• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.49-59
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• 2001

In this paper, we introduce an extended notion of regular homomorphism of minimal sets by considering a certain subgroup of the group of automorphisms of a universal minimal transfomation group.

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.27-33
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• 1987

Minimal s-Urysohn and minimal s-regular spaces are studied. An s-Urysohn (respectively, s-regular) space (X, $\mathfrak{T}$) is said to be minimal s-Urysohn (respectively, minimal s-regular) if for no topology $\mathfrak{T}^{\prime}$ on X which is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) is s-Urysohn (respectively s-regular). Several characterizations and other related properties of these classes of spaces have been obtained. The present paper is a study of minimal P-spaces where P refers to the property of being an s-Urysohn space or an s-regular space. A P-space (X, $\mathfrak{T}$) is said to be minimal P if for no topology $\mathfrak{T}^{\prime}$ on X such that $\mathfrak{T}^{\prime}$ is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) has the property P. A space X is said to be s-Urysohn [2] if for any two distinct points x and y of X there exist semi-open set U and V containing x and y respectively such that $clU{\bigcap}clV={\phi}$, where clU denotes the closure of U. A space X is said to be s-regular [6] if for any point x and a closed set F not containing x there exist disjoint semi-open sets U and V such that $x{\in}U$ and $F{\subseteq}V$. Throughout the paper the spaces are assumed to be Hausdorff.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.103-111
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• 1999

In this paper, we introduce a generalized regular homomorphism as the extending notion of the regular homomorphism.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.683-695
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• 2007

A tournament is an orientation of a complete graph, and in general a multipartite or c-partite tournament is an orientation of a complete c-partite graph. In a recent article, the authors proved that a regular c-partite tournament with $r{\geq}2$ vertices in each partite set contains a cycle with exactly r-1 vertices from each partite set, with exception of the case that c=4 and r=2. Here we will examine the existence of cycles with r-2 vertices from each partite set in regular multipartite tournaments where the r-2 vertices are chosen arbitrarily. Let D be a regular c-partite tournament and let $X{\subseteq}V(D)$ be an arbitrary set with exactly 2 vertices of each partite set. For all $c{\geq}4$ we will determine the minimal value g(c) such that D-X is Hamiltonian for every regular multipartite tournament with $r{\geq}g(c)$.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.73-79
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• 2003

A subgroup S(X, ${\gamma}$) of the group of automorphisms of a universal minimal transformation group is introduced and a necessary and sufficient condition for two subgroups to be identical is obtained.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.555-562
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• 2008

In this paper, it will be given a necessary and sufficient condition for a function to be an r-homomorphism in connection with the subgroups of the automorphism group of a universal minimal set.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.181-187
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• 2013

In this paper we give some results on homomorphisms of pointed minimal sets. In particular, we investigate some characterizations on quasi-Ellis groups.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.583-590
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• 2014

In this paper we give some relationships between quasi-Ellis groups and some subgroups of the automorphism group. In particular, we investigate several characterizations on some subgroups of the automorphism group.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.117-124
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• 1993

In this paper, we introduce a concept of quasi $O_{z}$ -spaces which generalizes that of $O_{z}$ -spaces. Indeed, a completely regular space X is a quasi $O_{z}$ -space if for any regular closed set A in X, there is a zero-set Z in X with A = c $l_{x}$ (in $t_{x}$ (Z)). We then show that X is a quasi $O_{z}$ -space iff every open subset of X is $Z^{#}$-embedded and that X is a quasi $O_{z}$ -spaces are left fitting with respect to covering maps. Observing that a quasi $O_{z}$ -space is an extremally disconnected iff it is a cloz-space, the minimal extremally disconnected cover, basically disconnected cover, quasi F-cover, and cloz-cover of a quasi $O_{z}$ -space X are all equivalent. Finally it is shown that a compactification Y of a quasi $O_{z}$ -space X is again a quasi $O_{z}$ -space iff X is $Z^{#}$-embedded in Y. For the terminology, we refer to [6].[6].

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.9
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• pp.3274-3297
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• 2021

Permission delegation is an important research issue in access control. It allows a user to delegate some of his permissions to others to reduce his workload, or enables others to complete some tasks on his behalf when he is unavailable to do so. As an ideal solution for controlling read access on outsourced data objects on the cloud, Ciphertext-Policy Attribute-Based Encryption (CP-ABE) has attracted much attention. Some existing CP-ABE schemes handle the read permission delegation through the delegation of the user's private key to others. Still, these schemes lack the further consideration of granularity and traceability of the permission delegation. To this end, this article proposes a flexible and fine-grained CP-ABE key delegation approach that supports white-box traceability. In this approach, the key delegator first examines the relations between the data objects, read permission thereof that he intends to delegate, and the attributes associated with the access policies of these data objects. Then he chooses a minimal attribute set from his attributes according to the principle of least privilege. He constructs the delegation key with the minimal attribute set. Thus, we can achieve the shortest delegation key and minimize the time of key delegation under the premise of guaranteeing the delegator's access control requirement. The Key Generation Center (KGC) then embeds the delegatee's identity into the key to trace the route of the delegation key. Our approach prevents the delegatee from combining his existing key with the new delegation key to access unauthorized data objects. Theoretical analysis and test results show that our approach helps the KGC transfer some of its burdensome key generation tasks to regular users (delegators) to accommodate more users.