• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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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.

• Proceedings of the KIEE Conference
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• 2003.07b
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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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• v.1 no.2
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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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• v.26 no.4
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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.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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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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• v.14 no.4
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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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• v.11 no.3
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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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• v.13 no.2
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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]).

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.2
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• pp.20-28
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• 2003

Recently we need a faster and more accurate motion vector search algorithm for ASIC(Application Specific IC) or small systems. Block motion estimation using Full Search(FS) algorithm provides the best visual quality and PSNR, but it requires intensive computations. The previously proposed fast algorithms reduced the number of computations by limiting the number of searching locations. This is accomplished at the expense of less accuracy of motion estimation and gives rise to an appreciably higher SAD(Sum of Absolute Difference) for motion compensated images. In this paper we exploit the spatial correlation of motion vectors and present a fast motion estimation scheme which uses the predicted motion vector(PMV). The PMV scheme is more clear and simpler than the previously proposed algorithms which also use adjacent motion vectors. Simulation results with standard video sequences show that the PMV scheme is faster and more accurate than other algorithms such as Nearest-Neighbors Search(NNS) algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.1
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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.