• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.541-551
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• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.111-119
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• 2007

We consider the growth norm of a measurable function f defined by defined by $${\parallel}f{\parallel}-\sigma=ess\;sup\{\delta_D(z)^\sigma{\mid}f(z)\mid:z{\in}D\}$$, where $\delta_D(z)$ denote the distance from z to ${\partial}D$. We prove some kind of optimal growth norm estimates for a on convex domains.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.121-126
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• 2006

Modern Ocean wave forecasting systems predict the mean sea state, as characterized by the wave spectrum, in a box of size ${\Delta}x{\Delta}y$ surrounding a grid point at location x. It is shown that this approach also allows the determination of deviations from the mean sea state, i.e. the probability distribution function of the surface elevation. Hence, ocean wave forecasting may provide valuable information on extreme sea states.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.305-317
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• 2004

We construct the empirical Bayes (EB)estimation of the parameter in two-side truncated distribution families with asymmetric Linex loss using negatively associated (NA) samples. The asymptotical optimality and convergence rate of the EB estimation is obtained. We will show that the convergence rate can be arbitrarily close to $O(n^{-q}),\;q\;=\;{\lambda}s(\delta\;-\;2)/\delta(s\;+\;2)$.

• East Asian mathematical journal
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• v.32 no.5
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• pp.651-658
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• 2016

In a bounded domain, we consider $$u_{tt}-{\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;g(t-{\tau}){\Delta}ud{\tau}+u_t={\mid}u{\mid}^pu$$, where p > 0 and g is a nonnegative and decaying function. We establish a general decay result which is not necessarily of exponential or polynomial type.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.321-328
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• 1995

Ibragimov(1975) showed the central limit theorem and the invariance principle for $\rho$-mixing random variables satisfying $\sigma^2(n) = nh(n) \longrightarrow \infty$ and $E$\mid$\zeta_0$\mid$^{2+\delta} < \infty$ for some $\delta > 0$ where $\sigma^2(n)$ denotes the variance of the partial sum $S_n$ and h(n) is a slowly varying function.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.87-97
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• 1992

Sequential procedure with ${\beta}$-protection for the mean vector ${\mu}(\theta)$ of a p(> 1)-variate multivariate distribution $P_{\theta}$, ${\theta}{\in}{\Theta}$, with covariance matrix ${\sum}(\theta)$ is considered when the only nuisance parameters is ${\sum}(\theta)$. We obtain a confidence set for ${\mu}(\theta)$ with coverage probability condition and ${\beta}$-protection at ${\mu}-{\delta}(\mu)$ for some imprecision function ${\delta}:\mathbb{R}^p{\rightarrow}\mathbb{R}^p$.

• Proceedings of the Korean Ceranic Society Conference
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• 2002.10a
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• pp.172.1-172
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• 2002

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.475-484
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• 2019

We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number ${\delta}$ between 0 and ${\frac{1}{2}}\;{\log}\;q$, there is a discrete subgroup ${\Gamma}$ acting without inversion on a (q+1)-regular tree whose critical exponent is equal to ${\delta}$. Explicit construction of edge-indexed graphs corresponding to a quotient graph of groups are given.

• Journal of the Korean Society for Nondestructive Testing
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• v.16 no.4
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• pp.215-224
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• 1997

A study has been made to investigate the acoustic emission(AE) behavior during the tensile and fracture tests of an Al-Li 8090 alloy, and to correlate it with the deformation mechanisms as a function of microstructure and plate orientation. Mechanical tests and AE measurements were conducted on the specimens with different microstructures (the ${\delta}'$ phase dominant microstructure and the $S'+{\delta}'$ microstructure) and with different orientations (L and ST). In the ${\delta}'$ structure, continuous emissions were produced in both the L and ST oriented specimens, while only the burst emissions were observed to occur in the $S'+{\delta}'$ structure. It was inferred from the above results that continuous type emissions were mainly attributed to the shearing of coherent ${\delta}'$ precipitates in the ${\delta}'$ structure, while the burst type emissions were produced due to the shearing or microcracking of incoherent S' phase in the $S'+{\delta}'$ structure. As to the effect of plate orientation, the ST oriented specimens showed more burst emissions than the LT oriented ones. A large number of burst emissions produced in the ST specimen were presumably due to the rapid crack propagation along the intergranular boundary located parallel to the crack propagation direction.