class $\mathcal{M}$, and show that this generalized semi-convexity is also closed under Minkowski sum.

• Kyungpook Mathematical Journal
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• 제13권2호
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• pp.235-240
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• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• 대한전자공학회논문지SP
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• 제40권2호
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• pp.20-28
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• 2003

최근 들어 ASIC(Application Specific IC)이나 소형 시스템에서 사용할 수 있는 더 빠르고 정확한 움직임 벡터 예측방법이 요구되고 있다. 전역탐색(Full Search: FS) 방법은 탐색영역의 모든 화소들을 탐색하여 움직임 벡터를 예측하는 방법으로 화질과 PSNR은 좋지만 반면에 많은 계산량이 요구된다. 기존의 고속 알고리즘들은 탐색 회수를 제한함으로써 계산량을 줄였기 때문에 움직임 벡터 예측의 정확도가 낮고, 움직임 보상시 SAD(Sum of Absolute Difference) 값이 높아지는 것을 감수해야한다. 본 논문에서는 영상에서의 현재 블록과 주변 블록과의 공간적인 상관도를 고려하여 예측된 움직임 벡터 (Predicted Motion Vector: PMV)를 이용하는 고속 움직임 탐색 방법을 제안한다. PMV 방법은 주변 블록의 움직임 벡터를 이용한 기존 방법들 보다 명확하고 간결하게 탐색을 수행할 수 있다. PMV 방법이 대표적인 기존 방법인 Nearest-Neighbors Search(NNS) 방법보다 속도 및 정확도 면에서 성능이 양호함을 대표적인 실험 시퀀스를 통하여 보였다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권1호
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• pp.40-52
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• 2020

In this paper, we consider a precoder design problem for multiuser interference channel. Most of the conventional schemes for precoder design utilize a signal-to-interference-plus-noise ratio (SINR) as a cost function. However, since the SINR metric of a desired transmitter-receiver pair is a function of precoding vectors of all transmitters in the multiuser interference channel, an analytic closed-form solution is not available for the precoding vector of a desired transmitter that maximizes the SINR metric. To eliminate coupling between the precoding vectors of all transmitters and to find a closed-form solution for the precoding vector of the desired transmitter, we use a signal-to-leakage-plus-noise ratio (SLNR) instead as a cost function because the SLNR at a transmitter is a function of the precoding vector of the desired transmitter only. In addition, channel estimation errors for undesired links are considered when designing the precoding vector because they are inevitable in a multiuser interference channel. In this case, we propose a design scheme for the precoding vector that is robust to the channel estimation error. In the proposed scheme, the precoding vector is designed to maximize the worst-case SLNR. Through computer simulation, we show that the proposed scheme has better performance than the conventional scheme in terms of SLNR, SINR, and sum rate of all users.