• East Asian mathematical journal
• /
• 제36권1호
• /
• pp.61-71
• /
• 2020

Up to the present day, the best solution we can get to the truncated moment problem (TMP) is probably the Flat Extension Theorem. It says that if the corresponding moment matrix of a moment sequence admits a rank-preserving positive extension, then the sequence has a representing measure. However, constructing a flat extension for most higher-order moment sequences cannot be executed easily because it requires to allow many parameters. Recently, the author has considered various decompositions of a moment matrix to find a solution to TMP instead of an extension. Using a new approach with the Hadamard product, the author would like to introduce more techniques related to moment matrix decompositions.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제13권4호
• /
• pp.281-294
• /
• 2006

Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제17권3호
• /
• pp.139-170
• /
• 2013

We extend a p-hierarchical decomposition of the second degree finite element space of N$\acute{e}$d$\acute{e}$lec for tetrahedral meshes in three dimensions given in [1] to meshes with hexahedral elements, and derive p-hierarchical decompositions of the second degree finite element space of Raviart-Thomas in two dimensions for triangular and quadrilateral meshes. After having proved stability of these subspace decompositions and requiring certain saturation assumptions to hold, we construct a local a posteriori error estimator for fem and bem coupling of a time-harmonic electromagnetic eddy current problem in $\mathbb{R}^3$. We perform some numerical tests to underline reliability and efficiency of the estimator and test its usefulness in an adaptive refinement scheme.

• 대한수학회보
• /
• 제55권1호
• /
• pp.149-163
• /
• 2018

In recent years, the study of slice Dirac operators has attracted more and more attention in the literature. In this paper, Almansitype decompositions for null solutions to the iterated slice Dirac operator and the generalized slice Dirac operator are obtained without a star-like domain centered at the origin. As applications, we investigate Riquier type problems and Dirichlet type problems in the theory of slice monogenic functions.

• Communications for Statistical Applications and Methods
• /
• 제14권1호
• /
• pp.215-227
• /
• 2007

Variable selection algorithm for Sliced Inverse Regression using penalty function is proposed. We noted SIR models can be expressed as generalized eigenvalue decompositions and incorporated penalty functions on them. We found from small simulation that the HARD penalty function seems to be the best in preserving original directions compared with other well-known penalty functions. Also it turned out to be effective in forcing coefficient estimates zero for irrelevant predictors in regression analysis. Results from illustrative examples of simulated and real data sets will be provided.

• 대한수학회보
• /
• 제35권1호
• /
• pp.33-43
• /
• 1998

Matlis posed the following question in 1958: if N is a direct summand of a direct sum M of indecomposable injectives, then is N itself a direct sum of indecomposable innjectives\ulcorner It will be proved that the Matlis problem has an affirmative answer when M is a multiplication module, and that a weaker condition then that of M being a multiplication module can be given to module M when M is a countable direct sum of indecomposable injectives.

• 정보교육학회논문지
• /
• 제20권6호
• /
• pp.553-562
• /
• 2016

소프트웨어 교육이 학습자의 Computational Thinking(CT) 역량 계발을 지향하고 있지만 CT역량 계발을 위해 수업을 설계하고 CT역량 계발 효과를 측정하는 것에는 아직 많은 연구가 필요한 실정이다. 본 연구의 목적은 예비교원의 CT 역량을 계발하기 위해 CT기반으로 설계된 교재를 활용하여 SW교육을 진행하고 본 수업이 예비교원의 CT 역량에 미치는 영향을 알아보는 것이다. 본 연구에서는 문헌 연구를 통해 CT의 다섯 가지 주요 세부 역량을 알고리즘적 사고, 평가, 분해, 추상화 및 일반화로 설정하였다. 본 연구의 대상은 국내 한 교육대학교에서 한 학기 동안 수업을 수강한 47명의 예비교원이며, CT관련 설문을 개발하여 실시하고 팀프로젝트를 CT의 세부 핵심 역량에 초점을 두고 질적으로 분석하여 연구 결과를 도출하였다. 본 연구의 결과는 예비교사가 지각한 CT경험과 프로젝트를 통해 나타난 CT세부 핵심 역량 측면의 질적 분석을 통해 향후 교원양성기관에서의 소프트웨어 교육의 교수설계 및 운영에 대해 시사점을 제공하고 있다는 점에서 의의가 있다.

• International Journal of Control, Automation, and Systems
• /
• 제3권2호
• /
• pp.159-165
• /
• 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.

• International Journal of Control, Automation, and Systems
• /
• 제3권3호
• /
• pp.419-429
• /
• 2005

This paper considers eigenstructure assignment in high-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related with a type of so-called high-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically very simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effect of the proposed approaches.

• 한국정보과학회논문지:시스템및이론
• /
• 제34권5_6호
• /
• pp.195-201
• /
• 2007

트리의 최소단말경로분할이란 트리를 에지가 서로 소인 단말 노드 간 경로들로 분할하되, 가장 긴 경로의 길이를 최소화하는 문제이다. 본 논문에서는 트리의 최소단말경로분할을 $O({\mid}V{\mid}^2$시간에 구하는 알고리즘을 제시한다. 이 알고리즘은 주어진 최적화 문제를 이에 대응하는 결정 문제, 즉 최소단말경로 분할의 비용이 l 이하인지를 결정하는 문제를 이용한 이진 탐색으로 환원한다. 결정 문제는 트리를 한 차례 순회하는 동안 동적 계획법에 의해 해결된다