• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.349-359
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• 2023

In this paper, we study ∆-transitivity, ∆-weak mixing and ∆-mixing for semigroup actions and give several characterizations of them, which generalize related results in the literature.

• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.203-211
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• 2003

A new result of weak convergence of the empirical process is established for a stationary ${\phi}-mixing$ sequence of random variables, which relaxes the existing conditions on mixing coefficients. The result is basically obtained from bounds for even moments of sums of ${\phi}-mixing$ r.v.'s useful for handling triangular arrays with entries decreasing in size.

• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.81-93
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• 2015

Validity of the stationary bootstrap of Politis and Romano (1994) is proved for U-statistics under strong mixing. Weak and strong consistencies are established for the stationary bootstrap of U-statistics. The theory is applied to a symmetry test which is a U-statistic regarding a kernel density estimator. The theory enables the bootstrap confidence intervals of the means of the U-statistics. A Monte-Carlo experiment for bootstrap confidence intervals confirms the asymptotic theory.

• Smart Structures and Systems
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• v.30 no.6
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• pp.639-648
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• 2022

This study aims at numerically and experimentally investigating torsional guided wave mixing with weak material nonlinearity under acoustoelastic effect in tubular structures. The acoustoelastic effect on single central frequency guided wave propagation in structures has been well-established. However, the acoustoelastic on guided wave mixing has not been fully explored. This study employs a three-dimensional (3D) finite element (FE) model to simulate the effect of stress on guided wave mixing in tubular structures. The nonlinear strain energy function and theory of incremental deformation are implemented in the 3D FE model to simulate the guided wave mixing with weak material nonlinearity under acoustoelastic effect. Experiments are carried out to measure the nonlinear features, such as combinational harmonics and second harmonics in related to different levels of applied stresses. The experimental results are compared with the 3D FE simulation. The results show that the generation combinational harmonic at sum frequency provides valuable stress information for tubular structures, and also useful for damage diagnosis. The findings of this study provide physical insights into the effect of applied stresses on the combinational harmonic generation due to wave mixing. The results are important for applying the guided wave mixing for in-situ monitoring of structures, which are subjected to different levels of loadings under operational condition.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.2
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• pp.328-335
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• 2002

In this study, experiments were performed to investigate the characteristics of flame stabilization of the LFG mixing gas. LFG has merely half heating value compared with liquified natural gas but can be greatly utilized as a commercial fuel. In order to use LFG in practical combustors, Webbe Index and heating value of LFG mixing gas were adjusted by mixing LPG with LFG. The comparisons were conducted between CH$_4$and LFG mixing gas for searching the region of flame stabilization based upon the flame blowout at maximum fuel stream velocity. As a result, the flame stability of LFG mixing gas was not improved with that of CH$_4$in non-swirl and weak swirl diffusion flame. However, LFG mixing gas had wide flame stabilization region rather than CH$_4$with increasing ambient flow rate in strong swirl. It was also found that flame stability was affected by included quantity of inert gas such as CO$_2$in the weak swirl but by heating value of fuel in strong swirl.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.221-228
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• 2008

In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.2
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• pp.50.2-50.2
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• 2021

There is increasing evidence that the convective mixing length (α) in stellar evolution models depends on metallicity of stars. In order to confirm a more precise metallicity-dependent mixing length trend, we investigate the effective temperature and metallicity of 14 red supergiant stars (RSGs) in the irregular dwarf galaxy IC 1613 using the near-infrared spectra observed with the MMIRS on the MMT telescope. From the synthetic spectral fitting to the observed spectra, we find that the mean metallicity is about [Fe/H]=0.69 with a weak bimodal distribution. We also find that the effective temperature of RSGs in IC 1613 is higher by about 250 K than that of the SMC on average. We compare the RSG position with stellar evolutionary tracks on the HR diagram, finding that models with α = 2.2-2.4 H_p can best reproduce the effective temperatures of the RSGs in IC 1613. It is evident that the mixing length values for IC 1613 is lower than that of the Milky Way. This result supports our previous study on a metallicity-dependent mixing length: mixing length decreases with decreasing metallicity of host galaxies. However, this dependency becomes relatively weak for RSGs having a metallicity equal to or less than the SMC metallicity.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.57-72
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• 2016

We establish maximal moment inequalities of partial sums under ${\psi}$-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with ${\psi}$-weakly dependent innovations.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.647-653
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• 2015

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1139-1153
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• 2010

Let {$X_j,\;j\geq1$} be a strictly stationary $\phi$-mixing sequence of non-degenerate random variables with $EX_1$ = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {$X_j$} under the condition that L(x) := $EX_1^2I{|X_1|{\leq}x}$ is a slowly varying function at $\infty$, without any higher moment conditions.