It is proved that every large integerN≡5 (mod 24) can be written as $N = p_1^2 + ... + p_5^2 $ with each primep j satisfying $|p_j - \sqrt {N/5} | \leqslant N^{\frac{{12}}{{25}} + E} $ , which gives a short interval ...It is proved that every large integerN≡5 (mod 24) can be written as $N = p_1^2 + ... + p_5^2 $ with each primep j satisfying $|p_j - \sqrt {N/5} | \leqslant N^{\frac{{12}}{{25}} + E} $ , which gives a short interval version of a classical theorem of Hua.展开更多
Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well ...Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data,which lead to large deviation under conditions of small sample size and zero?failure data. To improve this problem,a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high?speed train,the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time,a concave method is employed to obtain the relationships between accumulation failure prob?abilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation,and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally,the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system,which shows that the change in the reliability and failure rate among the di erent hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under condi?tions of small sample size and zero?failure data.展开更多
Sulfidation of zero-valent iron(ZVI)has attracted broad attention in recent years for improving the sequestration of contaminants from water.However,sulfidated ZVI(S-ZVI)is mostly synthesized in the aqueous phase,whic...Sulfidation of zero-valent iron(ZVI)has attracted broad attention in recent years for improving the sequestration of contaminants from water.However,sulfidated ZVI(S-ZVI)is mostly synthesized in the aqueous phase,which usually causes the formation of a thick iron oxide layer on the ZVI surface and hinders the efficient electron transfer to the contaminants.In this study,an alcohothermal strategy was employed for S-ZVI synthesis by the one-step reaction of iron powder with elemental sulfur.It is found that ferrous sulfide(FeS)with high purity and fine crystallization was formed on the ZVI surface,which is extremely favorable for electron transfer.Cr(Ⅵ)removal experiments confirm that the rate constant of SZVI synthesized by the alcohothermal method was 267.1-and 5.4-fold higher than those of un-sulfidated ZVI and aqueous-phase synthesized S-ZVI,respectively.Systematic characterizations proved that Cr(Ⅵ)was reduced and co-precipitated on S-ZVI in the form of a Fe(Ⅲ)/Cr(Ⅲ)/Cr(Ⅵ)composite,suggesting its environmental benignancy.展开更多
Highly precise acoustic impedance inversion is a key technology for pre-drilling prediction by VSP data. In this paper, based on the facts that VSP data has high resolution, high signal to noise ratio, and the downgoi...Highly precise acoustic impedance inversion is a key technology for pre-drilling prediction by VSP data. In this paper, based on the facts that VSP data has high resolution, high signal to noise ratio, and the downgoing and upgoing waves can be accurately separated, we propose a method of predicting the impedance below the borehole in front of the bit using VSP data. First, the method of nonlinear iterative inversion is adopted to invert for impedance using the VSP corridor stack. Then, by modifying the damping factor in the iteration and using the preconditioned conjugate gradient method to solve the equations, the stability and convergence of the inversion results can be enhanced. The results of theoretical models and actual data demonstrate that the method is effective for pre-drilling prediction using VSP data.展开更多
文摘It is proved that every large integerN≡5 (mod 24) can be written as $N = p_1^2 + ... + p_5^2 $ with each primep j satisfying $|p_j - \sqrt {N/5} | \leqslant N^{\frac{{12}}{{25}} + E} $ , which gives a short interval version of a classical theorem of Hua.
基金Supported by National Natural Science Foundation of China(Grant No.51175028)Great Scholars Training Project(Grant No.CIT&TCD20150312)Beijing Recognized Talent Project(Grant No.2014018)
文摘Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data,which lead to large deviation under conditions of small sample size and zero?failure data. To improve this problem,a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high?speed train,the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time,a concave method is employed to obtain the relationships between accumulation failure prob?abilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation,and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally,the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system,which shows that the change in the reliability and failure rate among the di erent hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under condi?tions of small sample size and zero?failure data.
基金the National Key Research and Development Program of China(No.2019YFC1806203)for financial support。
文摘Sulfidation of zero-valent iron(ZVI)has attracted broad attention in recent years for improving the sequestration of contaminants from water.However,sulfidated ZVI(S-ZVI)is mostly synthesized in the aqueous phase,which usually causes the formation of a thick iron oxide layer on the ZVI surface and hinders the efficient electron transfer to the contaminants.In this study,an alcohothermal strategy was employed for S-ZVI synthesis by the one-step reaction of iron powder with elemental sulfur.It is found that ferrous sulfide(FeS)with high purity and fine crystallization was formed on the ZVI surface,which is extremely favorable for electron transfer.Cr(Ⅵ)removal experiments confirm that the rate constant of SZVI synthesized by the alcohothermal method was 267.1-and 5.4-fold higher than those of un-sulfidated ZVI and aqueous-phase synthesized S-ZVI,respectively.Systematic characterizations proved that Cr(Ⅵ)was reduced and co-precipitated on S-ZVI in the form of a Fe(Ⅲ)/Cr(Ⅲ)/Cr(Ⅵ)composite,suggesting its environmental benignancy.
文摘Highly precise acoustic impedance inversion is a key technology for pre-drilling prediction by VSP data. In this paper, based on the facts that VSP data has high resolution, high signal to noise ratio, and the downgoing and upgoing waves can be accurately separated, we propose a method of predicting the impedance below the borehole in front of the bit using VSP data. First, the method of nonlinear iterative inversion is adopted to invert for impedance using the VSP corridor stack. Then, by modifying the damping factor in the iteration and using the preconditioned conjugate gradient method to solve the equations, the stability and convergence of the inversion results can be enhanced. The results of theoretical models and actual data demonstrate that the method is effective for pre-drilling prediction using VSP data.
