• Communications of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.213-230
• /
• 2019

We construct new metric outer measures (multifractal analogues of the Hewitt-Stromberg measure) $H^{q,t}_{\mu}$ and $P^{q,t}_{\mu}$ lying between the multifractal Hausdorff measure ${\mathcal{H}}^{q,t}_{\mu}$ and the multifractal packing measure ${\mathcal{P}}^{q,t}_{\mu}$. We set up a necessary and sufficient condition for which multifractal Hausdorff and packing measures are equivalent to the new ones. Also, we focus our study on some regularities for these given measures. In particular, we try to formulate a new version of Olsen's density theorem when ${\mu}$ satisfies the doubling condition. As an application, we extend the density theorem given in [3].

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

• Korean Journal of Mathematics
• /
• v.26 no.2
• /
• pp.271-283
• /
• 2018

In this paper, we generelize the Olsen's density theorem to any measurable set, allowing us to extend the main results of H.K. Baek in (Proc. Indian Acad. Sci. (Math. Sci.) Vol. 118, (2008), pp. 273-279.). In particular, we tried through these results to improve the decomposition theorem of Besicovitch's type for the regularities of multifractal Hausdorff measure and packing measure.

• Kyungpook Mathematical Journal
• /
• v.62 no.1
• /
• pp.29-41
• /
• 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
• /
• v.24 no.1
• /
• pp.91-97
• /
• 1987

• Language and Information
• /
• v.7 no.1
• /
• pp.1-22
• /
• 2003

Quantifier floating is one of the much studied phenomena in natural languages where quantifying expressions may appear in places other than their original prenominal one. Its presence is especially prominent in languages such as Korean that allow more or less free word order. We find that, in addition to what is described in the literature, there are other remarkable regularities in the way the language allows quantifiers to “float” with respect to various constructions including coordination, relative clauses, and embedded clauses. These regularities are captured syntactically in a combinatory categorial grammar (CCG) framework for Korean. We also show how to derive semantic representations for Korean quantifier floating in the same CCG framework.

• Geomechanics and Engineering
• /
• v.13 no.5
• /
• pp.793-807
• /
• 2017

Regularities of temperature variation were determined in points of subgrade of the highway. Measurement of temperature was performed by special sensors, based on the effect of thermal resistance. Regular measurements of temperature were performed for two sections of the highway with asphalt concrete and cement concrete pavements for continuous period from November 2010 to March 2016. Multi-year experimental data, which we obtained, allowed establishing of peculiarities for temperature variation in points of subgrade in time and temperature distribution in the depth for annual cycle. Characteristics were determined for winter period-depth, duration and freezing rate, duration and defreezing rate for pavement and subgrade of the highway.

• Journal of the Chungcheong Mathematical Society
• /
• v.5 no.1
• /
• pp.185-193
• /
• 1992

In this paper we shall study the properties of regular relations. We also define syndetically regular relations as the generalizations of syndetical proximalities.

• Korean Journal of Mathematics
• /
• v.10 no.2
• /
• pp.173-177
• /
• 2002

The purpose of this paper is to study and characterize the flows of characteristic 0. It is shown that the homomorphic image of distal flow of characteristic 0 is a distal flow of characteristic 0. It is also shown that the closure of every orbit in a 0-graphic flow is regular minimal.

• Honam Mathematical Journal
• /
• v.31 no.4
• /
• pp.529-540
• /
• 2009

The authors have investigated several properties of endomorphism rings of modules. In particular, a closedly simple module and a closedly semi-simple module were defined and then the regularities of its rings of endomorphisms were discussed.