Next generation wireless communication is based on a global system of fixed and wireless mobile services thatare transportable across different network back-bones,network service providers and network geographical bou...Next generation wireless communication is based on a global system of fixed and wireless mobile services thatare transportable across different network back-bones,network service providers and network geographical boundaries.This paper presents an approach to investigate the effects of soft handover and perfect power control on the forward link ina DS-CDMA cellular system.Especially,the relationships between the size ofhandover zone and the capacity gain are e-valuated under the log-normal shadow channel.Then the optimization of maximum forward capacity is very necessary tobe done with the maximum size of soft handover zone to the various system characteristics.展开更多
Before joining the Beijing Dragon Shadow Puppetry Art Theatre,this group of young people rarely had the chance to meet people like themselves,lacked friends,faced obstacles at work,and felt alienated from society.Now,...Before joining the Beijing Dragon Shadow Puppetry Art Theatre,this group of young people rarely had the chance to meet people like themselves,lacked friends,faced obstacles at work,and felt alienated from society.Now,they have gained appreciation,recognition,confidence,friendships,and love.展开更多
Modeling time headways between vehicles has attracted increasing interest in the traffic flow research field recently, because the corresponding statistics help to reveal the intrinsic interactions governing the vehic...Modeling time headways between vehicles has attracted increasing interest in the traffic flow research field recently, because the corresponding statistics help to reveal the intrinsic interactions governing the vehicle dynamics. However, most previous micro-simulation models cannot yield the observed log-normal distributed headways. This paper designs a new car-following model inspired by the Galton board to reproduce the observed time-headway distributions as well as the complex traffic phenomena. The consistency between the empirical data and the simulation results indicates that this new car-following model provides a reasonable description of the car-following behaviours.展开更多
In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original...In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.展开更多
Medical research data are often skewed and heteroscedastic. It has therefore become practice to log-transform data in regression analysis, in order to stabilize the variance. Regression analysis on log-transformed dat...Medical research data are often skewed and heteroscedastic. It has therefore become practice to log-transform data in regression analysis, in order to stabilize the variance. Regression analysis on log-transformed data estimates the relative effect, whereas it is often the absolute effect of a predictor that is of interest. We propose a maximum likelihood (ML)-based approach to estimate a linear regression model on log-normal, heteroscedastic data. The new method was evaluated with a large simulation study. Log-normal observations were generated according to the simulation models and parameters were estimated using the new ML method, ordinary least-squares regression (LS) and weighed least-squares regression (WLS). All three methods produced unbiased estimates of parameters and expected response, and ML and WLS yielded smaller standard errors than LS. The approximate normality of the Wald statistic, used for tests of the ML estimates, in most situations produced correct type I error risk. Only ML and WLS produced correct confidence intervals for the estimated expected value. ML had the highest power for tests regarding β1.展开更多
We have observed weather clutter containing targets (ships) using an S-band radar with a frequency 3.05 GHz, a beam width 1.8°, and a pulsewidth 0.5 μs. To investigate the weather clutter amplitude statistics, w...We have observed weather clutter containing targets (ships) using an S-band radar with a frequency 3.05 GHz, a beam width 1.8°, and a pulsewidth 0.5 μs. To investigate the weather clutter amplitude statistics, we introduce the Akaike Information Criterion (AIC). We have found that the weather clutter amplitudes obey the log-normal, Weibull, and log-Weibull distributions with the shape parameters of 0.308 to 0.470, 4.42 to 4.51, and 15.91 to 16.44, respectively, for small data within the beam width of an antenna. We have proposed the log-normal/CFAR circuit modified a Cell-Averaging (CA) LOG/CFAR circuit. It is found that weather clutter is suppressed with improvement of 51.58 dB by log-normal/CFAR. As a result, we have showed that weather clutter observed by S-band radar does not obey the Rayleigh distribution and our log-normal/CFAR circuit has an effect on suppression of clutter and detection of target, while conventional LOG/CFAR circuit does not. In addition, if our circuit can be realized, we will have an advantage economically.展开更多
Digital twin(DT)technology has been utilised in many applications including electric vehicles(EVs).A DT is a virtual representation of a physical object,enabled through real-time data integration,simulation,and optimi...Digital twin(DT)technology has been utilised in many applications including electric vehicles(EVs).A DT is a virtual representation of a physical object,enabled through real-time data integration,simulation,and optimisation tools.Unlike conventional simulations,which are typically offline and lack real-time interaction,a DT continuously synchronises with the physical system,enabling dynamic performance monitoring and predictive an-alytics.Achieving a full DT involves progressive stages,with the digital shadow(DS)being the final step before realising a bidirectional DT.Building a DS provides a scalable real-time performance monitoring and fault detection framework,enabling proactive decision-making in EV operations.This study introduces a DS system specifically designed to monitor the performance of a permanent magnet synchronous motor(PMSM)drive system in EVs,marking a critical phase towards a complete DT.The methodology for creating the DS is detailed,including the establishment of a compre-hensive test bench for the EV powertrain as the physical reference model.The mathe-matical model of the EV-PMSM was formulated,and an advanced estimation model utilising the extended Kalman filter(EKF)was implemented.MATLAB/Simulink was employed to develop the motor’s digital model.Real-time data acquisition from the physical model was facilitated through a data acquisition system(DAS)equipped with a controller area network(CAN)communication interface.The digital model underwent thorough validation against sensory data collected from the test bench.The motor digital model was deployed to a DS framework enabled through real-time data flow from the actual EV during real-world driving conditions.The results demonstrated a high accuracy of 97%between the DS predictions and the corresponding EV data,confirming the DS’s reliability.These findings pave the way for future advancements,including bidirectional interaction and the realisation of a full DT.展开更多
In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the...In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes(QNMs)and shadow cast.To do this,we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins:massless scalar field,electromagnetic field and gravitational field.Then,using the sixth-order Wentzel-Kramers-Brillouin approximation,we examine QNMs of the BH disturbed by the three fields and derive quasinormal frequencies.The changes in QNM versus the core density parameter and the cloud string parameter for three disturbances are explored.We also investigate how the core density and the cloud string parameter affect the photon sphere and shadow radius.Interestingly,the study shows that the influence of Dehnen-type DM and cloud strings increases both the photon sphere and the shadow radius.Finally,we employ observational data from Sgr A^(*) and M87^(*) to set limitations on the BH parameters.展开更多
In this paper,we investigate the optical properties of a non-rotating charged black hole(BH)in the Einstein-Maxwell-scalar(EMS)theory,together with a plasma medium.We first consider the photon sphere and shadow radius...In this paper,we investigate the optical properties of a non-rotating charged black hole(BH)in the Einstein-Maxwell-scalar(EMS)theory,together with a plasma medium.We first consider the photon sphere and shadow radius under the impact of the plasma medium existing in the environment surrounding the BH in the EMS theory.We show that the radius of the photon sphere and the BH shadow decrease under the influence of the parameterβ.We further study gravitational weak lensing in detail by adapting general methods and derive the light ray's deflection angle around the BH together with the plasma environment.It is found that for uniform plasma,the deflection angle increases with the rise of the plasma parameter,whereas it decreases with the increase of the plasma parameter for non-uniform plasma.Besides,we also study the magnification of image brightness.展开更多
Permanently shadowed regions(PSRs)on the Moon are potential reservoirs for water ice,making them hot spots for future lunar exploration.The water ice in PSRs would cause distinctive changes in space weathering there,i...Permanently shadowed regions(PSRs)on the Moon are potential reservoirs for water ice,making them hot spots for future lunar exploration.The water ice in PSRs would cause distinctive changes in space weathering there,in particular reduction-oxidation processes that diff er from those in illuminated regions.To determine the characteristics of products formed during space weathering in PSRs,the lunar meteorite NWA 10203 with artifi cially added water was irradiated with a nanosecond laser to simulate a micro-meteorite bombardment of lunar soil containing water ice.The TEM results of the water-incorporated sample showed distinct amorphous rims that exhibited irregular thickness,poor stratifi cation,the appearance of bubbles,and a reduced number of npFe^(0).Additionally,EELS analysis showed the presence of ferric iron at the rim of the nanophase metallic iron particles(npFe^(0))in the amorphous rim with the involvement of water.The results suggest that water ice is another possible factor contributing to oxidation during micrometeorite bombardment on the lunar surface.In addition,it off ers a reference for a new space weathering model that incorporates water in PSRs,which could be widespread on asteroids with volatiles.展开更多
The photon region surrounding a black hole is crucial for distant observers to receive the emitted spectrum from its vicinity.This paper investigates the optical features of a regular spinning antide Sitter(AdS)black ...The photon region surrounding a black hole is crucial for distant observers to receive the emitted spectrum from its vicinity.This paper investigates the optical features of a regular spinning antide Sitter(AdS)black hole.These kinds of black holes hold deviation parameter k,and the cosmological constant A including their mass M and spin a.The cosmological parameter depends on the curvature radius by A=-3/l~2.We investigate the structure of geodesics for unstable circular orbits of photons as observed by an observer at specific Boyer-Lindquist coordinates(r_(O),v_(O))in the region between the outer and cosmological horizon,so-called the domain of outer communication.Our investigations include the analysis of three observables from its shadow plot:the black hole shadow radius(R_(s)),the distortion of the black hole(δ_(s)),and shadow area A.With the help of these observables,we calculate the angular diameter of the apparent size of the shadow.The shadows cast by spinning regular spacetimes are smaller compared to those produced by rotating black holes in both general relativity and regular spacetimes.We also calculate the rate at which energy is emitted from the black hole.展开更多
Strong low-frequency energy beneath a hydrocarbon reservoir is called a seismic low-frequency shadow and can be used as a hydrocarbon indicator （Tarter et al., 1979） bu the physical mechanism of the observed low-fre...Strong low-frequency energy beneath a hydrocarbon reservoir is called a seismic low-frequency shadow and can be used as a hydrocarbon indicator （Tarter et al., 1979） bu the physical mechanism of the observed low-frequency shadow is still unclear. To stud） the mechanism, we performed seismic numerical simulation of geological models with a hydrocarbon-bearing zone using the 2-D diffusive-viscous wave equation which car effectively model the characteristics of velocity dispersion and transform the seismic dat~ centered in a target layer slice within a time window to the time-frequency domain by usinl time-frequency signal analysis and sort the frequency gathers to common frequency cubes. Then, we observe the characteristics of the seismic low-frequency shadow in the common frequency cubes. The numerical simulations reveal that the main mechanism of seismic lowfrequency shadows is attributed to high attenuation of the medium to high seismic frequency components caused by absorption in the hydrocarbon-filled reservoir. Results from a practical example of seismic low-frequency shadows show that it is possible to identify the reservoir by the low-frequency shadow with high S/N seismic data.展开更多
The seed shadow of oak ( Quercus liaotungensis Koidz.) was investigated in a broad_leaved deciduous forest in Dongling Mountain in 1997. The seed rain patterns under oak tree crown for three out of four oak trees fit...The seed shadow of oak ( Quercus liaotungensis Koidz.) was investigated in a broad_leaved deciduous forest in Dongling Mountain in 1997. The seed rain patterns under oak tree crown for three out of four oak trees fit quadratic distribution, with high coefficients of determination. For each of the four trees selected in this study the seed rain size estimated from the viable acorns collected from the traps deployed under the crown was low, ranging from 26 to 259. For each of the four oak trees, the average density of the seed rain under oak tree crown ranged from 0.76 to 7.26 seeds/m 2. The average seed rain density estimated from the acorns in the traps deployed randomly in the field was 1.57 seeds/m 2. After all viable acorns fell, the acorn ground density estimated from the acorns in the quadrats was 0.13 seeds/m 2, but no viable acorns were found on the ground under the tree crown of the four oak trees, although the area under the crown was over 5 folds than the area of the combined quadrats. These results indicated that a large number of acorns was removed or predated by vertebrates once the acorns fell on the ground and acorns predation was more intensive in the sites directly under the parent trees than the sites away from the parent trees; this supports the distance_dependent hypothesis. Of the total acorns of all four oak trees, the viable acorns only accounted for 18.1%, and 17.8% for acorns infected by insect larvae, 12.1% for immature acorns, 3.6% for decayed acorns, and the acorns predated by rodent directly in the crown was the highest, accounting for 48.4%. The proportion of acorns predated by animals including vertebrates and invertebrates amounts up to 78.3%, indicating that acorn predation by animals is a limiting factor affecting acorn survival before seed dispersal. The sustained time of viable acorn fall ranged from September 8 to October 3 for the four oak trees, with the peak between 16th and 26th September. The number of acorns was not significantly different among the four directions around the trunk base.展开更多
文摘Next generation wireless communication is based on a global system of fixed and wireless mobile services thatare transportable across different network back-bones,network service providers and network geographical boundaries.This paper presents an approach to investigate the effects of soft handover and perfect power control on the forward link ina DS-CDMA cellular system.Especially,the relationships between the size ofhandover zone and the capacity gain are e-valuated under the log-normal shadow channel.Then the optimization of maximum forward capacity is very necessary tobe done with the maximum size of soft handover zone to the various system characteristics.
文摘Before joining the Beijing Dragon Shadow Puppetry Art Theatre,this group of young people rarely had the chance to meet people like themselves,lacked friends,faced obstacles at work,and felt alienated from society.Now,they have gained appreciation,recognition,confidence,friendships,and love.
基金supported partly by the National Basic Research Program of China (Grant No. 2006CB705506)the National Hi-Tech Research and Development Program of China (Grant Nos. 2006AA11Z215 and 2007AA11Z222)the National Natural Science Foundation of China (Grant Nos. 50708055, 60774034 and 10872194)
文摘Modeling time headways between vehicles has attracted increasing interest in the traffic flow research field recently, because the corresponding statistics help to reveal the intrinsic interactions governing the vehicle dynamics. However, most previous micro-simulation models cannot yield the observed log-normal distributed headways. This paper designs a new car-following model inspired by the Galton board to reproduce the observed time-headway distributions as well as the complex traffic phenomena. The consistency between the empirical data and the simulation results indicates that this new car-following model provides a reasonable description of the car-following behaviours.
基金The NSF(11271155) of ChinaResearch Fund(20070183023) for the Doctoral Program of Higher Education
文摘In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.
文摘Medical research data are often skewed and heteroscedastic. It has therefore become practice to log-transform data in regression analysis, in order to stabilize the variance. Regression analysis on log-transformed data estimates the relative effect, whereas it is often the absolute effect of a predictor that is of interest. We propose a maximum likelihood (ML)-based approach to estimate a linear regression model on log-normal, heteroscedastic data. The new method was evaluated with a large simulation study. Log-normal observations were generated according to the simulation models and parameters were estimated using the new ML method, ordinary least-squares regression (LS) and weighed least-squares regression (WLS). All three methods produced unbiased estimates of parameters and expected response, and ML and WLS yielded smaller standard errors than LS. The approximate normality of the Wald statistic, used for tests of the ML estimates, in most situations produced correct type I error risk. Only ML and WLS produced correct confidence intervals for the estimated expected value. ML had the highest power for tests regarding β1.
文摘We have observed weather clutter containing targets (ships) using an S-band radar with a frequency 3.05 GHz, a beam width 1.8°, and a pulsewidth 0.5 μs. To investigate the weather clutter amplitude statistics, we introduce the Akaike Information Criterion (AIC). We have found that the weather clutter amplitudes obey the log-normal, Weibull, and log-Weibull distributions with the shape parameters of 0.308 to 0.470, 4.42 to 4.51, and 15.91 to 16.44, respectively, for small data within the beam width of an antenna. We have proposed the log-normal/CFAR circuit modified a Cell-Averaging (CA) LOG/CFAR circuit. It is found that weather clutter is suppressed with improvement of 51.58 dB by log-normal/CFAR. As a result, we have showed that weather clutter observed by S-band radar does not obey the Rayleigh distribution and our log-normal/CFAR circuit has an effect on suppression of clutter and detection of target, while conventional LOG/CFAR circuit does not. In addition, if our circuit can be realized, we will have an advantage economically.
基金Estonian Research Competency Council,Grant/Award Number:PSG453,Eesti Teadusagentuur。
文摘Digital twin(DT)technology has been utilised in many applications including electric vehicles(EVs).A DT is a virtual representation of a physical object,enabled through real-time data integration,simulation,and optimisation tools.Unlike conventional simulations,which are typically offline and lack real-time interaction,a DT continuously synchronises with the physical system,enabling dynamic performance monitoring and predictive an-alytics.Achieving a full DT involves progressive stages,with the digital shadow(DS)being the final step before realising a bidirectional DT.Building a DS provides a scalable real-time performance monitoring and fault detection framework,enabling proactive decision-making in EV operations.This study introduces a DS system specifically designed to monitor the performance of a permanent magnet synchronous motor(PMSM)drive system in EVs,marking a critical phase towards a complete DT.The methodology for creating the DS is detailed,including the establishment of a compre-hensive test bench for the EV powertrain as the physical reference model.The mathe-matical model of the EV-PMSM was formulated,and an advanced estimation model utilising the extended Kalman filter(EKF)was implemented.MATLAB/Simulink was employed to develop the motor’s digital model.Real-time data acquisition from the physical model was facilitated through a data acquisition system(DAS)equipped with a controller area network(CAN)communication interface.The digital model underwent thorough validation against sensory data collected from the test bench.The motor digital model was deployed to a DS framework enabled through real-time data flow from the actual EV during real-world driving conditions.The results demonstrated a high accuracy of 97%between the DS predictions and the corresponding EV data,confirming the DS’s reliability.These findings pave the way for future advancements,including bidirectional interaction and the realisation of a full DT.
基金supported by the National Natural Science Foundation of China under Grant No.11675143the National Key Research and Development Program of China under Grant No.2020YFC2201503。
文摘In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes(QNMs)and shadow cast.To do this,we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins:massless scalar field,electromagnetic field and gravitational field.Then,using the sixth-order Wentzel-Kramers-Brillouin approximation,we examine QNMs of the BH disturbed by the three fields and derive quasinormal frequencies.The changes in QNM versus the core density parameter and the cloud string parameter for three disturbances are explored.We also investigate how the core density and the cloud string parameter affect the photon sphere and shadow radius.Interestingly,the study shows that the influence of Dehnen-type DM and cloud strings increases both the photon sphere and the shadow radius.Finally,we employ observational data from Sgr A^(*) and M87^(*) to set limitations on the BH parameters.
基金supported by the National Natural Science Foundation of China under Grant No.11675143the National Key Research and Development Program of China under Grant No.2020YFC2201503。
文摘In this paper,we investigate the optical properties of a non-rotating charged black hole(BH)in the Einstein-Maxwell-scalar(EMS)theory,together with a plasma medium.We first consider the photon sphere and shadow radius under the impact of the plasma medium existing in the environment surrounding the BH in the EMS theory.We show that the radius of the photon sphere and the BH shadow decrease under the influence of the parameterβ.We further study gravitational weak lensing in detail by adapting general methods and derive the light ray's deflection angle around the BH together with the plasma environment.It is found that for uniform plasma,the deflection angle increases with the rise of the plasma parameter,whereas it decreases with the increase of the plasma parameter for non-uniform plasma.Besides,we also study the magnification of image brightness.
基金support from the Youth Innovation Promotion Association,Chinese Academy of Sciences(2020395)Strategic Priority Research Program of the Chinese Academy of Sciences grant XDB 41000000(Y.L.)+4 种基金National Natural Science Foundation of China(Nos.42273042 and 41931077)"From 0 to 1"Original Exploration Cultivation Project,Institute of Geochemistry,Chinese Academy of Sciences(DHSZZ2023-3)Guizhou Provincial Foundation for Excellent Scholars Program(No.GCC[2023]088)Guizhou Provincial Science and Technology Projects:QKHJCZK[2023]-General 473NSFC Young Scientist Fund(Nos.42303041 and 42403043)。
文摘Permanently shadowed regions(PSRs)on the Moon are potential reservoirs for water ice,making them hot spots for future lunar exploration.The water ice in PSRs would cause distinctive changes in space weathering there,in particular reduction-oxidation processes that diff er from those in illuminated regions.To determine the characteristics of products formed during space weathering in PSRs,the lunar meteorite NWA 10203 with artifi cially added water was irradiated with a nanosecond laser to simulate a micro-meteorite bombardment of lunar soil containing water ice.The TEM results of the water-incorporated sample showed distinct amorphous rims that exhibited irregular thickness,poor stratifi cation,the appearance of bubbles,and a reduced number of npFe^(0).Additionally,EELS analysis showed the presence of ferric iron at the rim of the nanophase metallic iron particles(npFe^(0))in the amorphous rim with the involvement of water.The results suggest that water ice is another possible factor contributing to oxidation during micrometeorite bombardment on the lunar surface.In addition,it off ers a reference for a new space weathering model that incorporates water in PSRs,which could be widespread on asteroids with volatiles.
基金supported by the National Postdoctoral Fellowship of the Science and Engineering Research Board(SERB),Department of Science and Technology(DST),Government of India,File No.PDF/2021/003491。
文摘The photon region surrounding a black hole is crucial for distant observers to receive the emitted spectrum from its vicinity.This paper investigates the optical features of a regular spinning antide Sitter(AdS)black hole.These kinds of black holes hold deviation parameter k,and the cosmological constant A including their mass M and spin a.The cosmological parameter depends on the curvature radius by A=-3/l~2.We investigate the structure of geodesics for unstable circular orbits of photons as observed by an observer at specific Boyer-Lindquist coordinates(r_(O),v_(O))in the region between the outer and cosmological horizon,so-called the domain of outer communication.Our investigations include the analysis of three observables from its shadow plot:the black hole shadow radius(R_(s)),the distortion of the black hole(δ_(s)),and shadow area A.With the help of these observables,we calculate the angular diameter of the apparent size of the shadow.The shadows cast by spinning regular spacetimes are smaller compared to those produced by rotating black holes in both general relativity and regular spacetimes.We also calculate the rate at which energy is emitted from the black hole.
基金国家重点基础研究发展规划(973)(the National Grand Fundamental Research 973 Program of China under Grant No．2002CB312103)河南省自然科学基金(the Natural Science Foundation of Henan Province of China under Grant No．0611051900)。
基金supported by the National Hi-tech Research and Development Program of China (863 Program) (Grant No. 2006AA0AA 02 - 2).
文摘Strong low-frequency energy beneath a hydrocarbon reservoir is called a seismic low-frequency shadow and can be used as a hydrocarbon indicator （Tarter et al., 1979） bu the physical mechanism of the observed low-frequency shadow is still unclear. To stud） the mechanism, we performed seismic numerical simulation of geological models with a hydrocarbon-bearing zone using the 2-D diffusive-viscous wave equation which car effectively model the characteristics of velocity dispersion and transform the seismic dat~ centered in a target layer slice within a time window to the time-frequency domain by usinl time-frequency signal analysis and sort the frequency gathers to common frequency cubes. Then, we observe the characteristics of the seismic low-frequency shadow in the common frequency cubes. The numerical simulations reveal that the main mechanism of seismic lowfrequency shadows is attributed to high attenuation of the medium to high seismic frequency components caused by absorption in the hydrocarbon-filled reservoir. Results from a practical example of seismic low-frequency shadows show that it is possible to identify the reservoir by the low-frequency shadow with high S/N seismic data.
文摘The seed shadow of oak ( Quercus liaotungensis Koidz.) was investigated in a broad_leaved deciduous forest in Dongling Mountain in 1997. The seed rain patterns under oak tree crown for three out of four oak trees fit quadratic distribution, with high coefficients of determination. For each of the four trees selected in this study the seed rain size estimated from the viable acorns collected from the traps deployed under the crown was low, ranging from 26 to 259. For each of the four oak trees, the average density of the seed rain under oak tree crown ranged from 0.76 to 7.26 seeds/m 2. The average seed rain density estimated from the acorns in the traps deployed randomly in the field was 1.57 seeds/m 2. After all viable acorns fell, the acorn ground density estimated from the acorns in the quadrats was 0.13 seeds/m 2, but no viable acorns were found on the ground under the tree crown of the four oak trees, although the area under the crown was over 5 folds than the area of the combined quadrats. These results indicated that a large number of acorns was removed or predated by vertebrates once the acorns fell on the ground and acorns predation was more intensive in the sites directly under the parent trees than the sites away from the parent trees; this supports the distance_dependent hypothesis. Of the total acorns of all four oak trees, the viable acorns only accounted for 18.1%, and 17.8% for acorns infected by insect larvae, 12.1% for immature acorns, 3.6% for decayed acorns, and the acorns predated by rodent directly in the crown was the highest, accounting for 48.4%. The proportion of acorns predated by animals including vertebrates and invertebrates amounts up to 78.3%, indicating that acorn predation by animals is a limiting factor affecting acorn survival before seed dispersal. The sustained time of viable acorn fall ranged from September 8 to October 3 for the four oak trees, with the peak between 16th and 26th September. The number of acorns was not significantly different among the four directions around the trunk base.
