Global solar radiation（GSR） is the most direct source and form of global energy, and calculation of its quantity is highly complex due to influences of local topography and terrain inter-shielding. Digital elevation...Global solar radiation（GSR） is the most direct source and form of global energy, and calculation of its quantity is highly complex due to influences of local topography and terrain inter-shielding. Digital elevation model（DEM） data as a representation of the complex terrain and multiplicity condition produces a series of topographic factors（e.g. slope, aspect, etc.）. Based on 1 km resolution DEM data, meteorological observations and NOAA-AVHRR remote sensing data, a distributed model for the calculation of GSR over rugged terrain within the Yangtze River Basin has been developed. The overarching model permits calculation of astronomical solar radiation for rugged topography and comprises a distributed direct solar radiation model, a distributed diffuse radiation model and a distributed terrain reflectance radiation model. Using the developed model, a quantitative simulation of the GSR space distribution and visualization has been undertaken, with results subsequently analyzed with respect to locality and terrain. Analyses suggest that GSR magnitude is seasonally affected, while the degree of influence was found to increase in concurrence with increasing altitude. Moreover, GSR magnitude exhibited clear spatial variation with respect to the dominant local aspect; GSR values associated with the sunny southern slopes were significantly greater than those associated with shaded slopes. Error analysis indicates a mean absolute error of 12.983 MJm-2 and a mean relative error of 3.608%, while the results based on a site authentication procedure display an absolute error of 22.621 MJm-2 and a relative error of 4.626%.展开更多
The question of how many shuffles are required to randomize an initially ordered deck of cards is a problem that has fascinated mathematicians, scientists, and the general public. The two principal theoretical approac...The question of how many shuffles are required to randomize an initially ordered deck of cards is a problem that has fascinated mathematicians, scientists, and the general public. The two principal theoretical approaches to the problem, which differed in how each defined randomness, has led to statistically different threshold numbers of shuffles. This paper reports a comprehensive experimental analysis of the card randomization problem for the purposes of determining 1) which of the two theoretical approaches made the more accurate prediction, 2) whether different statistical tests yield different threshold numbers of randomizing shuffles, and 3) whether manual or mechanical shuffling randomizes a deck more effectively for a given number of shuffles. Permutations of 52-card decks, each subjected to sets of 19 successive riffle shuffles executed manually and by an auto-shuffling device were recorded sequentially and analyzed in respect to 1) the theory of runs, 2) rank ordering, 3) serial correlation, 4) theory of rising sequences, and 5) entropy and information theory. Among the outcomes, it was found that: 1) different statistical tests were sensitive to different patterns indicative of residual order;2) as a consequence, the threshold number of randomizing shuffles could vary widely among tests;3) in general, manual shuffling randomized a deck better than mechanical shuffling for a given number of shuffles;and 4) the mean number of rising sequences as a function of number of manual shuffles matched very closely the theoretical predictions based on the Gilbert-Shannon-Reed (GSR) model of riffle shuffles, whereas mechanical shuffling resulted in significantly fewer rising sequences than predicted.展开更多
基金National Natural Science Foundation of China,No.41175077 National Natural Science Foundation for Young Scholars,No.S0508016001 Guizhou Branch Major Projects[2011],No.6003
文摘Global solar radiation（GSR） is the most direct source and form of global energy, and calculation of its quantity is highly complex due to influences of local topography and terrain inter-shielding. Digital elevation model（DEM） data as a representation of the complex terrain and multiplicity condition produces a series of topographic factors（e.g. slope, aspect, etc.）. Based on 1 km resolution DEM data, meteorological observations and NOAA-AVHRR remote sensing data, a distributed model for the calculation of GSR over rugged terrain within the Yangtze River Basin has been developed. The overarching model permits calculation of astronomical solar radiation for rugged topography and comprises a distributed direct solar radiation model, a distributed diffuse radiation model and a distributed terrain reflectance radiation model. Using the developed model, a quantitative simulation of the GSR space distribution and visualization has been undertaken, with results subsequently analyzed with respect to locality and terrain. Analyses suggest that GSR magnitude is seasonally affected, while the degree of influence was found to increase in concurrence with increasing altitude. Moreover, GSR magnitude exhibited clear spatial variation with respect to the dominant local aspect; GSR values associated with the sunny southern slopes were significantly greater than those associated with shaded slopes. Error analysis indicates a mean absolute error of 12.983 MJm-2 and a mean relative error of 3.608%, while the results based on a site authentication procedure display an absolute error of 22.621 MJm-2 and a relative error of 4.626%.
文摘The question of how many shuffles are required to randomize an initially ordered deck of cards is a problem that has fascinated mathematicians, scientists, and the general public. The two principal theoretical approaches to the problem, which differed in how each defined randomness, has led to statistically different threshold numbers of shuffles. This paper reports a comprehensive experimental analysis of the card randomization problem for the purposes of determining 1) which of the two theoretical approaches made the more accurate prediction, 2) whether different statistical tests yield different threshold numbers of randomizing shuffles, and 3) whether manual or mechanical shuffling randomizes a deck more effectively for a given number of shuffles. Permutations of 52-card decks, each subjected to sets of 19 successive riffle shuffles executed manually and by an auto-shuffling device were recorded sequentially and analyzed in respect to 1) the theory of runs, 2) rank ordering, 3) serial correlation, 4) theory of rising sequences, and 5) entropy and information theory. Among the outcomes, it was found that: 1) different statistical tests were sensitive to different patterns indicative of residual order;2) as a consequence, the threshold number of randomizing shuffles could vary widely among tests;3) in general, manual shuffling randomized a deck better than mechanical shuffling for a given number of shuffles;and 4) the mean number of rising sequences as a function of number of manual shuffles matched very closely the theoretical predictions based on the Gilbert-Shannon-Reed (GSR) model of riffle shuffles, whereas mechanical shuffling resulted in significantly fewer rising sequences than predicted.
