The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameteri...The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.展开更多
Let f denote a normalized Maass cusp form for SL（2, Z）, which is an eigenfunction of all the Hecke operators T（n） as well as the reflection operator T-1： z →z. We obtain a zero-density result of the L-function a...Let f denote a normalized Maass cusp form for SL（2, Z）, which is an eigenfunction of all the Hecke operators T（n） as well as the reflection operator T-1： z →z. We obtain a zero-density result of the L-function attached to f near σ = 1. This improves substantially the previous results in this direction.展开更多
Let L/K be a Galois extension of number fields with Galois group G.We show that if the density of prime ideals in K that split totally in L tends to 1/|G|with a power saving error term,then the density of prime ideals...Let L/K be a Galois extension of number fields with Galois group G.We show that if the density of prime ideals in K that split totally in L tends to 1/|G|with a power saving error term,then the density of prime ideals in K whose Frobenius is a given conjugacy class C■G tends to|C|/|G|with the same power saving error term.We deduce this by relating the poles of the corresponding Dirichlet series to the zeros ofζ_L(s)/ζ_K(s).展开更多
Two automatic measurement methods of bidirectional reflection distribution function （BRDF） are presented based on absolute and relative definition. Measurement principle and scheme of the methods are analyzed. A rea...Two automatic measurement methods of bidirectional reflection distribution function （BRDF） are presented based on absolute and relative definition. Measurement principle and scheme of the methods are analyzed. A real-time measurement device is developed, the measurement spectral range of which is from ultraviolet to near infrared with 2.4-nm wavelength resolution, and the angular range is 0° - 360° in azimuth angle and 0° - 85° in zenith angle with 0.01° angle resolution. Absolute measurements of BRDF on tinfoil and ceramic tile are performed and the test materials present apparent specular reflection characteristics. The theoretical error in the experiment is about 6.05%. The BRDF measurement results are closely related to the precision of measurement platform, the sensitivity of measurement instrument, and the stability of illuminating light source.展开更多
Population density functions have long been used to describe the spatial structure of regional population distributions.Several studies have been conducted to examine the population distribution in Shandong Province,C...Population density functions have long been used to describe the spatial structure of regional population distributions.Several studies have been conducted to examine the population distribution in Shandong Province,China,but few have applied regional density functions to the analysis.Therefore,based on the 2000,2010,and 2020 population censuses,this study used monocentric and polycentric regional density functions to study the characteristics of population agglomeration and diffusion in Shandong.This is followed by an in-depth discussion based on population growth rate data and hot-and cold-spot analyses.The results showed that the Shandong Province population was spatially unevenly distributed.Population growth rates were higher in urban centers and counties,with more significant changes in population size in the eastern coastal areas than in the inland areas.As verified in this study,the logarithmic form of the single-center regional density function R2 was greater than 0.8,which was in line with the population spatial structure of Shandong Province.During the study period,the estimated population density of the regional center and the absolute value of the regional population density gradient both increased,indicating a clear and increasing trend of centripetal agglomeration of regional centers over the study period.Overall,the R2 value of the multicenter region density function was higher than that of the single-center region density function.The polycentric regional density function showed that the population density gradient of some centers had a downward trend,which reflected the spatial development trend of outward diffusion in these centers.Meanwhile,the variation in the estimated population density and the population density gradient exhibited differences in the central population distribution patterns at different levels.展开更多
We prove that the density function of the gradient of a sufficiently smooth function , obtained via a random variable transformation of a uniformly distributed random variable, is increasingly closely approximated by ...We prove that the density function of the gradient of a sufficiently smooth function , obtained via a random variable transformation of a uniformly distributed random variable, is increasingly closely approximated by the normalized power spectrum of ?as the free parameter . The frequencies act as gradient histogram bins. The result is shown using the stationary phase approximation and standard integration techniques and requires proper ordering of limits. We highlight a relationship with the well-known characteristic function approach to density estimation, and detail why our result is distinct from this method. Our framework for computing the joint density of gradients is extremely fast and straightforward to implement requiring a single Fourier transform operation without explicitly computing the gradients.展开更多
The average bit error rate （BER） performance of a free-space optical （FOS） system based on the multi-hop parallel decode-and-forward cooperative communication method with an M-ary phase shift keying subcarrier int...The average bit error rate （BER） performance of a free-space optical （FOS） system based on the multi-hop parallel decode-and-forward cooperative communication method with an M-ary phase shift keying subcarrier intensity modulation is studied systematically. With the max-min criterion as the best path selection scheme, the probability density function and the cumulative distribution function of the gamma-gamma distribution random variable signal-to-noise ratio are derived. The analytical BER expression is then obtained in terms of the Gauss-Laguerre quadrature rule. Monte Carlo simulation is also provided to confirm the validity of the presented average BER model.展开更多
In this work,the Fukui functions of the two ~2P resonance states of Be,a ~2P resonance state of Mg~–,and a ~2D resonance state of Ca~– have been determined.The trajectories of these resonance states,in conjunction w...In this work,the Fukui functions of the two ~2P resonance states of Be,a ~2P resonance state of Mg~–,and a ~2D resonance state of Ca~– have been determined.The trajectories of these resonance states,in conjunction with the complex rotation of the Hamiltonian,were used to determine their wave functions.The electron densities,Fukui functions,and values of the hyper-radius<r^2>were computed from these wave functions.The Fukui functions have negative regions in the valence shell in addition to the inner shell regions,indicating screening effects of the outer temporary electron.Selected configuration interactions with up to quadruple excitations were used along the trajectories and for computing the final wave function.Based on this data,the densities,Fukui functions,and<r^2>were calculated.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.42175099,42027804,42075073)the Innovative Project of Postgraduates in Jiangsu Province in 2023(Grant No.KYCX23_1319)+3 种基金supported by the National Natural Science Foundation of China(Grant No.42205080)the Natural Science Foundation of Sichuan(Grant No.2023YFS0442)the Research Fund of Civil Aviation Flight University of China(Grant No.J2022-037)supported by the National Key Scientific and Technological Infrastructure project“Earth System Science Numerical Simulator Facility”(Earth Lab)。
文摘The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.
文摘Let f denote a normalized Maass cusp form for SL（2, Z）, which is an eigenfunction of all the Hecke operators T（n） as well as the reflection operator T-1： z →z. We obtain a zero-density result of the L-function attached to f near σ = 1. This improves substantially the previous results in this direction.
基金supported by the Rényi Intézet Lendület Automorphic Research Group and NKFIH(National Research,Development and Innovation Office)(Grant No.K 143876)supported in part by a grant from the National Science Foundationa Simons Investigator Award from the Simons Foundation。
文摘Let L/K be a Galois extension of number fields with Galois group G.We show that if the density of prime ideals in K that split totally in L tends to 1/|G|with a power saving error term,then the density of prime ideals in K whose Frobenius is a given conjugacy class C■G tends to|C|/|G|with the same power saving error term.We deduce this by relating the poles of the corresponding Dirichlet series to the zeros ofζ_L(s)/ζ_K(s).
基金supported by the National"863"Project of China under Grant No.2006AA704214-5.
文摘Two automatic measurement methods of bidirectional reflection distribution function （BRDF） are presented based on absolute and relative definition. Measurement principle and scheme of the methods are analyzed. A real-time measurement device is developed, the measurement spectral range of which is from ultraviolet to near infrared with 2.4-nm wavelength resolution, and the angular range is 0° - 360° in azimuth angle and 0° - 85° in zenith angle with 0.01° angle resolution. Absolute measurements of BRDF on tinfoil and ceramic tile are performed and the test materials present apparent specular reflection characteristics. The theoretical error in the experiment is about 6.05%. The BRDF measurement results are closely related to the precision of measurement platform, the sensitivity of measurement instrument, and the stability of illuminating light source.
基金This research was funded by the Shandong Provincial Natural Science Foundation(grant number ZR202102240088).
文摘Population density functions have long been used to describe the spatial structure of regional population distributions.Several studies have been conducted to examine the population distribution in Shandong Province,China,but few have applied regional density functions to the analysis.Therefore,based on the 2000,2010,and 2020 population censuses,this study used monocentric and polycentric regional density functions to study the characteristics of population agglomeration and diffusion in Shandong.This is followed by an in-depth discussion based on population growth rate data and hot-and cold-spot analyses.The results showed that the Shandong Province population was spatially unevenly distributed.Population growth rates were higher in urban centers and counties,with more significant changes in population size in the eastern coastal areas than in the inland areas.As verified in this study,the logarithmic form of the single-center regional density function R2 was greater than 0.8,which was in line with the population spatial structure of Shandong Province.During the study period,the estimated population density of the regional center and the absolute value of the regional population density gradient both increased,indicating a clear and increasing trend of centripetal agglomeration of regional centers over the study period.Overall,the R2 value of the multicenter region density function was higher than that of the single-center region density function.The polycentric regional density function showed that the population density gradient of some centers had a downward trend,which reflected the spatial development trend of outward diffusion in these centers.Meanwhile,the variation in the estimated population density and the population density gradient exhibited differences in the central population distribution patterns at different levels.
文摘We prove that the density function of the gradient of a sufficiently smooth function , obtained via a random variable transformation of a uniformly distributed random variable, is increasingly closely approximated by the normalized power spectrum of ?as the free parameter . The frequencies act as gradient histogram bins. The result is shown using the stationary phase approximation and standard integration techniques and requires proper ordering of limits. We highlight a relationship with the well-known characteristic function approach to density estimation, and detail why our result is distinct from this method. Our framework for computing the joint density of gradients is extremely fast and straightforward to implement requiring a single Fourier transform operation without explicitly computing the gradients.
基金supported by the National Natural Science Foundation of China(No.61474090)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2014JM8340)+3 种基金the China Postdoctoral Science Special Foundation(No.201104659)the China Postdoctoral Science Foundation(No.20100481322)the Fundamental Research Funds for the Central Universities(No.NSIY041404)supported by the 111 Project of China(No.B08038)
文摘The average bit error rate （BER） performance of a free-space optical （FOS） system based on the multi-hop parallel decode-and-forward cooperative communication method with an M-ary phase shift keying subcarrier intensity modulation is studied systematically. With the max-min criterion as the best path selection scheme, the probability density function and the cumulative distribution function of the gamma-gamma distribution random variable signal-to-noise ratio are derived. The analytical BER expression is then obtained in terms of the Gauss-Laguerre quadrature rule. Monte Carlo simulation is also provided to confirm the validity of the presented average BER model.
文摘In this work,the Fukui functions of the two ~2P resonance states of Be,a ~2P resonance state of Mg~–,and a ~2D resonance state of Ca~– have been determined.The trajectories of these resonance states,in conjunction with the complex rotation of the Hamiltonian,were used to determine their wave functions.The electron densities,Fukui functions,and values of the hyper-radius<r^2>were computed from these wave functions.The Fukui functions have negative regions in the valence shell in addition to the inner shell regions,indicating screening effects of the outer temporary electron.Selected configuration interactions with up to quadruple excitations were used along the trajectories and for computing the final wave function.Based on this data,the densities,Fukui functions,and<r^2>were calculated.
