• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.669-679
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• 2022

We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

• 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.35 no.4
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• pp.1057-1073
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• 2020

In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple geometric sequences. In particular, we provide a complete description of the rational multicyclic monoids M that are hereditarily atomic (i.e., every submonoid of M is atomic). Additionally, we show that the sets of lengths of certain rational multicyclic monoids are finite unions of multidimensional arithmetic progressions, while their unions satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we realize arithmetic progressions as the sets of distances of some additive submonoids of the nonnegative rational numbers.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.203-206
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• 1995

We investigate the applicability of the theory of robust stabilization with respect to additive, stable perturbations of a normalized left-coprime factorization to controller design of a flexible arm with uncertain parameters.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.515-528
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• 2023

In this paper, we formulate the set of all saturated numerical semigroups with prime multiplicity. We characterize the catenary degrees of elements of the semigroups we obtained which are important invariants in factorization theory. We also give the proper characterizations of the semigroups under consideration.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.56-59
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• 1996

Worst-case state estimation will be proposed in this paper. By using the worst-case disturbance and worst-case state estimation, we can obtain right/left constrained coprime factors. If constrained coprime factors are used in designing a controller, the infinity-norm of closed-loop transfer matrix can be smaller than any constant .gamma.(> .gamma.$_{opt}$) without matrix dilation optimization. The derivation of left/right constrained coprime factors is achieved by doubly coprime factorization for the plant constrained by the infinity norm. And the parameterization of stabilizing controllers gives us easily understanding for H$_{\infty}$ control theory.ry.

• The Mathematical Education
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• v.54 no.4
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• pp.365-383
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• 2015

Factorization asks the recognition of the structure of polynomials, compared to polynomial expansion with process characteristic. Therefore it makes students experience a lot of difficulties. This study aims to figure out causes of the difficulties by identifying students' cognitive characteristics in factorizing in the perspective of 'structure sense'. To do this, we gave six factorizing problems of three types to middle school students and selected six participants as interviewees based on the test results. They were classified into two categories, structure sense and non-structure sense. Through this interview, we figured out the interviewee's cognitive characteristics and the causes of difficulty in the perspective of structure sense. Furthermore, we suggested some didactical implications for encouraging structure sense in factorizing by identifying assistances and obstacles for recognition of structures.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.579-591
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• 2002

New fixed Point results for the (equation omitted) selfmaps ale given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.11
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• pp.1285-1295
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• 1999

본 논문은 방대한 크기의 볼륨 데이타를 효율적으로 렌더링하기 위한 셀 기반 웨이브릿 압축 방법을 제시한다. 이 방법은 볼륨을 작은 크기의 셀로 나누고, 셀 단위로 웨이브릿 변환을 한 다음 복원 순서에 따른 런-길이(run-length) 인코딩을 수행하여 높은 압축율과 빠른 복원을 제공한다. 또한 최근 복원 정보를 캐쉬 자료 구조에 효율적으로 저장하여 복원 시간을 단축시키고, 에러 임계치의 정규화로 비정규화된 웨이브릿 압축보다 빠른 속도로 정규화된 압축과 같은 고화질의 이미지를 생성하였다. 본 연구의 성능을 평가하기 위하여 {{}} 해상도의 볼륨 데이타를 압축하여 쉬어-？ 분해(shear-warp factorization) 알고리즘에 적용한 결과, 손상이 거의 없는 상태로 약 27:1의 압축율이 얻어졌고, 약 3초의 렌더링 시간이 걸렸다.Abstract This paper presents an efficient cell-based wavelet compression method of large volume data. Volume data is divided into individual cell of {{}} voxels, and then wavelet transform is applied to each cell. The transformed cell is run-length encoded according to the reconstruction order resulting in a fairly good compression ratio and fast reconstruction. A cache structure is used to speed up the process of reconstruction and a threshold normalization scheme is presented to produce a higher quality rendered image. We have combined our compression method with shear-warp factorization, which is an accelerated volume rendering algorithm. Experimental results show the space requirement to be about 27:1 and the rendering time to be about 3 seconds for {{}} data sets while preserving the quality of an image as like as using original data.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.159-165
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• 2005

This paper designs observers for matrix second-order linear systems on the basis of generalized eigenstructure assignment via unified parametric approach. It is shown that the problem is closely related with a type of so-called generalized matrix second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass system is utilized to show the effect of the proposed approaches.