• Journal of the Korean Statistical Society
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• v.14 no.1
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• pp.29-38
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• 1985

Cyclic Factorial Association Scheme (CFAS) for incomplete block designs in a factorial experiment is defined. It is a generalization of EGD/($2^n-1$)-PBIB designs defined by Hinkelmann (1964) or Binary Number Association Scheme (BNAS) named by Paik and Federer (1973). A property of PBIB designs having CFAS is investigated and it is shown that the structural matrix NN' of such designs has a pattern of multi-nested block circulant matrix. The generalized inverse of (rI-NN'/k) is obtained. Generalized Cyclic incomplete block designs for factorial experiments introduced by John (1973) are presented as the examples of CFAS-PBIB designs. Finally, the relationship between CFAS and BNAS in block designs is briefly discussed.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.343-352
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• 2013

In this paper, we give a formula of $(P+Q)^D$ under the conditions $P^2Q+QPQ=0$ and $P^3Q=0$. Then applying it to give some results of block matrix $M=(^A_C^B_D)$ (A and D are square matrices) with generalized Schur complement is zero under some conditions. Finally, numerical examples are given to illustrate our results.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.281-294
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• 2009

Accuracy of the scaling function is very crucial in wavelet theory, or correspondingly, in the study of wavelet filter banks. We are mainly interested in vector-valued filter banks having matrix factorization and indicate how to choose block central symmetric matrices to construct multi-wavelets with suitable accuracy.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.197-205
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• 2018

In this note we give a relationship between the degree and coprime-ness of matrix-valued rational functions.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.499-516
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• 2020

In this paper, we denote by L the block matrix linear relation, acting on the Banach space X ⊕ Y, of the form ${\mathcal{L}}=\(\array{A&B\\C&D}\)$, where A, B, C and D are four linear relations with dense domains. We first try to determine the conditions under which a block matrix linear relation becomes a demicompact block matrix linear relation (see Theorems 4.1 and 4.2). Second we study Shechter spectra using demicompact linear relations and relatively demicompact linear relations (see Theorem 5.1).

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.169-180
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• 2006

We study convergence of multisplitting method associated with a block diagonal conformable multisplitting for solving a linear system whose coefficient matrix is a symmetric positive definite matrix which is not an H-matrix. Next, we study the validity of m-step multisplitting polynomial preconditioners which will be used in the preconditioned conjugate gradient method.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.988-991
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• 1996

The purpose of this thesis is to develop methods of designing robust LQR/LQG controllers for time-varying systems with real parametric uncertainties. Controller design that meet desired performance and robust specifications is one of the most important unsolved problems in control engineering. We propose a new framework to solve these problems using Linear Matrix Inequalities (LMls) which have gained much attention in recent years, for their computational tractability and usefulness in control engineering. In Robust LQR case, the formulation of LMI based problem is straightforward and we can say that the obtained solution is the global optimum because the transformed problem is convex. In Robust LQG case, the formulation is difficult because the objective function and constraint are all nonlinear, therefore these are not treatable directly by LMI. We propose a sequential solving method which consist of a block-diagonal approach and a full-block approach. Block-diagonal approach gives a conservative solution and it is used as a initial guess for a full-block approach. In full-block approach two LMIs are solved sequentially in iterative manner. Because this algorithm must be solved iteratively, the obtained solution may not be globally optimal.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1435-1438
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• 2005

In hands-free telephone systems, the received speech signal is fed back to the microphone and constitutes the so-called echo. To cancel the effect of this time-varying echo path, it is necessary to device an adaptive filter between the receiving and the transmitting ends. For a typical FIR realization, the length of the fullband adaptive filter results in high computational complexity and low convergence rate. Consequently, subband adaptive filtering schemes have been proposed to improve the performance. In this work, we use deterministic approach to analyze the relationship between fullband and subband adaptive filtering structures. With block adaptive filtering structure as an intermediate stage, the analysis is divided into two parts. First, to avoid aliasing, it is found that the matrix of block adaptive filters is in the form of pseudocirculant, and the elements of this matrix are the polyphase components of the fullband adaptive filter. Second, to transmit the near-end voice signal faithfully, the analysis and the synthesis filter banks in the subband adaptive filtering structure must form a perfect reconstruction pair. Using polyphase representation, the relationship between the block and the subband adaptive filters is derived.

• Fashion & Textile Research Journal
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• v.9 no.4
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• pp.418-424
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• 2007

The purpose of this study is to propose a standard of converting 3D shape of men in twenties to 2D patterns. This can be a basis for scientific and automatic pattern making for high quality custom clothes. Firstly, representative 3D body shape of men was modeled. Then the 3D model was divided into 3 shells, front, side and back. Among them, the front shell was divided into 4 blocks by bust line and princess line. Secondly, curves are generated on each block according to matrix combination by grid method. Then triangles were developed into 2D pieces by reflecting the 3D curve length. The grid was arranged to maintain outer curve length. Next, the area of developed pieces and block were calculated and difference ratio between the block area and the developed pieces' area is calculated. Also, area difference ratio by the number of triangles is calculated. The difference ratio was represented as graphs and optimal section is selected by the shape of graphs. The optimal matrix was set considering connection with other blocks. Curves of torso upper front shell were regenerated by the optimal matrix and developed into pieces. We validated it's suitability by comparing difference ratio between the block area and the developed pieces' area of optimal section. The results showed that there was no significant difference between block area and the pieces' area developed by optimal matrix. The optimal matrix for 2D developing could be characterized as two types according to block's shape characteristics, one is affected by triangle number, the other is affected by number of raws more than columns. Through this study, both the 2D pattern developing from 3D body shape and 3D modeling from 2D pattern is possible, so it's standardization also possible.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.403-426
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• 1998

We present an algorithm to find an approximation for the stationary distribution for the general ergodic spatially-inhomogeneous block-partitioned upper Hessenberg form. Our approximation makes use of an associated upper block-Hessenberg matrix which is spa-tially homogeneous except for a finite number of blocks. We treat the MAP/G/1 retrial queue and the retrial queue with two types of customer as specific instances and give some numerical examples. The numerical results suggest that our method is superior to the ordinary finite-truncation method.