• 대한수학회보
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• 제54권1호
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• pp.71-84
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• 2017

We discuss the qualitative uncertainty principle for Gabor transform on certain classes of the locally compact groups, like abelian groups, ${\mathbb{R}}^n{\times}K$, K ⋉ ${\mathbb{R}}^n$ where K is compact group. We shall also prove a weaker version of qualitative uncertainty principle for Gabor transform in case of compact groups.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.129-151
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• 2015

In this paper, we prove an $L^p$ version of Donoho-Stark's uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$. Next, using the ultracontractive properties of the semigroups generated by the Heckman-Opdam Laplacian operator, we obtain an $L^p$ Heisenberg-Pauli-Weyl uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$.

• 한국토양비료학회지
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• 제44권5호
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• pp.944-958
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• 2011

Soil hydraulic properties such as hydraulic conductivity or water retention which are costly to measure can be indirectly generated by soil pedotransfer function (PTF) using easily obtainable soil data. The field soil structure description which is routinely recorded could also be used in PTF as an input to reduce the uncertainty. The purposes of this study were to use qualitative morphological soil structure descriptions and soil structural index into PTF and to evaluate their contribution in the prediction of soil hydraulic properties. We transformed categorical morphological descriptions of soil structure into quantitative values using categorical principal component analysis (CATPCA). This approach was tested with a large data set from the US National Pedon Characterization database with the aid of a categorical regression tree analysis. Six different PTFs were used to predict the saturated hydraulic conductivity and those results were averaged to quantify the uncertainty. Quantified morphological description was successively used in multiple linear regression approach to predict the averaged ensemble saturated conductivity. The selected stepwise regression model with only the transformed morphological variables and structural index as predictors predicted the $K_{sat}$ with $r^2$ = 0.48 (p = 0.018), indicating the feasibility of CATPCA approach. In a regression tree analysis, soil structure index and soil texture turned out to be important factors in the prediction of the hydraulic properties. Among structural descriptions size class turned out to be an important grouping parameter in the regression tree. Bulk density, clay content, W33 and structural index explained clusters selected by a two step clustering technique, implying the morphologically described soil structural features are closely related to soil physical as well as hydraulic properties. Although this study provided relatively new method which related soil structure description to soil structure index, the same approach should be tested using a datasets containing the actual measurement of hydraulic properties. More insight on the predictive power of soil structure index to estimate hydraulic properties would be achieved by considering measured the saturated hydraulic conductivity and the soil water retention.