We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environmen...We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.展开更多
We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in ...We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.展开更多
Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit t...Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.展开更多
In recent years big strides have been made in the exploration of ores in the central-south segment of the Da Hinggan Ling Range,though some debates still exist on the metallogenesis and sources of ore-forming material...In recent years big strides have been made in the exploration of ores in the central-south segment of the Da Hinggan Ling Range,though some debates still exist on the metallogenesis and sources of ore-forming materials.Pyrite and other sulfides in direct relation to the Pb-Zn-Ag ore deposits were chosen for the He and Ar isotopic analysis of ore-forming fluids,and the first He and Ar isotope data have been obtained from the study region.3He/4He ratios in 14 samples collected from 7 mining districts are 2.17×10-6-12.52×10-6,averaging 6.86×10-6 and their R/Ra ratios are 1.56-9.01 Ra,averaging 4.37 Ra.By projecting the data points onto the 3He-4He concentrations diagram,all the points fall near the mantle helium area.The calculated mantle-source helium ratios are within the range of 19.58%-76.96%,with an average of 49.52%.Argon isotopic characteristics are close to those of mantle source,indicating that the ore-forming material was transport upwards via the multi-stage evolution of mantle plume and concentrated as ores in the favorable loci of mantle branch structures.展开更多
The process of building central and branch libraries since the year 2000 accelerates the equalization of public library services. This process can be divided into three stages. In the first stage(2000-2006), attempts ...The process of building central and branch libraries since the year 2000 accelerates the equalization of public library services. This process can be divided into three stages. In the first stage(2000-2006), attempts are made to solve problems related to government-led administration, Borrow Anywhere, Return Anywhere(BARA) service, technical support, and centralized management. In the second stage(2007-2010), some central and branch libraries expanded their scale and achieved remarkable progress through professional reform. Theoretical research in this period shed light on the objective laws in building the central and branch libraries. The third stage(2011-present) has witnessed libraries’ active participation in building 'National Demonstration Zones for Public Cultural Services', which is initiated by the Ministry of Culture and the Ministry of Finance. Researchers have been focusing on factors related to the sustainable development of central-branch libraries system. Such research directly promotes the promulgation of Guidance on Promoting the County Central-branch Cultural Center System and Central-branch Library System Development. Centering its discussions on the Guidance, this paper puts forward several issues that require special attention in building central and branch libraries in the new development stage. First, correctly understanding and handling the relationship between local conditions and professional requirements. Building central-branch libraries requires appropriate solutions that avoid conflicts with institutional barriers, so as to meet to the maximum the professional requirements in concept and design. Second, issues in building central-branch libraries at the county level are addressed in this paper. Third, providing universal and equitable services and fulfilling missions of the public library requires the construction of branch libraries in physical form. New types of services can only serve as integral parts and supplement of central-branch libraries. Fourth, the service innovation of 'library plus' should reflect the service concepts of public libraries, and guard against the establishment of service barriers or threshold.展开更多
Purpose: To analyse the parameters of frequency domain and time domain of the OPs in branch retinal vein occlusion (BRVO) and central retinal vein occlusion (CRVO). Methods : OPs from 9 eyes of BRVO, 9 eyes of CRVO an...Purpose: To analyse the parameters of frequency domain and time domain of the OPs in branch retinal vein occlusion (BRVO) and central retinal vein occlusion (CRVO). Methods : OPs from 9 eyes of BRVO, 9 eyes of CRVO and 40 normal control eyes were tested . The frequency spectra of the OPs were derived through Fast Fourier Transform (FFT) . The mean frequency spectra, the total power, the maximum magnitude, the maximum power and the dominant frequency in frequency domain of the OPs from the eyes of BRVO, CRVO and the normal control group were compared with each other. The OPs waveforms were reconstructed with the OPs frequency spectra data by counter-FFT. In time domain, the latencies, the amplitudes and the sum of the amplitudes of the four wavelets of OPs were measured and compared in the above subjects.Results: There were no statistically significant differences in the magnitudes of frequency spectra, the total power, the maximum magnitude and the maximum power in the frequency range from 110 to 250展开更多
基金partially supported by the National Natural Science Foundation of China(NSFC,11101039,11171044,11271045)a cooperation program between NSFC and CNRS of France(11311130103)+1 种基金the Fundamental Research Funds for the Central UniversitiesHunan Provincial Natural Science Foundation of China(11JJ2001)
文摘We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.
基金supported by the National Natural Science Foundation of China(11571052,11731012)the Hunan Provincial Natural Science Foundation of China(2018JJ2417)the Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(2018MMAEZD02)。
文摘We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.
基金Supported by Shandong Provincial Natural Science Foundation(Grant No.ZR2021MA085)National Natural Science Foundation of China(Grant No.11971063)。
文摘Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.
文摘In recent years big strides have been made in the exploration of ores in the central-south segment of the Da Hinggan Ling Range,though some debates still exist on the metallogenesis and sources of ore-forming materials.Pyrite and other sulfides in direct relation to the Pb-Zn-Ag ore deposits were chosen for the He and Ar isotopic analysis of ore-forming fluids,and the first He and Ar isotope data have been obtained from the study region.3He/4He ratios in 14 samples collected from 7 mining districts are 2.17×10-6-12.52×10-6,averaging 6.86×10-6 and their R/Ra ratios are 1.56-9.01 Ra,averaging 4.37 Ra.By projecting the data points onto the 3He-4He concentrations diagram,all the points fall near the mantle helium area.The calculated mantle-source helium ratios are within the range of 19.58%-76.96%,with an average of 49.52%.Argon isotopic characteristics are close to those of mantle source,indicating that the ore-forming material was transport upwards via the multi-stage evolution of mantle plume and concentrated as ores in the favorable loci of mantle branch structures.
文摘The process of building central and branch libraries since the year 2000 accelerates the equalization of public library services. This process can be divided into three stages. In the first stage(2000-2006), attempts are made to solve problems related to government-led administration, Borrow Anywhere, Return Anywhere(BARA) service, technical support, and centralized management. In the second stage(2007-2010), some central and branch libraries expanded their scale and achieved remarkable progress through professional reform. Theoretical research in this period shed light on the objective laws in building the central and branch libraries. The third stage(2011-present) has witnessed libraries’ active participation in building 'National Demonstration Zones for Public Cultural Services', which is initiated by the Ministry of Culture and the Ministry of Finance. Researchers have been focusing on factors related to the sustainable development of central-branch libraries system. Such research directly promotes the promulgation of Guidance on Promoting the County Central-branch Cultural Center System and Central-branch Library System Development. Centering its discussions on the Guidance, this paper puts forward several issues that require special attention in building central and branch libraries in the new development stage. First, correctly understanding and handling the relationship between local conditions and professional requirements. Building central-branch libraries requires appropriate solutions that avoid conflicts with institutional barriers, so as to meet to the maximum the professional requirements in concept and design. Second, issues in building central-branch libraries at the county level are addressed in this paper. Third, providing universal and equitable services and fulfilling missions of the public library requires the construction of branch libraries in physical form. New types of services can only serve as integral parts and supplement of central-branch libraries. Fourth, the service innovation of 'library plus' should reflect the service concepts of public libraries, and guard against the establishment of service barriers or threshold.
文摘Purpose: To analyse the parameters of frequency domain and time domain of the OPs in branch retinal vein occlusion (BRVO) and central retinal vein occlusion (CRVO). Methods : OPs from 9 eyes of BRVO, 9 eyes of CRVO and 40 normal control eyes were tested . The frequency spectra of the OPs were derived through Fast Fourier Transform (FFT) . The mean frequency spectra, the total power, the maximum magnitude, the maximum power and the dominant frequency in frequency domain of the OPs from the eyes of BRVO, CRVO and the normal control group were compared with each other. The OPs waveforms were reconstructed with the OPs frequency spectra data by counter-FFT. In time domain, the latencies, the amplitudes and the sum of the amplitudes of the four wavelets of OPs were measured and compared in the above subjects.Results: There were no statistically significant differences in the magnitudes of frequency spectra, the total power, the maximum magnitude and the maximum power in the frequency range from 110 to 250
