• Honam Mathematical Journal
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• v.41 no.4
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• pp.799-812
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• 2019

We introduce flat e-covers of modules and define e-perfect rings as a generalization of perfect rings. We prove that a ring is right perfect if and only if it is semilocal and right e-perfect which generalizes a result due to N. Ding and J. Chen. Moreover, in the light of the fact that a ring R is right perfect if and only if flat covers of any R-module are projective covers, we study on the rings over which flat covers of modules are (generalized) locally projective covers, and obtain some characterizations of (semi) perfect, A-perfect and B-perfect rings.

• Language and Information
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• v.4 no.1
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• pp.21-42
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• 2000

In this paper, I explore the semantic interpretation of the English present perfect by arguing that the perfect is analogous to modals in its interpretation. The perfect produces several different readings, i.e., the resultative and the current relevant reading, to mention a few. Despite this, the meaning of the perfect remains invariable in sentences where it occurs. Instead, the semantic variability of the perfect is due to the nature of the conversational background. This indicates that just as modals are context-dependent, so is the perfect, which inspires a modal-based approach to the semantics of the perfect. By incorporating such an approach into its semantic analysis, we can present a unified account of the different meanings of the perfect.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.15-29
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• 2024

Many academics employ various structures to expand topological space, including the idea of topology, as a result of the importance of topological space in analysis and some applications. One of the most notable of the generalizations was the definition of perfect functions in bitopological spaces, which was presented by Ali.A.Atoom and H.Z.Hdeib. We propose the notion of α- pairwise perfect functions in bitopological spaces and define different types of this concept in this study. Pairwise -T - α- perfect functions, pairwise -α-irr-perfect functions, and pairwise -T - α- irr-perfect functions, are all characterized in addition to pairwise -α-perfect functions. We go through their primary characteristics and show how they interact. Finally, under these functions, we introduce the images and inverse images of certain bitopological features. About these concepts, some product theorems have been discovered.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.691-699
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• 2007

The notion of perfect filters and concrete filters in WFI-algebras is introduced, and several properties are investigated. Relations between a filter, a perfect filter and a concrete filter are given, and characterizations of a perfect filter and a concrete filter are provided. An extension property for a concrete filter and a perfect filter is established.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.653-662
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• 2005

In this paper we shall give the relationships among $T_R,\;End_{R}(M),\;SEnd_{R}(M)\;and\;SAut_R(M)$ when M is a perfect R-module. If M and N are perfect modules, we get $SAut_{R}(M {\times}N){\cong}SAut_{R}(M){\times}SAut_R(N)$. Also we shall discuss that $_x(M)_H$ is a subgroup of $_x(M)$ if M is quasi-perfect and $_x(M)_H$ is a normal subgroup of $_x(M)$ if M is perfect.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.145-159
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• 2005

In this paper we introduced the concept of perfect folding defined on $E^2$ which equipped by perfect k-coloring of r-monohedral tillings. Then we studied the different cases of perfect foldings of 4-monohedral and 3-monohedral tillings of $E^2$. Also the permutations describe each folding are obtained.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.349-359
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• 2020

We study perfect 2-colorings of regular graphs. In particular, we consider the 4-regular case. We obtain a characterization of perfect 2-colorings of toroidal grids.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.689-698
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• 1995

The purpose of this paper is to introduce a new fuzzy semi-topogenous order which agrees with the fuzzy points and investigate some properties of this order and define a fuzzy proximity structure by using this order.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.751-763
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• 2015

Let ${\alpha}$ be a positive integer, and let $p_1$, $p_2$ be two distinct prime numbers with $p_1$ < $p_2$. By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form $2^{\alpha}p_1p_2$ and $2^{\alpha}p_1^2p_2$, and obtain a lot of new near-perfect numbers which involve some special kinds of prime number pairs. One kind is exactly the new Mersenne conjecture's prime number pair. Another kind has the form $p_1=2^{{\alpha}+1}-1$ and $p_2={\frac{p^2_1+p_1+1}{3}}$, where the former is a Mersenne prime and the latter's behavior is very much like a Fermat number.

• Journal of Internet Computing and Services
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• v.2 no.4
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• pp.55-67
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• 2001

Commercial machine translation systems have been announcing recently, However, there are problems that the systems have shown mistranslations, yet. Among these mistranslations, this paper is interested in the mistakes of tense processing. The paper compares Korean tenses with 12 English ones: present. past, future, present perfect. past perfect, future perfect. present progressive, past progressive, future progressive, present perfect progressive, past perfect progressive. future perfect progressive. Next, we perform the meaning analysis of Korean tenses. Then we describe the structure of the tenses based on Conceptual Graph(CG). In the experiment. the paper implements the program that translates sentences included in the tenses into CG.