• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1923-1936
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• 2013

We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^*_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by BMO functions are also considered.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.939-962
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• 2018

In this paper, we show that the commutator of the intrinsic square function with BMO symbols is bounded on the variable exponent Lebesgue spaces $L^{p({\cdot})}({\mathbb{R}}^n)$ applying a generalization of the classical Rubio de Francia extrapolation. As a consequence we further establish its boundedness on the variable exponent Morrey spaces $\mathcal{M_{p({\cdot}),u}$, Morrey-Herz spaces $M{\dot{K}}^{{\alpha}({\cdot}),{\lambda}}_{q,p({\cdot})}({\mathbb{R}}^n)$ and Herz type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q}_{p({\cdot})}({\mathbb{R}}^n)$, where the exponents ${\alpha}({\cdot})$ and $p({\cdot})$ are variable. Observe that, even when ${\alpha}({\cdot}){\equiv}{\alpha}$ is constant, the corresponding main results are completely new.

• Economic and Environmental Geology
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• v.27 no.6
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• pp.557-561
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• 1994

Q estimates are made by direct measurements of energy loss per cycle from primary P and S waves, as a function of frequency. Assuming that intrinsic Q is frequency independent and scattering Q is frequency dependent over the frequencies of interest, the relative contributions of each, to a total observed Q, may be estimated. Test examples are produced by computing viscoelastic synthetic seismograms using a pseudo spectral solution with inclusion of relaxation mechanisms (for intrinsic Q) and a fractal distribution of scatterers (for scattering Q). The composite theory implies that when the total Q for S-waves is smaller than that for P-waves (the usual situation), intrinsic Q is dominating; when it is larger, scattering Q is dominating. In the inverse problem, performed by a global least squares search, intrinsic $Q_p$ and $Q_s$ estimates are reliable and unique when their absolute values are sufficiently low that their effects are measurable in the data. Large $Q_p$ and $Q_s$ have no measurable effect and hence are not resolvable. Standard deviation of velocity $({\sigma})$ and scatterer size (A) are less unique as they exhibit a tradeoff as predicted by Blair's equation. For the P-waves, intrinsic and scattering contributions are of approximately the same importance, for S-waves, the intrinsic contributions dominate.

• The Journal of Engineering Geology
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• v.29 no.3
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• pp.303-314
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• 2019

Surface permeability and shallow geological structures play significant roles in shaping the groundwater recharge of shallow aquifers. Surface permeability can be characterized by two concepts, intrinsic permeability and hydraulic conductivity, with the latter obtained from previous near-surface geological investigations. Here we propose a hydraulic equation via the cross-correlation analysis of the rainfall-groundwater levels using a regression equation that is based on the cross-correlation between the grain size distribution curve for unconsolidated sediments and the rainfall-groundwater levels measured in the Gyeongju area, Korea, and discuss its application by comparing these results to field-based aquifer test results. The maximum cross-correlation equation between the hydraulic conductivity derived from Zunker's observation equation in a sandy alluvial aquifer and the rainfall-groundwater levels increases as a natural logarithmic function with high correlation coefficients (0.95). A 2.83% difference between the field-based aquifer test and root mean square error is observed when this regression equation is applied to the other observation wells. Therefore, rainfall-groundwater level monitoring data as well as aquifer test are very useful in estimating hydraulic conductivity.

• Journal of Korea Water Resources Association
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• v.48 no.12
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• pp.981-993
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• 2015

The analysis of hydrologic time series data is crucial for the effective management of water resources. Therefore, it has been widely used for the long-term forecasting of hydrologic variables. In tradition, time series analysis has been used to predict a time series without considering exogenous variables. However, many studies using decomposition have been widely carried out with the assumption that one data series could be mixed with several frequent factors. In this study, the empirical mode decomposition method was performed for decomposing a hydrologic time series data into several components, and each component was applied to the time series models, autoregressive moving average (ARMA). After constructing the time series models, the forecasting values are added to compare the results with traditional time series model. Finally, the forecasted estimates from ARMA model with empirical mode decomposition method showed better performance than sole traditional ARMA model indicated from comparing the root mean square errors of the two methods.