• Proceedings of the KSR Conference
• /
• 2007.11a
• /
• pp.352-364
• /
• 2007

It is essential to reduce track maintenance costs and to extend the periodic replacements of continuous welded rails based on accumulated passing tonnage. As recently train load decrease and rail joints wear down less, the periodic replacements of continuous welded rails can be extended. There are many kinds of rail damage like squat, head-check and corrugation. These can be taken nondestructive or naked eye test. So the periodic replacements of continuous welded rails based on accumulated passing tonnage were examine with focusing on a crack of rail bottom of continuous welded rail. Therefore, this study measure dynamic response of track by metro train load, it compute impact coefficient and track spring coefficient for estimating a condition of actual track system. Also, it is converted the measured stress waveform into stress frequency histogram by the rain-flow counting methods, and then the equivalence of stress is calculated. As apply s-n curve of a new welded rail, accumulated fatigue damage ratio of laid rail and remaining service lives is estimated. This study suggest a plan of the periodic replacements of continuous welded rails based on accumulated passing tonnage classified by the types of track system.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.31 no.4
• /
• pp.193-197
• /
• 2018

The ratio of the period of a diffractive element to the input beam size is a critical parameter in a diffractive beam shaper. We measured and calculated the Fraunhofer diffraction patterns of a periodic hologram with an input beam size similar to the period of the hologram. The measured intensities show very complicated patterns and are strongly dependent upon the center position of the laser beam relative to the hologram. Using a diffraction formula for a periodic hologram, we calculated the diffracted light intensities and fit them to the measured ones. The measured and calculated intensities are in good agreement even when the beam diameter of the incident laser is similar to the period of the hologram. We can therefore use this formula to estimate the output of a periodic beam shaper even under such an extreme condition.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.609-622
• /
• 1997

We investigate the existence of solutions of the nonlinear beam equation under the Dirichlet boundary condition on the interval $-\frac{2}{\pi}, \frac{2}{\pi}$ and periodic condition on the varible t, $Lu + bu^+ -au^- = f(x, t)$, when the jumping nonlinearity crosses the first positive eigenvalue.

• Kyungpook Mathematical Journal
• /
• v.60 no.2
• /
• pp.401-413
• /
• 2020

In this article we consider the following system of piecewise linear difference equations: x_n+1 = |x_n| - y_n - 1 and y_n+1 = x_n + |y_n| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.

• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.1071-1086
• /
• 2005

In this paper, we introduce a discrete time to the model to describe the time between infection of a CD4$^{+}$ T-cells, and the emission of viral particles on a cellular level. We study the effect of the time delay on the stability of the endemically infected equilibrium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. We also obtain the condition for existence of an orbitally asymptotically stable periodic solution.

• Korean Journal of Mathematics
• /
• v.22 no.3
• /
• pp.471-489
• /
• 2014

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

• 한국전산유체공학회:학술대회논문집
• /
• 2003.10a
• /
• pp.286-288
• /
• 2003

The physical model considered here is a horizontal layer of fluid heated below and cooled above with a periodic array of evenly spaced square cylinders placed at the center of the layer, whose aspect ratio here varies from unity to six. Periodic boundary condition is employed along the horizontal direction to allow for lateral freedom for the convection cells. Two-dimensional solution for unsteady natural convection is obtained using an accurate and efficient Chebyshev spectral multi-domain methodology for a given Rayleigh numbers of $10^6$

• Journal of applied mathematics & informatics
• /
• v.7 no.3
• /
• pp.1029-1038
• /
• 2000

In this paper, we show that if x is a positively Lyapunov stable point of an expansive homeomorphism with the pseudo-orbit-tracing-property, then x is a periodic point or its positive limit set consists of only one periodic orbit, and their periods are predictable. We give a necessary and sufficient condition that a basic set is to be a sink or source. Also, we consider some dynamical properties of basic sets.

• Communications of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.1153-1162
• /
• 2023

In this paper, for the bounded solution of the non-densely defined non-autonomous evolution equation, we present the condition for asymptotic periodicity by using the circular spectral theory of functions on the half line and the extrapolation theory of non-densely defined evolution equation.

• Korean Journal of Mathematics
• /
• v.4 no.1
• /
• pp.51-64
• /
• 1996

In this paper we investigate the existence of weak solutions of a nonlinear beam equation under Dirichlet boundary condition on the interval $-\frac{\pi}{2}<x<\frac{\pi}{2}$ and periodic condition on the variable $t$, $u_{tt}+u_{xxxx}=p(x,t,u)$. We show that if $p$ satisfies condition $(p_1)-(p_3)$, then the nonlinear beam equation possesses at least one weak solution.