• 대한수학회논문집
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• 제27권3호
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• pp.621-627
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• 2012

Star operations are defined by R. E. Hodel in 1994. In this paper some relations among star operators, sequential closure operators and closure operators are discussed. Moreover, we introduce an induced topology by a family of subsets of a space, and some interesting results about star operators are established by the induced topology.

• 대한수학회논문집
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• 제25권3호
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• pp.477-484
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• 2010

In this paper, we introduce a new property (*) of a topological space and prove that if X satisfies one of the following conditions (1) and (2), then compactness, countable compactness and sequential compactness are equivalent in X; (1) Each countably compact subspace of X with (*) is a sequential or AP space. (2) X is a sequential or AP space with (*).

• 호남수학학술지
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• 제39권4호
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• pp.655-663
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• 2017

In this paper we define $AP_c$ and $AP_{cc}$ spaces which are stronger than the property of approximation by points(AP). We investigate operations on their subspaces and study function theorems on $AP_c$ and $AP_{cc}$ spaces. Using those results, we prove that every continuous image of a countably compact Hausdorff space with AP is AP. Finally, we prove a theorem that every compact ${\kappa}$-WAP space is ${\kappa}$-pseudoradial, and prove a theorem that the product of a compact ${\kappa}$-radial space and a compact ${\kappa}$-WAP space is a ${\kappa}$-WAP space.

• 대한수학회지
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• 제55권4호
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.

• 대한수학회지
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• 제51권2호
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• pp.251-266
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• 2014

In this paper, we use Newton's method to approximate a locally unique solution of an equation in Banach spaces and introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton's method than before [1]-[13], in some interesting cases, provided that the Fr$\acute{e}$chet-derivative of the operator involved is p-H$\ddot{o}$lder continuous (p${\in}$(0, 1]). Numerical examples involving two boundary value problems are also provided.

• 대한수학회논문집
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• 제33권2호
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• 정보과학회 논문지
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• 제43권1호
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• pp.40-46
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• 2016

도로지도 생성은 인공위성 촬영이나 현장실사를 기반으로 한다. 그리하여 도로지도를 생성하고 수정하는데 많은 시간과 비용이 든다. 이러한 이유로 차량 GPS 데이터를 이용해 도로지도를 생성하는 연구가 활발히 진행되고 있다. 도로지도 생성 연구에서 가장 중요한 문제는 주도로와 같은 대표궤적을 추출하는 것이다. 대표궤적 추출을 수행할 때에는 시작과 끝이 비슷한 궤적데이터들의 집합을 전제로 하여 궤적을 추출한다. 따라서 대표궤적을 추출하기에 앞서 전처리 과정으로 궤적 클러스터링 작업이 필요하다. 본 논문에서는 이러한 문제를 해결하기 위해 하나의 영역을 일정한 격자로 분할하고, Sweep Line 알고리즘을 응용해 유사궤적들을 탐색한다. 마지막으로 프레쉐거리를 이용하여 궤적 간 유사도를 계산하였다. 실제로 서울의 강남구 지역에 있는 500대의 차량 GPS 궤적을 가지고 클러스터링 작업을 수행하였다. 또한, 실험을 통하여 격자분할 접근방식의 빠른 수행시간과 안정성을 보였다.