Based on the pulse-shaping unit in the front end of high-power laser facilities,we propose a new hybrid scheme in a closed-loop control system including wavelet threshold denoising for pretreatment and a first derivat...Based on the pulse-shaping unit in the front end of high-power laser facilities,we propose a new hybrid scheme in a closed-loop control system including wavelet threshold denoising for pretreatment and a first derivative adaptive smoothing filter for smooth pulse recovery,so as to effectively restrain the influence of electrical noise and FM-to-AM modulation in the time–power curve,and enhance the calibration accuracy of the pulse shape in the feedback control system.The related simulation and experiment results show that the proposed scheme can obtain a better shaping effect on the high-contrast temporal shape in comparison with the cumulative average algorithm and orthogonal matching pursuit algorithm combined with a traditional smoothing filter.The implementation of the hybrid scheme mechanism increased the signal-to-noise ratio of the laser pulse from about 11 dB to 30 dB,and the filtered pulse is smooth without modulation,with smoothness of about 98.8%.展开更多
Background:Controlling the coronavirus disease 2019(COVID-19)epidemic requires information beyond new and cumulative cases.This study aims to conduct an in-depth analysis by geographic strata:Wuhan City(hereafter refe...Background:Controlling the coronavirus disease 2019(COVID-19)epidemic requires information beyond new and cumulative cases.This study aims to conduct an in-depth analysis by geographic strata:Wuhan City(hereafter referred to as Wuhan)only,Hubei Province(hereafter referred to as Hubei)excluding Wuhan,and China excluding Hubei.Methods:Daily cumulative confirmed COVID-19 cases between December 8,2019(the date of symptom onset based on patients'recall during the investigation),and March 1,2020,from official sources and published studies were analyzed.The second derivative model was used for information extraction.Data analysis was conducted separately for the three strata.Results:A total of 80026 diagnosed COVID-19 cases were reported during the first 85 days of the epidemic,with 49315 cases from Wuhan,17788 from Hubei excluding Wuhan,and 12923 from China excluding Hubei.Analytical results indicate that the COVID-19 epidemic consists of an Acceleration,a Deceleration,and a Stabilization Phase in all three geographic strata,plus a Silent Attack Phase for Wuhan only.Given the reported incubation period of 14 days,effects of the massive anti-epidemic actions were revealed by both the Acceleration and Deceleration Phases.The Acceleration Phase signaled the effect of the intervention to detect the infected;the Deceleration Phase signaled the declines in new infections after the infected were detected,treated and quarantined.Conclusion:Findings of the study provide new evidence to better monitor the epidemic,evaluate its response to intervention,and predict the trend long.In addition to re-evaluating the control of the COVID-19 epidemic in China,this study provided a model for monitoring outbreaks of COVID-19 in different countries across the world.展开更多
The hyperbolic function proposed by Abbo- Sloan was employed not only to approach the Mohr- Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr-Coulomb yield and po...The hyperbolic function proposed by Abbo- Sloan was employed not only to approach the Mohr- Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr-Coulomb yield and potential surfaces was achieved by increasing the transition angle and proven to be highly efficient in numerical convergence. When a Gaussian integral point goes into plastic state, two cases on yield stress adjustments were introduced. They may avoid solving the second derivative of the plastic potential function and the inverse matrix compared with the existing subroutine. Based on the above approaches, a fully implicit backward Euler integral regression algorithm was adopted. The two- and three-di- mensional user subroutines which can consider the asso- ciated or non-associated flow rule were developed on the platform of the finite element program--ABAQUS. To verify the reliability of these two subroutines, firstly, the numerical simulations of the indoor conventional triaxial compression and uniaxial tensile tests were performed, and their results were compared with those of the embedded Mohr-Coulomb model and the analytical approach. Then the main influential factors including the associated or non- associated flow rule, the judgment criteria of slope failure, and the tensile strength of soil were analyzed, and the application of the two-dimensional subroutine in the sta- bility analysis of a typical soil slope was discussed in detail through comparisons with the embedded model and the limit analysis method, which shows that this subroutine is more applicable and reliable than the latter two.展开更多
Typically extrema filtration techniques are based on non-parametric properties such as magnitude of prominences and the widths at half prominence, which cannot be used with data that possess a dynamic nature. In this ...Typically extrema filtration techniques are based on non-parametric properties such as magnitude of prominences and the widths at half prominence, which cannot be used with data that possess a dynamic nature. In this work, an extrema identification that is totally independent of derivative-based approaches and independent of quantitative attributes is introduced. For three consecutive positive terms arranged in a line, the ratio (R) of the sum of the maximum and minimum to the sum of the three terms is always 2/n, where n is the number of terms and 2/3 ≤ R ≤ 1 when n = 3. R > 2/3 implies that one term is away from the other two terms. Applying suitable modifications for the above stated hypothesis, the method was developed and the method is capable of identifying peaks and valleys in any signal. Furthermore, three techniques were developed for filtering non-dominating, sharp, gradual, low and high extrema. Especially, all the developed methods are non-parametric and suitable for analyzing processes that have dynamic nature such as biogas data. The methods were evaluated using automatically collected biogas data. Results showed that the extrema identification method was capable of identifying local extrema with 0% error. Furthermore, the non-parametric filtering techniques were able to distinguish dominating, flat, sharp, high, and low extrema in the biogas data with high robustness.展开更多
Let f be a Maass cusp form for Г0(N) with Fourier coefficients 1 k2. λf(n) and Laplace eigenvalue 1/4 +k2 For real α≠0 and β 〉 0, consider the sum Sx(f; α,β) = ∑n λf(n)e(αnβ)φ(n/X), where ...Let f be a Maass cusp form for Г0(N) with Fourier coefficients 1 k2. λf(n) and Laplace eigenvalue 1/4 +k2 For real α≠0 and β 〉 0, consider the sum Sx(f; α,β) = ∑n λf(n)e(αnβ)φ(n/X), where φ is a smooth function of compact support. We prove bounds for the second spectral moment of Sx (f;α, β), with the eigenvalue tending towards infinity. When the eigenvalue is sufficiently large, we obtain an average bound for this sum in terms of X. This implies that if f has its eigenvalue beyond X1/2+ε, the standard resonance main term for Sx(f; ±2√q 1/2), q ∈Z+, cannot appear in general. The method is adopted from proofs of subconvexity bounds for Rankin-Selberg L-functions for GL(2) × GL(2). It contains in particular a proof of an asymptotic expansion of a well-known oscillatory integral with an enlarged range of Kε≤ L≤ K1-ε. The same bounds can be proved in a similar way for holomorphie cusp forms.展开更多
The subject matter of this paper is an integral with exponential oscillation of phase f(x) weighted by g(x) on a finite interval [α, β]. When the phase f(x) has a single stationary point in (α,β), an nth-o...The subject matter of this paper is an integral with exponential oscillation of phase f(x) weighted by g(x) on a finite interval [α, β]. When the phase f(x) has a single stationary point in (α,β), an nth-order asymptotic expansion of this integral is proved for n ≥ 2. This asymptotic expansion sharpens the classical result for n = 1 by M. N. Huxley. A similar asymptotic expansion was proved by V. Blomer, R. Khan and M. Young under the assumptions that f(x) and g(x) are smooth and g(x) is compactly supported on R. In the present paper, however, these functions are only assumed to be continuously differentiable on [α,β] 2n + 3 and 2n + 1 times, respectively. Because there are no requirements on the vanishing of g(x) and its derivatives at the endpoints α and β, the present asymptotic expansion contains explicit boundary terms in the main and error terms. The asymptotic expansion in this paper is thus applicable to a wider class of problems in analysis, analytic number theory, and other fields.展开更多
基金the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDA25020303).
文摘Based on the pulse-shaping unit in the front end of high-power laser facilities,we propose a new hybrid scheme in a closed-loop control system including wavelet threshold denoising for pretreatment and a first derivative adaptive smoothing filter for smooth pulse recovery,so as to effectively restrain the influence of electrical noise and FM-to-AM modulation in the time–power curve,and enhance the calibration accuracy of the pulse shape in the feedback control system.The related simulation and experiment results show that the proposed scheme can obtain a better shaping effect on the high-contrast temporal shape in comparison with the cumulative average algorithm and orthogonal matching pursuit algorithm combined with a traditional smoothing filter.The implementation of the hybrid scheme mechanism increased the signal-to-noise ratio of the laser pulse from about 11 dB to 30 dB,and the filtered pulse is smooth without modulation,with smoothness of about 98.8%.
文摘Background:Controlling the coronavirus disease 2019(COVID-19)epidemic requires information beyond new and cumulative cases.This study aims to conduct an in-depth analysis by geographic strata:Wuhan City(hereafter referred to as Wuhan)only,Hubei Province(hereafter referred to as Hubei)excluding Wuhan,and China excluding Hubei.Methods:Daily cumulative confirmed COVID-19 cases between December 8,2019(the date of symptom onset based on patients'recall during the investigation),and March 1,2020,from official sources and published studies were analyzed.The second derivative model was used for information extraction.Data analysis was conducted separately for the three strata.Results:A total of 80026 diagnosed COVID-19 cases were reported during the first 85 days of the epidemic,with 49315 cases from Wuhan,17788 from Hubei excluding Wuhan,and 12923 from China excluding Hubei.Analytical results indicate that the COVID-19 epidemic consists of an Acceleration,a Deceleration,and a Stabilization Phase in all three geographic strata,plus a Silent Attack Phase for Wuhan only.Given the reported incubation period of 14 days,effects of the massive anti-epidemic actions were revealed by both the Acceleration and Deceleration Phases.The Acceleration Phase signaled the effect of the intervention to detect the infected;the Deceleration Phase signaled the declines in new infections after the infected were detected,treated and quarantined.Conclusion:Findings of the study provide new evidence to better monitor the epidemic,evaluate its response to intervention,and predict the trend long.In addition to re-evaluating the control of the COVID-19 epidemic in China,this study provided a model for monitoring outbreaks of COVID-19 in different countries across the world.
文摘The hyperbolic function proposed by Abbo- Sloan was employed not only to approach the Mohr- Coulomb criterion but also to express the plastic potential function. A better approximation to the Mohr-Coulomb yield and potential surfaces was achieved by increasing the transition angle and proven to be highly efficient in numerical convergence. When a Gaussian integral point goes into plastic state, two cases on yield stress adjustments were introduced. They may avoid solving the second derivative of the plastic potential function and the inverse matrix compared with the existing subroutine. Based on the above approaches, a fully implicit backward Euler integral regression algorithm was adopted. The two- and three-di- mensional user subroutines which can consider the asso- ciated or non-associated flow rule were developed on the platform of the finite element program--ABAQUS. To verify the reliability of these two subroutines, firstly, the numerical simulations of the indoor conventional triaxial compression and uniaxial tensile tests were performed, and their results were compared with those of the embedded Mohr-Coulomb model and the analytical approach. Then the main influential factors including the associated or non- associated flow rule, the judgment criteria of slope failure, and the tensile strength of soil were analyzed, and the application of the two-dimensional subroutine in the sta- bility analysis of a typical soil slope was discussed in detail through comparisons with the embedded model and the limit analysis method, which shows that this subroutine is more applicable and reliable than the latter two.
文摘Typically extrema filtration techniques are based on non-parametric properties such as magnitude of prominences and the widths at half prominence, which cannot be used with data that possess a dynamic nature. In this work, an extrema identification that is totally independent of derivative-based approaches and independent of quantitative attributes is introduced. For three consecutive positive terms arranged in a line, the ratio (R) of the sum of the maximum and minimum to the sum of the three terms is always 2/n, where n is the number of terms and 2/3 ≤ R ≤ 1 when n = 3. R > 2/3 implies that one term is away from the other two terms. Applying suitable modifications for the above stated hypothesis, the method was developed and the method is capable of identifying peaks and valleys in any signal. Furthermore, three techniques were developed for filtering non-dominating, sharp, gradual, low and high extrema. Especially, all the developed methods are non-parametric and suitable for analyzing processes that have dynamic nature such as biogas data. The methods were evaluated using automatically collected biogas data. Results showed that the extrema identification method was capable of identifying local extrema with 0% error. Furthermore, the non-parametric filtering techniques were able to distinguish dominating, flat, sharp, high, and low extrema in the biogas data with high robustness.
文摘Let f be a Maass cusp form for Г0(N) with Fourier coefficients 1 k2. λf(n) and Laplace eigenvalue 1/4 +k2 For real α≠0 and β 〉 0, consider the sum Sx(f; α,β) = ∑n λf(n)e(αnβ)φ(n/X), where φ is a smooth function of compact support. We prove bounds for the second spectral moment of Sx (f;α, β), with the eigenvalue tending towards infinity. When the eigenvalue is sufficiently large, we obtain an average bound for this sum in terms of X. This implies that if f has its eigenvalue beyond X1/2+ε, the standard resonance main term for Sx(f; ±2√q 1/2), q ∈Z+, cannot appear in general. The method is adopted from proofs of subconvexity bounds for Rankin-Selberg L-functions for GL(2) × GL(2). It contains in particular a proof of an asymptotic expansion of a well-known oscillatory integral with an enlarged range of Kε≤ L≤ K1-ε. The same bounds can be proved in a similar way for holomorphie cusp forms.
基金The authors would like to thank anonymous referees for critical readings and thoughtful comments. Gratitude is also due to Xiumin Ren who gave the authors many helpful suggestions. The second author was partially supported by the National Natural Science Foundation of China (Grant No. 11601271).
文摘The subject matter of this paper is an integral with exponential oscillation of phase f(x) weighted by g(x) on a finite interval [α, β]. When the phase f(x) has a single stationary point in (α,β), an nth-order asymptotic expansion of this integral is proved for n ≥ 2. This asymptotic expansion sharpens the classical result for n = 1 by M. N. Huxley. A similar asymptotic expansion was proved by V. Blomer, R. Khan and M. Young under the assumptions that f(x) and g(x) are smooth and g(x) is compactly supported on R. In the present paper, however, these functions are only assumed to be continuously differentiable on [α,β] 2n + 3 and 2n + 1 times, respectively. Because there are no requirements on the vanishing of g(x) and its derivatives at the endpoints α and β, the present asymptotic expansion contains explicit boundary terms in the main and error terms. The asymptotic expansion in this paper is thus applicable to a wider class of problems in analysis, analytic number theory, and other fields.