In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MWpr,α(Td), 1 < p < ∞, in the norm of Lq(Td), 1 < q < ∞, by...In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MWpr,α(Td), 1 < p < ∞, in the norm of Lq(Td), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.展开更多
The use of carbon-ion radiotherapy(CIRT)is gradually increasing.Owing to the generation of high-energy secondary neutrons during CIRT,its use presents new challenges in radiation protection.Thus,secondary neutron dose...The use of carbon-ion radiotherapy(CIRT)is gradually increasing.Owing to the generation of high-energy secondary neutrons during CIRT,its use presents new challenges in radiation protection.Thus,secondary neutron dose distributions must be explored and evaluated under clinical scenarios based on different treatment configurations.However,neutron dose and energy spectrum measurements are often difficult.This can be primarily attributed to the inherent limitations of most neutron detectors,such as their unsuitability for spectral measurements and inaccurate responses to neutrons with energies above 20 MeV.Numerical calculation methods based on probabilistic statistical theory are fast and convenient for neutron dose evaluation.In this study,external secondary neutron doses at the heavy ion medical machine in Wuwei,which is equipped with a passive beam delivery system,were calculated using the Monte Carlo method.The dependence of neutron doses on various treatment parameters(incident carbon-ion beam energy,spatial location,field size,and spread-out Bragg peak(SOBP)width)was investigated.Furthermore,the feasibility of applying an analytical model to predict the ambient dose equivalent was verified.For the combination involving an energy of 400 MeV=u and SOBP width of 6 cm,the ambient dose equivalent per therapeutic dose(H=D)at the isocenter was 79.87 mSv=Gy:The H=D value decreased rapidly with increasing spatial distance and slightly with increasing aperture size and SOBP width.The H=D values derived from the Monte Carlo simulations were in good agreement with the results reported in the literature.The analytical model could be used to quickly predict the H=D value along the incidence direction of the beam with an error of less than 20%.Thus,our study contributes to the understanding of the relationship between neutron radiation and treatment configuration parameters,which establishes a basis for predicting non-therapeutic radiation doses in CIRT.展开更多
重金属汞污染是危害粮食安全的重要问题,直接进样测汞法的检测过程中需要对检测结果做好质量控制。检测结果需要识别实验过程中各环节对结果的影响大小。基于GB/T 27404—2008《实验室质量控制规范食品理化检测》附录F中对实验室开展新...重金属汞污染是危害粮食安全的重要问题,直接进样测汞法的检测过程中需要对检测结果做好质量控制。检测结果需要识别实验过程中各环节对结果的影响大小。基于GB/T 27404—2008《实验室质量控制规范食品理化检测》附录F中对实验室开展新项目所需验证的各种项目:回收率、标准曲线、测定低限、精密度、准确度等。使用自适应蒙特卡洛法(adaptive Monte Carlo method,MCM)和测量不确定度表示指南方法(Guide to the expression of uncertainty in measurement,GUM)分别对直接进样测汞法开展不确定度评定。GUM法得到的不确定范围为(0.0193±0.0017)mg/kg(k=2);MCM法得到的不确定度置信区间(95%)为[0.0177,0.0211];使用MCM Alchimia软件对2种方法的不确定度概率密度拟合曲线,MCM法与GUM法评价结果一致性较好。分析不确定度评定过程中各不确定度贡献率,回收率和标准曲线拟合过程引入不确定度在检出限处引入的不确定度分量较大,建议在方法验证和不确定度评定中使用定量限作为加标回收率和标准曲线最小浓度点。展开更多
The current researches mainly adopt "Guide to the expression of uncertainty in measurement(GUM)" to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not...The current researches mainly adopt "Guide to the expression of uncertainty in measurement(GUM)" to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profile error because the mathematical model of profile error is strongly non-linear. An improved second-order GUM method(GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in different coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method(AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the difference between the improved second-order GUM and the AMCM is smaller than the difference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profile error.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10671019)the Research Fund for the Doctoral Program of Higher Education (Grant No. 20050027007)
文摘In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MWpr,α(Td), 1 < p < ∞, in the norm of Lq(Td), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.
基金the National Natural Science Foundation of China(Nos.12005271 and 12005273)the National Key Research and Development Program of China(No.E022223Y)+1 种基金the Western Talent Program of Chinese Academy of Sciences(No.29Y86205)the Key Deployment Project of Chinese Academy of Sciences(No.KFZD-SW-222).
文摘The use of carbon-ion radiotherapy(CIRT)is gradually increasing.Owing to the generation of high-energy secondary neutrons during CIRT,its use presents new challenges in radiation protection.Thus,secondary neutron dose distributions must be explored and evaluated under clinical scenarios based on different treatment configurations.However,neutron dose and energy spectrum measurements are often difficult.This can be primarily attributed to the inherent limitations of most neutron detectors,such as their unsuitability for spectral measurements and inaccurate responses to neutrons with energies above 20 MeV.Numerical calculation methods based on probabilistic statistical theory are fast and convenient for neutron dose evaluation.In this study,external secondary neutron doses at the heavy ion medical machine in Wuwei,which is equipped with a passive beam delivery system,were calculated using the Monte Carlo method.The dependence of neutron doses on various treatment parameters(incident carbon-ion beam energy,spatial location,field size,and spread-out Bragg peak(SOBP)width)was investigated.Furthermore,the feasibility of applying an analytical model to predict the ambient dose equivalent was verified.For the combination involving an energy of 400 MeV=u and SOBP width of 6 cm,the ambient dose equivalent per therapeutic dose(H=D)at the isocenter was 79.87 mSv=Gy:The H=D value decreased rapidly with increasing spatial distance and slightly with increasing aperture size and SOBP width.The H=D values derived from the Monte Carlo simulations were in good agreement with the results reported in the literature.The analytical model could be used to quickly predict the H=D value along the incidence direction of the beam with an error of less than 20%.Thus,our study contributes to the understanding of the relationship between neutron radiation and treatment configuration parameters,which establishes a basis for predicting non-therapeutic radiation doses in CIRT.
文摘重金属汞污染是危害粮食安全的重要问题,直接进样测汞法的检测过程中需要对检测结果做好质量控制。检测结果需要识别实验过程中各环节对结果的影响大小。基于GB/T 27404—2008《实验室质量控制规范食品理化检测》附录F中对实验室开展新项目所需验证的各种项目:回收率、标准曲线、测定低限、精密度、准确度等。使用自适应蒙特卡洛法(adaptive Monte Carlo method,MCM)和测量不确定度表示指南方法(Guide to the expression of uncertainty in measurement,GUM)分别对直接进样测汞法开展不确定度评定。GUM法得到的不确定范围为(0.0193±0.0017)mg/kg(k=2);MCM法得到的不确定度置信区间(95%)为[0.0177,0.0211];使用MCM Alchimia软件对2种方法的不确定度概率密度拟合曲线,MCM法与GUM法评价结果一致性较好。分析不确定度评定过程中各不确定度贡献率,回收率和标准曲线拟合过程引入不确定度在检出限处引入的不确定度分量较大,建议在方法验证和不确定度评定中使用定量限作为加标回收率和标准曲线最小浓度点。
基金Supported by National Natural Science Foundation of China(Grant No.51675378)National Science and Technology Major Project of China(Grant No.2014ZX04014-031)
文摘The current researches mainly adopt "Guide to the expression of uncertainty in measurement(GUM)" to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profile error because the mathematical model of profile error is strongly non-linear. An improved second-order GUM method(GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in different coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method(AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the difference between the improved second-order GUM and the AMCM is smaller than the difference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profile error.
