• 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.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.49-67
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• 2012

In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.7
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• pp.1543-1549
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• 1997

In this paper, rank-based nonparmetric detection of composite signals in additive noise is considered. Based on signs and ranks of observations, the locally optimum detector is deived for weak-signal detection under any specified noise probability density funhction. This detector has similarities to the locally optimum detector for comjposite signals in additive noise. The asymptotic performance of this nonparametric detector is shown to be as good as that of the locally optimum detector.

• Korean Journal of Microbiology
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• v.28 no.3
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• pp.278-282
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• 1990

Diffusion and partition of progesterone into the polyacrylamide gel was examined. Diffusion coefficient of progesterone decreased down to an asymptotic value as the concentration of the organic solvents in the diffusing medium increased. However the partition coefficient diminished steadily. Crosslinking density in the gel didn't affected the diffusion coefficient considerably but lowered the partition coefficient due to the contraction of pore volume of the gel. Progesterone showed higher diffusion coefficient as well as partition coefficient in the polyurethane than in the polyacrylamide gel, which seems to be ascribed to the difference in hydrophobicity, pore volume and pore size of the polymer matrix.

• Journal of the Korean Society of Industry Convergence
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• v.9 no.1
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• pp.37-44
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• 2006

Stress and displacement fields of a Mode III crack propagating along the normal to gradient in an orthotropic functionally gradient materials (OFGM), which has (1) an exponential variation of shear modulus and density, and (2) linear variation of shear modulus with a constant density, are derived. The equations of motion in OFGM are developed and solution to the displacement and stress fields for a propagating crack at constant speed though an asymptotic analysis. The first three terms in expansion of stress and displacement are derived to explicitly bring out the influence of nonhomogeneity. When the FGM constant ${\zeta}$ is zero or $r{\rightarrow}0$, the fields for OFGM are almost same as the those for homogeneous orthotropic material. Using the stress components, the effects of nonhomogeneity on stress components are discussed.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.479-491
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• 2017

We investigate the zeros of Epstein zeta functions associated with positive definite quadratic forms with rational coefficients in the vertical strip ${\sigma}_1$ < ${\Re}s$ < ${\sigma}_2$, where 1/2 < ${\sigma}_1$ < ${\sigma}_2$ < 1. When the class number h of the quadratic form is bigger than 1, Voronin gave a lower bound and Lee gave an asymptotic formula for the number of zeros. Recently Gonek and Lee improved their results by providing a new upper bound for the error term when h > 3. In this paper, we consider the cases h = 2, 3 and provide an upper bound for the error term, smaller than the one for the case h > 3.

• The Journal of the Acoustical Society of Korea
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• v.18 no.5
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• pp.28-34
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• 1999

The effects of the viscosity of an adjacent viscous fluid on the characteristics of the elastic waves have been studied theoretically and experimentally. Expressions for the wave speed and attenuation of the elastic waves of transverse motion, such as the torsional wave propagating in a circular cylinder and the Love wave in a layered half-space solid, have been obtained as functions of the viscosity and mass density of the fluid by exact and asymptotic analyses. The theoretical results have been compared with experimental observations, and it has been demonstrated that a device described herein can be used as a sensor for measuring the viscosity of a fluid with a known mass density.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.343-358
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• 2017

Let {$X_i$} be a sequence of stationary ${\alpha}-mixing$ random variables with probability density function f(x). The recursive kernel estimators of f(x) are defined by $$\hat{f}_n(x)={\frac{1}{n\sqrt{b_n}}{\sum_{j=1}^{n}}b_j{^{-\frac{1}{2}}K(\frac{x-X_j}{b_j})\;and\;{\tilde{f}}_n(x)={\frac{1}{n}}{\sum_{j=1}^{n}}{\frac{1}{b_j}}K(\frac{x-X_j}{b_j})$$, where 0 < $b_n{\rightarrow}0$ is bandwith and K is some kernel function. Under appropriate conditions, we establish the Berry-Esseen bounds for these estimators of f(x), which show the convergence rates of asymptotic normality of the estimators.

• Proceedings of the IEEK Conference
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• 2002.06a
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• pp.323-326
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• 2002

In this paper, we study the improved bounds on the performance of low-density parity-check (LDPC) codes over binary-input additive white Gaussian noise (AWGN) channels with belief propagation (BP) decoding in log domain. We define an extended Gallager ensemble based on a new method of constructing parity check matrix and make use of this way to improve upper bound of LDPC codes. At the same time, many simulation results are presented in this paper. These results indicate the extended Gallager ensembles based on Hamming codes have typical minimum distance ratio, which is very close to the asymptotic Gilbert Varshamov bound and the superior performance which is better than the original Gallager ensembles.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1383-1392
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• 2020

Let H_n be the n-th harmonic number and let ν_n be its denominator. Shiu proved that there are infinitely many positive integers n with ν_n = ν_n+1. Recently, Wu and Chen proved that the set of positive integers n with ν_n = ν_n+1 has density one. They also proved that the same result is true for the denominators of alternating harmonic numbers. In this paper, we prove that the result is true for the denominators of 𝜀-harmonic numbers, where 𝜀 = {𝜀_i}^∞_i=1 is a pure recurring sequence with 𝜀_i ∈ {-1, 1}.