• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.4
• /
• pp.409-415
• /
• 2006

In this paper, we study the condition that a given homeomorphism has a square root and give an example of a wandering homeomorphism without square roots.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.7 no.5
• /
• pp.221-229
• /
• 1999

We examined the governing factors of fatigue limit in annealed and austempered ductile iron specimens machined micro hole(dia.<0.4mm) in rotary bending fatigue test. Also, the quantitative relationship between fatigue limit and maximum defect size in specimens was investigated. Artificial defect(micro-pit type, dia.<0.4mm) on specimen surface did not bring about an obvious reduction of fatigue limit in austempered ductile iton(ADI) as compared with annealed ductile iron. According to the investigation of ${\sqrt{area}}_c$ which is the critical defect size to crack initiation at artificial defect, ${\sqrt{area}}_c$ of ADI was larger than that of annealed ductile iron. This shows that the situation of crack initiation at artificial defect in ADI is more difficult in comparison with annealed ductile iron. Maximum defect size is one of the important parameters to predict fatigue limit. And, the quantitative relationship, between the fatigue limit ${\sigma}_{\omega}$ and the maximum defect size ${\sqrt{area}}_{max}$ can be expressed to ${\sigma}_{\omega}^n{\cdot}{\sqrt{area}}_{max}=C_2$ where, $C_2$ are constant. Moreover, it is possible to explain the difference in fatigue limit between, austempered and annealed ductile iron by introducing the parameter ${\delta}(=N_{sg}/N_{total})$in a plain spectimen.

• Korean Journal of Mathematics
• /
• v.8 no.1
• /
• pp.27-32
• /
• 2000

In this paper, we show that for any continuous map $f$ of the circle $S^1$ to itself, (1) $x{\in}{\Omega}(f){\backslash}\overline{R(f)}$, then $x$ is not a turning point of $f$ and (2) if $P(f)$ is non-empty, then $R(f)$ is closed if and only if $AP(f)$ is closed.

• The Pure and Applied Mathematics
• /
• v.2 no.2
• /
• pp.157-162
• /
• 1995

Let I be the interval, $S^1$ the circle and let X be a compact metric space. And let $C^{circ}(X,\;X)$ denote the set of continuous maps from X into itself. For any f$f\in\;C\circ(X,\;X),\;let\;P(f),\;R(f),\;\Gamma(f),\;\Lambda(f)\;and\;\Omega(f)$ denote the collection of the periodic points, recurrent points, ${\gamma}-limit{\;}points,{\;}{\omega}-limit$ points and nonwandering points, respectively.(omitted)

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.1249-1258
• /
• 2022

In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

• Bulletin of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.233-242
• /
• 1988

• Journal of the Korean Mathematical Society
• /
• v.50 no.5
• /
• pp.1051-1066
• /
• 2013

By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.

• Journal of the Korean Society of Marine Environment & Safety
• /
• v.24 no.3
• /
• pp.325-331
• /
• 2018

This paper deals with the dynamical analysis of a vessel that leads to capsize in regular beam seas. The complete investigation of nonlinear behaviors includes sub-harmonic motion, bifurcation, and chaos under variations of control parameters. The vessel rolling motions can exhibit various undesirable nonlinear phenomena. We have employed a linear-plus-cubic type damping term (LPCD) in a nonlinear rolling equation. Using the fourth order Runge-Kutta algorithm with the phase portraits, various dynamical behaviors (limit cycles, bifurcations, and chaos) are presented in beam seas. On increasing the value of control parameter ${\Omega}$, chaotic behavior interspersed with intermittent periodic windows are clearly observed in the numerical simulations. The chaotic region is widely spread according to system parameter ${\Omega}$ in the range of 0.1 to 0.9. When the value of the control parameter is increased beyond the chaotic region, periodic solutions are dominant in the range of frequency ratio ${\Omega}=1.01{\sim}1.6$. In addition, one more important feature is that different types of stable harmonic motions such as periodicity of 2T, 3T, 4T and 5T exist in the range of ${\Omega}=0.34{\sim}0.83$.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.2
• /
• pp.123-135
• /
• 2011

In this paper, we present arc-length estimations for quadratic rational B$\acute{e}$zier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve exactly when the weight ${\omega}$ is 0, 1 and ${\infty}$. We show that for all ${\omega}$ > 0 our estimations are strictly increasing with respect to ${\omega}$. Moreover, we find the parameter ${\mu}^*$ which makes our estimation coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve when it is a circular arc too. We also show that ${\mu}^*$ has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of ${\mu}^*$ is an optimal estimation.

• The Bulletin of The Korean Astronomical Society
• /
• v.39 no.1
• /
• pp.34-34
• /
• 2014

We investigate the constraints on the matter density ${\Omega}m$ and the cosmological constant ${\Omega}{\Lambda}$ using the gravitational lensed QSO (Quasi Stellar Object) systems from the Sloan Digital Sky Survey (SDSS) by analyzing the distribution of image separation. The main sample consists of 16 QSO lens systems with measured source and lens redshifts. We use a lensing probability that is simply defined by the gaussian distribution. We perform the curvature test and the constraints on the cosmological parameters as the statistical tests. The statistical tests have considered well-defined selection effects and adopt parameter of velocity dispersion function. We also applied the same analysis to Monte-Carlo generated mock gravitational lens samples to assess the accuracy and limit of our approach. As the results of these statistical tests, we find that only the excessively positively curved universe (${\Omega}m+{\Omega}{\Lambda}$ > 1) are rejected at 95% confidence level. However, if the informations of the galaxy as play a lens are measured accurately, we confirm that the gravitational lensing statistics would be the most powerful tool.