• East Asian mathematical journal
• /
• v.30 no.3
• /
• pp.303-310
• /
• 2014

We study the existence of regular polygons and regular solids whose vertices have integer coordinates in the three dimensional space and study side lengths of such squares, cubes and tetrahedra. We show that except for equilateral triangles, squares and regular hexagons there is no regular polygon whose vertices have integer coordinates. By using this, we show that there is no regular icosahedron and no regular dodecahedron whose vertices have integer coordinates. We characterize side lengths of such squares and cubes. In addition to these results, we prove Ionascu's result [4, Theorem2.2] that every equilateral triangle of side length $\sqrt{2}m$ for a positive integer m whose vertices have integer coordinate can be a face of a regular tetrahedron with vertices having integer coordinates in a different way.

• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.671-677
• /
• 2021

For a distance-regular graph with valency k, second largest eigenvalue r and diameter D, it is known that r ≥ $min\{\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2},\;a_3\}$ if D = 3 and r ≥ $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ if D ≥ 4, where λ = a₁. This result can be generalized to the class of edge-regular graphs. For an edge-regular graph with parameters (v, k, λ) and diameter D ≥ 4, we compare $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ with the local valency λ to find a relationship between the second largest eigenvalue and the local valency. For an edge-regular graph with diameter 3, we look at the number $\frac{{\lambda}-\bar{\mu}+\sqrt{({\lambda}-\bar{\mu})^2+4(k-\bar{\mu})}}{2}$, where $\bar{\mu}=\frac{k(k-1-{\lambda})}{v-k-1}$, and compare this number with the local valency λ to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.

• Journal of Labour Economics
• /
• v.30 no.2
• /
• pp.1-31
• /
• 2007

The purpose of this paper is to analyse wage differentials between non-regular and regular works. Data from EAPS(Economically Active Population Survey) 2005 show that the monthly wage level of non-regular worker is only 63% of regular worker and thus there exist 37% wage differentials. However, these wage differentials do not control for hours of work, the amount of human capital, job characteristics, and other individual characteristics affecting wages. If these variables are added to the hourly wage regression equation, the wage gap between non-regular and regular workers drastically decreases to 2.2%. Furthermore, decomposition of the wage differentials by Oaxaca method shows that productivity difference between non-regular and regular workers explains up to 91% of the wage gap. This implies that the magnitude of wage discrimination against non-regular workers is at most 0.2% of hourly wage of regular workers. To control for unobserved individual heterogeneities more accurately, we also construct panel data and estimate wage differentials. The results from the panel data approach show that there is no difference in the hourly wages between non-regular and regular workers. In some specifications, the wage rate of non-regular worker is rather higher than that of regular worker. These results are consistent with economic theory. Other things being equal, workers with unstable employment may require higher wages to compensate their unstability. Firms are willing to pay higher wages if they can get more flexibility from non-regular employment. Empirical results in this paper cast doubt on the view that there is wage discrimination against non-regular workers in the labor market. Public policies should be targeted for disadvantaged groups among non-regular workers, not for non-regular workers in general.

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

• East Asian mathematical journal
• /
• v.14 no.2
• /
• pp.393-397
• /
• 1998

The author obtains ideal-theoretical characterizations of the following two classes of $\Gamma$-semigroups; (1) regular $\Gamma$-semigroups; (2) $\Gamma$-semigroups that are both regular and intra-regular.

• Korean Journal of Mathematics
• /
• v.9 no.2
• /
• pp.99-104
• /
• 2001

We give the characterization of left(right) semi-regular $po$-semigroups and $Ve$-semigroups.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.13-27
• /
• 2024

A regular t-balanced Cayley map on a group Γ is an embedding of a Cayley graph on Γ into a surface with certain special symmetric properties. We completely classify regular t-balanced Cayley maps for a class of split metacyclic 2-groups.

• Journal of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.241-257
• /
• 2013

An automorphism group of a graph is said to be $s$-regular if it acts regularly on the set of $s$-arcs in the graph. A graph is $s$-regular if its full automorphism group is $s$-regular. In the present paper, all $s$-regular cubic graphs of order $10p^3$ are classified for each $s{\geq}1$ and each prime $p$.

• Korean Journal of Mathematics
• /
• v.10 no.2
• /
• pp.117-122
• /
• 2002

In this paper, we give some properties of left(right) semi-regular and $g$-regular $po$-semigroups.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.125-140
• /
• 2006

Let $g(n,\;l_1,\;l_2,\;d,\;t,\;q)$ be the number of general4-regular graphs on n labelled vertices with $l_1+2l_2$ loops, d double edges, t triple edges and q quartet edges. We use inclusion and exclusion with five types of properties to determine the asymptotic behavior of $g(n,\;l_1,\;l_2,\;d,\;t,\;q)$ and hence that of g(2n), the total number of general 4-regular graphs where $l_1,\;l_2,\;d,\;t\;and\;q\;=\;o(\sqrt{n})$, respectively. We show that almost all general 4-regular graphs are 2-connected. Moreover, we determine the asymptotic numbers of general 4-regular graphs with given connectivities.