Browsing by Author "Lee, C. -K."

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Attosecond pulse synthesis and arbitrary waveform generation with cascaded harmonics of an injection-seeded high-power Q-switched Nd:YAG laser
(2012-03-01)
Chen, W. -J.
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Wang, H. -Z.
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Lin, R. -Y.
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Lee, C. -K.
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Pan, C. -L.
We propose a new scheme of attosecond pulse generation by starting from a narrow-band transform-limited high-power solid-state laser and phase lock the fundamental and its first four cascaded harmonics generated by the second-order nonlinear optical processes. The relative phase among the optical fields of the harmonics can be maintained a constant at least for thousands of nanosecond pulses. The worst-case relative phase fluctuation is 0.04p rad. It is shown that sub-single-cycle (similar to 0.37 cycle) sub-femtosecond (360 attosecond) pulses with carrier-envelope phase (CEP) control can be generated in this manner. The peak intensity of each pulse exceeds 1014 W/cm2 when it is focused to a spot size of 20 mu m. We also demonstrate synthesis of square and saw-tooth waveforms. ((c) 2012 by Astro Ltd., Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) ((c) 2011 by Astro Ltd., Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA)
On 2-protected nodes in random digital trees
(2016-04-04)
Fuchs, M.
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Lee, C. -K.
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Yu, G. -R.
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應用數學系
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Department of Applied Mathematics
In this paper, we consider the number of 2-protected nodes in random digital trees. Results for the mean and variance of this number for tries have been obtained by Gaither et al. (2012) [11] and Gaither and Ward (2013) [10] and for the mean in digital search trees by Du and Prodinger (2012) [5]. In this short note, we show that these previous results and extensions such as the variance in digital search trees and limit laws in both cases can be derived in a systematic way by recent approaches of Fuchs et al. (2012; 2014) [8, 15] and Fuchs and Lee (2014) [9]. Interestingly, the results for the moments we obtain by our approach are quite different from the previous ones and contain divergent series which have values by appealing to the theory of Abel summability. We also show that our tools apply to PATRICIA tries, for which the number of 2-protected nodes has not been investigated so far. (C) 2016 Elsevier B.V. All rights reserved.