Optimal scale is one of the important issues in ecology and geography.Based on land-use data of the Tarim River Basin in Xinjiang of China in the 1950s,regarding the area of land use types as the parameter in scale se...Optimal scale is one of the important issues in ecology and geography.Based on land-use data of the Tarim River Basin in Xinjiang of China in the 1950s,regarding the area of land use types as the parameter in scale selecting,the histograms of the patches in area are charted.Then,by reinforcing the normalized scale variances(NSV) with 3 landscape indi-ces,the scale characteristics of land use in the Tarim River Basin can be summarized.(1) NSV in the Tarim River up to a maximum at scale of 1:50,000 which is considered appropriate for the Tarim River.(2) Diversity indices of saline land are consistent with NSV's.Diversity indices and NSV of sandy land showed that the appropriate scale is in the same scale domain.There is a significant difference between diversity indices and NSV of forestland and shrub-land.(3) Fractal dimension of sandy land and saline land showed a hierarchical structure at a scale of 1:10,000.Fractal dimension of forestland and shrubland are distributed under the same hierarchical structure in the region.展开更多
This paper investigates the scaled prediction variances in the errors-in-variables model and compares the performance with those in classic model of response surface designs for three factors.The ordinary least square...This paper investigates the scaled prediction variances in the errors-in-variables model and compares the performance with those in classic model of response surface designs for three factors.The ordinary least squares estimators of regression coefficients are derived from a second-order response surface model with errors in variables.Three performance criteria are proposed.The first is the difference between the empirical mean of maximum value of scaled prediction variance with errors and the maximum value of scaled prediction variance without errors.The second is the mean squared deviation from the mean of simulated maximum scaled prediction variance with errors.The last performance measure is the mean squared scaled prediction variance change with and without errors.In the simulations,1 000 random samples were performed following three factors with 20 experimental runs for central composite designs and 15 for Box-Behnken design.The independent variables are coded variables in these designs.Comparative results show that for the low level errors in variables,central composite face-centered design is optimal;otherwise,Box-Behnken design has a relatively better performance.展开更多
The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the an...The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the analysis of characteristic lines and crossover behaviors within the supercritical region.By making use of the free energy,we introduce three key thermodynamic quantities:scaled variance,skewness,and kurtosis.Our results demonstrate that the Widom line,associated with the maximal scaled variance,can effectively differentiate between small and large black hole-like subphases,each displaying distinct thermodynamic behaviors within the supercritical region.Furthermore,by utilizing quasinormal modes,we identify the Frenkel line,offering a dynamic perspective to distinguish between small and large black hole-like subphases.These contribute to a deeper comprehension of black hole subphases in the supercritical region,thus illuminating new facets of black hole thermodynamics.展开更多
基金National Natural Science Foundation of China,No.40571030No.40730633
文摘Optimal scale is one of the important issues in ecology and geography.Based on land-use data of the Tarim River Basin in Xinjiang of China in the 1950s,regarding the area of land use types as the parameter in scale selecting,the histograms of the patches in area are charted.Then,by reinforcing the normalized scale variances(NSV) with 3 landscape indi-ces,the scale characteristics of land use in the Tarim River Basin can be summarized.(1) NSV in the Tarim River up to a maximum at scale of 1:50,000 which is considered appropriate for the Tarim River.(2) Diversity indices of saline land are consistent with NSV's.Diversity indices and NSV of sandy land showed that the appropriate scale is in the same scale domain.There is a significant difference between diversity indices and NSV of forestland and shrub-land.(3) Fractal dimension of sandy land and saline land showed a hierarchical structure at a scale of 1:10,000.Fractal dimension of forestland and shrubland are distributed under the same hierarchical structure in the region.
基金Supported by National Natural Science Foundation of China (No.70871087 and No.70931004)
文摘This paper investigates the scaled prediction variances in the errors-in-variables model and compares the performance with those in classic model of response surface designs for three factors.The ordinary least squares estimators of regression coefficients are derived from a second-order response surface model with errors in variables.Three performance criteria are proposed.The first is the difference between the empirical mean of maximum value of scaled prediction variance with errors and the maximum value of scaled prediction variance without errors.The second is the mean squared deviation from the mean of simulated maximum scaled prediction variance with errors.The last performance measure is the mean squared scaled prediction variance change with and without errors.In the simulations,1 000 random samples were performed following three factors with 20 experimental runs for central composite designs and 15 for Box-Behnken design.The independent variables are coded variables in these designs.Comparative results show that for the low level errors in variables,central composite face-centered design is optimal;otherwise,Box-Behnken design has a relatively better performance.
基金supported by the National Natural Science Foundation of China(Grant Nos.12473001,11975072,11875102,11835009,and 11965013)the National SKA Program of China(Grant Nos.2022SKA0110200 and 2022SKA0110203)+1 种基金the National 111 Project(Grant No.B16009)supported by Yunnan High-level Talent Training Support Plan Young&Elite Talents Project(Grant No.YNWR-QNBJ-2018-181).
文摘The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the analysis of characteristic lines and crossover behaviors within the supercritical region.By making use of the free energy,we introduce three key thermodynamic quantities:scaled variance,skewness,and kurtosis.Our results demonstrate that the Widom line,associated with the maximal scaled variance,can effectively differentiate between small and large black hole-like subphases,each displaying distinct thermodynamic behaviors within the supercritical region.Furthermore,by utilizing quasinormal modes,we identify the Frenkel line,offering a dynamic perspective to distinguish between small and large black hole-like subphases.These contribute to a deeper comprehension of black hole subphases in the supercritical region,thus illuminating new facets of black hole thermodynamics.
