• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.105-123
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• 2015

Let $f_{\beta}=h_{\beta}+\bar{g}_{\beta}$ and $F_a=H_a+\bar{G}_a$ be harmonic mappings obtained by shearing of analytic mappings $h_{\beta}+g_{\beta}=1/(2isin{\beta})log\((1+ze^{i{\beta}})/(1+ze^{-i{\beta}})\)$, 0 < ${\beta}$ < ${\pi}$ and $H_a+G_a=z/(1-z)$, respectively. Kumar et al. [7] conjectured that if ${\omega}(z)=e^{i{\theta}}z^n({\theta}{\in}\mathbb{R},n{\in}\mathbb{N})$ and ${\omega}_a(z)=(a-z)/(1-az)$, $a{\in}(-1,1)$ are dilatations of $f_{\beta}$ and $F_a$, respectively, then $F_a\tilde{\ast}f_{\beta}{\in}S^0_H$ and is convex in the direction of the real axis, provided $a{\in}[(n-2)/(n+2),1)$. They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture, in the affirmative, for ${\beta}={\pi}/2$ and for all $n{\in}\mathbb{N}$.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.1
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• pp.21-32
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• 1999

Mapping and precise point determination by photogrammetry have been shown to be an economic solution. But control points are necessary to determine the exterior orientation parameters. Although the number of required control points has been reduced based on extended bundle adjustment and reinforced cross-strip, the ground survey is a significant factor of whole expenses in photogrammetry. The status of GPS-photogrammetry with kinematic DGPS-positioning to overcome this disadvantages, is now steadly progressive since the first possibility has been proved. The completed satellite configuration, powerful receiver function and upgraded software for kinematic DGPS-positioning have extensively improved the accuracy of combined bundle adjustment. So the research for the operational use of GPS-photogrammetry is absolutely necessary. The presented test field was designed for identification of subsidences in a coal mining area, flown with 60％ sidelap and cross strips. Just with 6 control points and combined block adjustment instead of the traditionally used 21 horizontal and 81 vertical control points the same ground accuracy has been reached. The accuracy of kinematic GPS-positioning and combined block adjustment was independent upon the distance of the ground reference station. It also has been showed that the special model for the systematic error correction in the combined block adjustment.