• Korean Journal of Mathematics
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• v.7 no.1
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• pp.7-9
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• 1999

In this paper, we introduce the regularity, the hyperexactness and the hyperregularity, and we study on the extensions of regularity and the holomorphical regularity of the bounded linear operators.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.379-383
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• 2013

In this paper, we introduce more general concepts of regularity and S-unitality, that is, ${\pi}$-regularity and ${\pi}S$-unitality and then give some examples in near-rings, also investigate their characterization and proper-ties.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.627-635
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• 2018

In this paper, we use the notion of characters of transformations provided in [8] by Purisang and Rakbud to define a notion of weak regularity of transformations on an arbitrarily fixed set X. The regularity of a semigroup of weakly regular transformations on a set X is also investigated.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.341-347
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• 2009

In this paper, we begin with to show the characterization of regularity and S-unitality in near-rings, also consider their application. Next, we introduce more general concepts of regularity and S-unitality, that is, ${\pi}$-regularity and ${\pi}S$-unitality and then give some examples in near-rings, also investigate their characterization and properties.

• East Asian mathematical journal
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• v.36 no.3
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• pp.349-357
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• 2020

For a nondegenerate projective curve C ⊂ ℙ^r of degree d, it was shown that the Castelnuovo-Mumford regularity reg(C) of C is at most d - r + 2. And the curves of maximal regularity which attain the maximally possible value d - r + 2 are completely classified. In this short note, we first collect several known results about curves of maximal regularity. We provide a new proof and some partial results. Finally we suggest some interesting questions.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.29-41
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• 2022

We study the concept of a quasi-ideal and a generalized bi-ideal of an n-ary semigroup; give a construction of the quasi-ideal of an n-ary semigroup generated by its nonempty subset; and introduce the notions of regularities, namely, a left regularity and a left weakly regularity. Moreover, the notions of a right regularity, a right weak regularity and a complete regularity are given. Finally, characterizations of these regularities are presented.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.991-1018
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• 2006

Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product $\Delta=C_2*C_2*C_2$. In this correspondence, hypermaps correspond to conjugacy classes of subgroups of $\Delta$, and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out$(\Delta)$ of the triangle group $\Delta$. This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups $\Theta$ of $\Delta$ of finite index. This generalises the notion of regularity to some non-regular objects.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.29 no.4
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• pp.517-529
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• 2019

Introduction: Although shift work is an inevitable form of labor in modern society, it has been identified as a cause of many ailments, such as cancer and musculoskeletal disorders. Meanwhile, previous studies have also shown that musculoskeletal disorders account for a large proportion of total industrial accidents and a high prevalence rate of these ailments has been found in shift workers. Methods: Among the respondents to the 5th Korea Working Conditions Survey(KWCS) 3,916 shift workers(2,658 of whom have not experienced musculoskeletal pain and 1,258 who have experienced musculoskeletal pain) were asked how the work regularity of shift workers affected musculoskeletal pain. Results: The results of a dichotomous logistic regression by correcting the demographic characteristics of the study subjects showed a lower prevalence of musculoskeletal pain in the 'High' regularity group compared to the 'Intermediate' regularity group for the criterion 'Regularity of Time Fixation'. A lower prevalence of musculoskeletal pain was shown in the 'High' and 'Moderate' regularity group compared to the 'Very Low' regularity one. Conclusions: Based on these findings, it was found that musculoskeletal pain occurs less when the work regularity of shift workers is 'Very high' or 'Intermediate', and the effect of working regularity on musculoskeletal pain varies for each shift type of work. It is deemed that more precise observation and understanding are required when managing the working environment of shift workers, and further study of regarding this issue is needed.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.17-27
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• 2014

In order to study the propagation of singularities for solutions to second order quasilinear strictly hyperbolic equations with boundary, we have to consider the regularity of solutions of first order nonlinear equations satisfied by a characteristic hyper-surface. In this paper, we study the regularity compositions of the form v(${\varphi}$(x), x) with v and ${\varphi}$ assumed to have limited Sobolev regularities and we use it to prove the regularity of solutions of the first order nonlinear equations.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.619-626
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• 2015

This paper considers regularity for the p-harmonic and Ostwald-de Waele flows. Some Serrin's type regularity criteria are established for 1 < p < 2.