• 한국수학교육학회지시리즈A:수학교육
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• 제15권2호
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• pp.29-30
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• 1977

• 대한수학회지
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• 제47권1호
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• pp.215-222
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• 2010

A T$_1$ topological space X is called an almost GP-space if every dense G$_{\delta}$-set of X has nonempty interior. The behaviour of almost GP-spaces under taking subspaces and superspaces, images and preimages and products is studied. If each dense G$_{\delta}$-set of an almost GP-space X has dense interior in X, then X is called a GID-space. In this paper, some interesting properties of GID-spaces are investigated. We will generalize some theorems that hold in almost P-spaces.

• 대한수학회지
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• 제56권5호
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• 대한수학회논문집
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• 제33권4호
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• pp.1341-1356
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• 2018

The author devotes this paper to defining a new class of generalized soft open sets, namely soft somewhere dense sets and to investigating its main features. With the help of examples, we illustrate the relationships between soft somewhere dense sets and some celebrated generalizations of soft open sets, and point out that the soft somewhere dense subsets of a soft hyperconnected space coincide with the non-null soft ${\beta}$-open sets. Also, we give an equivalent condition for the soft csdense sets and verify that every soft set is soft somewhere dense or soft cs-dense. We show that a collection of all soft somewhere dense subsets of a strongly soft hyperconnected space forms a soft filter on the universe set, and this collection with a non-null soft set form a soft topology on the universe set as well. Moreover, we derive some important results such as the property of being a soft somewhere dense set is a soft topological property and the finite product of soft somewhere dense sets is soft somewhere dense. In the end, we point out that the number of soft somewhere dense subsets of infinite soft topological space is infinite, and we present some results which associate soft somewhere dense sets with some soft topological concepts such as soft compact spaces and soft subspaces.

• 대한수학회지
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• 제45권4호
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• pp.903-921
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• 2008

A continuous linear operator $T\;:\;X{\rightarrow}X$ is called hypercyclic if there exists an $x\;{\in}\;X$ such that the orbit ${T^nx}_{n{\geq}0}$ is dense. We consider the problem: given an operator $T\;:\;X{\rightarrow}X$, hypercyclic or not, is the restriction $T|y$ to some closed invariant subspace $y{\subset}X$ hypercyclic? In particular, it is well-known that any non-constant partial differential operator p(D) on $H({\mathbb{C}}^d)$ (entire functions) is hypercyclic. Now, if q(D) is another such operator, p(D) maps ker q(D) invariantly (by commutativity), and we obtain a necessary and sufficient condition on p and q in order that the restriction p(D) : ker q(D) $\rightarrow$ ker q(D) is hypercyclic. We also study hypercyclicity for other types of operators on subspaces of $H({\mathbb{C}}^d)$.

• 대한수학회논문집
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• 제39권1호
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• pp.259-266
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• 2024

The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to r-strongly irreducible r-ideals (endowed with Zariski topologies) of monoids, called terminal spaces. We show that terminal spaces are T₀, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. We characterize rarithmetic monoids in terms of terminal spaces. Finally, we provide necessary and sufficient conditions for the subspaces of r-maximal r-ideals and r-prime r-ideals to be dense in the corresponding terminal spaces.

• 디지털융복합연구
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• 제20권2호
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• pp.217-223
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• 2022

온라인 데이터 스트림에 대한 부분 공간 클러스터링은 데이터 공간 차원의 모든 부분 집합을 검사해야 하므로 많은 양의 메모리 자원을 필요로 한다. 유한한 메모리 공간에서 데이터 스트림에 대한 클러스터들의 지속적인 변화를 추적하기 위해 본 논문에서는 메모리 자원을 효과적으로 사용하는 격자기반 부분 공간 클러스터링 알고리즘을 제안한다. n차원 데이터 스트림이 주어지면 각 차원 데이터 공간에 있는 데이터 항목의 분포 정보를 격자셀 리스트에 의해 모니터링 된다. 첫번째 레벨의 격자셀 목록에서 데이터 항목의 빈도가 높아 단위 격자셀이 되면 해당 격자셀로부터 모든 가능한 부분 공간의 클러스터를 찾기 위해 다음 레벨의 격자셀 리스트를 자식 노드로 생성한다. 이와 같이 최대 다차원 n레벨의 격자셀 부분 공간 트리가 구성되고, k차원의 부분 공간 클러스터는 부분 공간 격자셀 트리의 k레벨에서 찾을 수 있다. 실험을 통해서 제안하는 방법이 기존 방법만큼 정확도를 유지하면서, 밀집 공간만 확장하여 컴퓨팅 자원을 보다 효율적으로 사용하는 것을 확인하였다.