This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of...This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.展开更多
A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was di...A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was divided into two aspects. Firstly, the approximation family was tight using the methods given by Billingsley; secondly, the finite-dimension distributions of approximation family converged weakly to the Rosenblatt process by proving the convergence of the corresponding characteristic functions.展开更多
Slacking experiments were performed on the red beds weak rock from vicinity of Changsha. Grain size distribution of the slacking rock was tested periodically during the experiments, which can be used to describe the p...Slacking experiments were performed on the red beds weak rock from vicinity of Changsha. Grain size distribution of the slacking rock was tested periodically during the experiments, which can be used to describe the physical transition of red beds weak rock during slacking process. According to the similar characters of many attributions such as environmental moisture, mineralogical composition, grain size and other factors between big rocks before slacking and its slacked product, the self-similar property of big rock and the small one can be induced. Fractal concept was introduced to construct the slacking model of red beds weak rock. Combining the supposed relationship of time for slacking and grain size of weak rock, the mathematic simulation of slacking process of red beds weak rock was conducted. To simplify the parameters back calculation, the fractal model proposed by Tyler and Wheatcraft was introduced to describe the characters of grain size distribution variation. The results show that the fractal dimension calculated from simulation data meet experiments data closely, which proves that the mathematic simulation method is reasonable and the parameters determination method is effective.展开更多
Assume that D is a nuclear space and D' its strong topological dual space. Let {B_t}t∈(0,∞) be a Wiener D'-process. In this paper, the real-valued and D'-valued weak stochastic integral with respect to {...Assume that D is a nuclear space and D' its strong topological dual space. Let {B_t}t∈(0,∞) be a Wiener D'-process. In this paper, the real-valued and D'-valued weak stochastic integral with respect to {B_t} are established.AMS Subject Classification. 60H05.展开更多
Signals from infrared detector are very weak in SO2 concentration measuring system.In order to improve the sensitivity of detection,combining with filter correlation technology and infrared absorption principle,the we...Signals from infrared detector are very weak in SO2 concentration measuring system.In order to improve the sensitivity of detection,combining with filter correlation technology and infrared absorption principle,the weak signal processing circuit is designed according to correlation detection technology.Under laboratory conditions,system performance of SO2 concentration is tested,and the experimental data are analyzed and processed.Then relationship of SO2 concentration and the measuring voltage is provided to prove that the design improves measuring sensitivity of the system.展开更多
We have developed a novel method for co-adding multiple under-sampled images that combines the iteratively reweighted least squares and divide-and-conquer algorithms.Our approach not only allows for the anti-aliasing ...We have developed a novel method for co-adding multiple under-sampled images that combines the iteratively reweighted least squares and divide-and-conquer algorithms.Our approach not only allows for the anti-aliasing of the images but also enables Point-Spread Function(PSF)deconvolution,resulting in enhanced restoration of extended sources,the highest peak signal-to-noise ratio,and reduced ringing artefacts.To test our method,we conducted numerical simulations that replicated observation runs of the China Space Station Telescope/the VLT Survey Telescope(VST)and compared our results to those obtained using previous algorithms.The simulation showed that our method outperforms previous approaches in several ways,such as restoring the profile of extended sources and minimizing ringing artefacts.Additionally,because our method relies on the inherent advantages of least squares fitting,it is more versatile and does not depend on the local uniformity hypothesis for the PSF.However,the new method consumes much more computation than the other approaches.展开更多
基金This paper is supported by NNSF project(10371059)China and Youth Teacher Foundation of Nankai University
文摘This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.
基金National Natural Science Foundation of China(No. 11171062)Innovation Program of Shanghai Municipal Education Commission,China(No. 12ZZ063)Natural Science Foundation of Bengbu College,China(No. 2010ZR10)
文摘A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was divided into two aspects. Firstly, the approximation family was tight using the methods given by Billingsley; secondly, the finite-dimension distributions of approximation family converged weakly to the Rosenblatt process by proving the convergence of the corresponding characteristic functions.
基金Project (95-05-01-45) supported by the Ministry of Communications of China
文摘Slacking experiments were performed on the red beds weak rock from vicinity of Changsha. Grain size distribution of the slacking rock was tested periodically during the experiments, which can be used to describe the physical transition of red beds weak rock during slacking process. According to the similar characters of many attributions such as environmental moisture, mineralogical composition, grain size and other factors between big rocks before slacking and its slacked product, the self-similar property of big rock and the small one can be induced. Fractal concept was introduced to construct the slacking model of red beds weak rock. Combining the supposed relationship of time for slacking and grain size of weak rock, the mathematic simulation of slacking process of red beds weak rock was conducted. To simplify the parameters back calculation, the fractal model proposed by Tyler and Wheatcraft was introduced to describe the characters of grain size distribution variation. The results show that the fractal dimension calculated from simulation data meet experiments data closely, which proves that the mathematic simulation method is reasonable and the parameters determination method is effective.
文摘Assume that D is a nuclear space and D' its strong topological dual space. Let {B_t}t∈(0,∞) be a Wiener D'-process. In this paper, the real-valued and D'-valued weak stochastic integral with respect to {B_t} are established.AMS Subject Classification. 60H05.
文摘Signals from infrared detector are very weak in SO2 concentration measuring system.In order to improve the sensitivity of detection,combining with filter correlation technology and infrared absorption principle,the weak signal processing circuit is designed according to correlation detection technology.Under laboratory conditions,system performance of SO2 concentration is tested,and the experimental data are analyzed and processed.Then relationship of SO2 concentration and the measuring voltage is provided to prove that the design improves measuring sensitivity of the system.
基金supported by the GHfund A(202302017475)supported by the Foundation for Distinguished Young Scholars of Jiangsu Province(No.BK20140050)+5 种基金the National Natural Science Foundation of China(Nos.11973070,11333008,11273061,11825303,and 11673065)the China Manned Space Project with No.CMS-CSST-2021-A01,CMSCSST-2021-A03,CMS-CSST-2021-B01the Joint Funds of the National Natural Science Foundation of China(No.U1931210)the support from Key Research Program of Frontier Sciences,CAS,grant No.ZDBS-LY-7013Program of Shanghai Academic/Technology Research Leaderthe support from the science research grants from the China Manned Space Project with CMS-CSST-2021-A04,CMS-CSST-2021-A07。
文摘We have developed a novel method for co-adding multiple under-sampled images that combines the iteratively reweighted least squares and divide-and-conquer algorithms.Our approach not only allows for the anti-aliasing of the images but also enables Point-Spread Function(PSF)deconvolution,resulting in enhanced restoration of extended sources,the highest peak signal-to-noise ratio,and reduced ringing artefacts.To test our method,we conducted numerical simulations that replicated observation runs of the China Space Station Telescope/the VLT Survey Telescope(VST)and compared our results to those obtained using previous algorithms.The simulation showed that our method outperforms previous approaches in several ways,such as restoring the profile of extended sources and minimizing ringing artefacts.Additionally,because our method relies on the inherent advantages of least squares fitting,it is more versatile and does not depend on the local uniformity hypothesis for the PSF.However,the new method consumes much more computation than the other approaches.
