Browsing by Author "Liu, Chia-An"

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A (FORGOTTEN) UPPER BOUND FOR THE SPECTRAL RADIUS OF A GRAPH
(2015-12)
Elphick, Clive
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Liu, Chia-An
;
應用數學系
;
Department of Applied Mathematics
The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating from 1983 is equivalent to their much more recent bound. This bound is then used to compare lower bounds for the clique number. A series of line graph degree-based upper bounds for the Q-index is then proposed and compared experimentally with a graph based bound. Finally a new lower bound for generalised r-partite graphs is proved, by extending a result due to Erdos.
A (FORGOTTEN) UPPER BOUND FOR THE SPECTRAL RADIUS OF A GRAPH
(2015-12-01)
Elphick, Clive
;
Liu, Chia-An
;
應用數學系
;
Department of Applied Mathematics
The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating from 1983 is equivalent to their much more recent bound. This bound is then used to compare lower bounds for the clique number. A series of line graph degree-based upper bounds for the Q-index is then proposed and compared experimentally with a graph based bound. Finally a new lower bound for generalised r-partite graphs is proved, by extending a result due to Erdos.
Silicon Nanowires for Solar Thermal Energy Harvesting: an Experimental Evaluation on the Trade-off Effects of the Spectral Optical Properties
(2016-01-04)
Sekone, Abdoul Karim
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Chen, Yu-Bin
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Lu, Ming-Chang
;
Chen, Wen-Kai
;
Liu, Chia-An
Silicon nanowire possesses great potential as the material for renewable energy harvesting and conversion. The significantly reduced spectral reflectivity of silicon nanowire to visible light makes it even more attractive in solar energy applications. However, the benefit of its use for solar thermal energy harvesting remains to be investigated and has so far not been clearly reported. The purpose of this study is to provide practical information and insight into the performance of silicon nanowires in solar thermal energy conversion systems. Spectral hemispherical reflectivity and transmissivity of the black silicon nanowire array on silicon wafer substrate were measured. It was observed that the reflectivity is lower in the visible range but higher in the infrared range compared to the plain silicon wafer. A drying experiment and a theoretical calculation were carried out to directly evaluate the effects of the trade-off between scattering properties at different wavelengths. It is clearly seen that silicon nanowires can improve the solar thermal energy harnessing. The results showed that a 17.8 % increase in the harvest and utilization of solar thermal energy could be achieved using a silicon nanowire array on silicon substrate as compared to that obtained with a plain silicon wafer.