本文的主要目的在于提高三维可压缩向列型液晶系统解的最高阶(S阶)空间导数的衰减率。如果初值的HS(S≥3)和范数都是有界的,并且其H3范数足够小,则应用纯能量法,我们给出了解的最高阶空间导数L2范数的最优衰减率为(1+t)−(S2+α2),而在魏...本文的主要目的在于提高三维可压缩向列型液晶系统解的最高阶(S阶)空间导数的衰减率。如果初值的HS(S≥3)和范数都是有界的,并且其H3范数足够小,则应用纯能量法,我们给出了解的最高阶空间导数L2范数的最优衰减率为(1+t)−(S2+α2),而在魏,李和姚的研究中其衰减率仅为(1+t)−(S−12+α2)。Abstract: The major objective of this thesis lies in improving the decay rates for the highest order (S-order) of spatial derivative of the solutions to the 3D system of compressible nematic liquid crystal. If the norms of both HS(S≥3)and for the initial value are bounded, as well as the norm of H3for that is small enough, with applying pure energy method, we give that the optimal decay rates for the highest order of spatial derivative of the solutions in norm of L2are (1+t)−(S2+α2), while that is just (1+t)−(S−12+α2)in Wei, Li and Yao’s study.展开更多
安全帽在保护施工人员免受事故伤害方面发挥着至关重要的作用。然而,由于种种原因,工人们并没有严格执行戴安全帽的规定。为了检测工人是否佩戴安全帽,本文提出了基于YOLOv8改进的目标检测算法(CPAM-P2-YOLOv8)。在YOLOv8的颈部添加CPA...安全帽在保护施工人员免受事故伤害方面发挥着至关重要的作用。然而,由于种种原因,工人们并没有严格执行戴安全帽的规定。为了检测工人是否佩戴安全帽,本文提出了基于YOLOv8改进的目标检测算法(CPAM-P2-YOLOv8)。在YOLOv8的颈部添加CPAM结构,增强网络对图片的特征提取,在YOLOv8的头部引入处理后的小目标检测层P2。CPAM-P2-YOLOv8提高了目标检测的精确度,实验结果表明,改进模型的精确度达到了91%。与YOLOv8对比,CPAM-P2-YOLOv8的mAP50提高了1.0%,参数量减少了17%,同时通过对比发现,CPAM-P2-YOLOv8比YOLOv8在检测小目标方面更有优势。与YOLOv10对比,CPAM-P2-YOLOv8的mAP50提高1.9%。使用知识蒸馏方法,使CPAM-P2-YOLOv8的精确度进一步提升,达到91.4%。Safety helmets play a crucial role in protecting construction workers from accidents and injuries. However, due to various reasons, workers did not strictly adhere to the rule of wearing safety helmets. To detect whether workers are wearing helmets, this article proposes an improved object detection algorithm based on YOLOv8 (CPAM-P2-YOLOv8). Add CPAM structure to the neck network of YOLOv8 to enhance the feature extraction of safety helmets, and introduce a processed small object detection layer P2 at the head of YOLOv8. CPAM-P2-YOLOv8 improved the accuracy of object detection, and experimental results showed that the improved model achieved an accuracy of 91%. Compared with the YOLOv8 model, CPAM-P2-YOLOv8 improved mAP50 by 1.0% and reduced parameter count by 17%. Through comparison, it was found that CPAM-P2-YOLOv8 has more advantages in detecting small targets than YOLOv8. Compared with YOLOv10, the mAP50 of CPAM-P2-YOLOv8 increased by 1.9%. By using the knowledge distillation, the precision of CPAM-P2-YOLOv8 was further improved to 91.4%.展开更多
本文研究并比较了基于MMAe赋权的模型平均下,Wald置信区间,MATA置信区间,及Bootstrap置信区间的覆盖率、区间长度、左右错误率等各方面的表现性能。不同信噪比水平下的模拟显示,Wald置信区间在低信噪比时有更好的覆盖率,高信噪比下,三...本文研究并比较了基于MMAe赋权的模型平均下,Wald置信区间,MATA置信区间,及Bootstrap置信区间的覆盖率、区间长度、左右错误率等各方面的表现性能。不同信噪比水平下的模拟显示,Wald置信区间在低信噪比时有更好的覆盖率,高信噪比下,三者覆盖率相近,MATA置信区间相对长度更短。在与MMA等其他模型平均方法的横向比较中,MMAe的赋权在Wald、MATA及Bootstrap三种置信区间的构建下,均比其他赋权方式在更低的样本量下更早达到名义覆盖率。最后在实例中考察MMAe在不同置信区间下的表现,与模拟表现一致。This article studies and compares the performance of models based on MMAe weighting in terms of coverage, interval length, left and right error rates under average, Wald confidence interval, MATA confidence interval, and Bootstrap confidence interval. Simulations at different levels of signal show that the Wald confidence interval has better coverage at low signal, while at high signal, the three’s confidence interval has similar coverage, and the MATA confidence interval is relatively shorter in length. In the horizontal comparison with other model averaging methods such as MMA, the weighting of MMAe reached nominal coverage earlier than other weighting methods at lower sample sizes under the construction of Wald, MATA, and Bootstrap confidence intervals. Finally, the performance of MMAe at different confidence intervals was examined in the example, which was consistent with the simulation results.展开更多
本文提出了求解具有不连续孔隙度和底部地形的一维多孔浅水方程的高阶平衡保正有限差分AWENO格式,所提出的格式保持了静水稳态的良好平衡特性。在这个数值框架中,采用静水重构方法具有两个主要优点:1) 使用任意单调通量和重新表述源项...本文提出了求解具有不连续孔隙度和底部地形的一维多孔浅水方程的高阶平衡保正有限差分AWENO格式,所提出的格式保持了静水稳态的良好平衡特性。在这个数值框架中,采用静水重构方法具有两个主要优点:1) 使用任意单调通量和重新表述源项的方法获得了良好平衡特性。2) 采用Lax-Friedrichs (LF)通量的一阶方案在适当的时间步长内保持了水高保正性。通过大量的数值算例验证了该格式具有高阶精度和良好平衡特性,所有算例的数值结果与解析解一致。In this paper, we propose a higher-order well-balanced and positivity-preserving finite-difference AWENO scheme for solving the one-dimensional porous shallow water equation with discontinuous porosity and bottom topography. The proposed format maintains the well-balanced property of the hydrostatic steady state. In this numerical framework, the hydrostatic reconstruction (HR) method is employed with two main advantages: 1) The method using arbitrary monotone fluxes and reformulated source terms obtains the well-balanced property. 2) The first-order scheme using Lax-Friedrichs (LF) fluxes and the HR method maintains the water height preserving properties with an appropriate time step. We verify that the scheme has high-order accuracy and well-balanced properties through a large number of numerical examples, and the numerical results of all cases agree with the analytical solutions.展开更多
文摘本文的主要目的在于提高三维可压缩向列型液晶系统解的最高阶(S阶)空间导数的衰减率。如果初值的HS(S≥3)和范数都是有界的,并且其H3范数足够小,则应用纯能量法,我们给出了解的最高阶空间导数L2范数的最优衰减率为(1+t)−(S2+α2),而在魏,李和姚的研究中其衰减率仅为(1+t)−(S−12+α2)。Abstract: The major objective of this thesis lies in improving the decay rates for the highest order (S-order) of spatial derivative of the solutions to the 3D system of compressible nematic liquid crystal. If the norms of both HS(S≥3)and for the initial value are bounded, as well as the norm of H3for that is small enough, with applying pure energy method, we give that the optimal decay rates for the highest order of spatial derivative of the solutions in norm of L2are (1+t)−(S2+α2), while that is just (1+t)−(S−12+α2)in Wei, Li and Yao’s study.
文摘安全帽在保护施工人员免受事故伤害方面发挥着至关重要的作用。然而,由于种种原因,工人们并没有严格执行戴安全帽的规定。为了检测工人是否佩戴安全帽,本文提出了基于YOLOv8改进的目标检测算法(CPAM-P2-YOLOv8)。在YOLOv8的颈部添加CPAM结构,增强网络对图片的特征提取,在YOLOv8的头部引入处理后的小目标检测层P2。CPAM-P2-YOLOv8提高了目标检测的精确度,实验结果表明,改进模型的精确度达到了91%。与YOLOv8对比,CPAM-P2-YOLOv8的mAP50提高了1.0%,参数量减少了17%,同时通过对比发现,CPAM-P2-YOLOv8比YOLOv8在检测小目标方面更有优势。与YOLOv10对比,CPAM-P2-YOLOv8的mAP50提高1.9%。使用知识蒸馏方法,使CPAM-P2-YOLOv8的精确度进一步提升,达到91.4%。Safety helmets play a crucial role in protecting construction workers from accidents and injuries. However, due to various reasons, workers did not strictly adhere to the rule of wearing safety helmets. To detect whether workers are wearing helmets, this article proposes an improved object detection algorithm based on YOLOv8 (CPAM-P2-YOLOv8). Add CPAM structure to the neck network of YOLOv8 to enhance the feature extraction of safety helmets, and introduce a processed small object detection layer P2 at the head of YOLOv8. CPAM-P2-YOLOv8 improved the accuracy of object detection, and experimental results showed that the improved model achieved an accuracy of 91%. Compared with the YOLOv8 model, CPAM-P2-YOLOv8 improved mAP50 by 1.0% and reduced parameter count by 17%. Through comparison, it was found that CPAM-P2-YOLOv8 has more advantages in detecting small targets than YOLOv8. Compared with YOLOv10, the mAP50 of CPAM-P2-YOLOv8 increased by 1.9%. By using the knowledge distillation, the precision of CPAM-P2-YOLOv8 was further improved to 91.4%.
文摘本文研究并比较了基于MMAe赋权的模型平均下,Wald置信区间,MATA置信区间,及Bootstrap置信区间的覆盖率、区间长度、左右错误率等各方面的表现性能。不同信噪比水平下的模拟显示,Wald置信区间在低信噪比时有更好的覆盖率,高信噪比下,三者覆盖率相近,MATA置信区间相对长度更短。在与MMA等其他模型平均方法的横向比较中,MMAe的赋权在Wald、MATA及Bootstrap三种置信区间的构建下,均比其他赋权方式在更低的样本量下更早达到名义覆盖率。最后在实例中考察MMAe在不同置信区间下的表现,与模拟表现一致。This article studies and compares the performance of models based on MMAe weighting in terms of coverage, interval length, left and right error rates under average, Wald confidence interval, MATA confidence interval, and Bootstrap confidence interval. Simulations at different levels of signal show that the Wald confidence interval has better coverage at low signal, while at high signal, the three’s confidence interval has similar coverage, and the MATA confidence interval is relatively shorter in length. In the horizontal comparison with other model averaging methods such as MMA, the weighting of MMAe reached nominal coverage earlier than other weighting methods at lower sample sizes under the construction of Wald, MATA, and Bootstrap confidence intervals. Finally, the performance of MMAe at different confidence intervals was examined in the example, which was consistent with the simulation results.
文摘本文提出了求解具有不连续孔隙度和底部地形的一维多孔浅水方程的高阶平衡保正有限差分AWENO格式,所提出的格式保持了静水稳态的良好平衡特性。在这个数值框架中,采用静水重构方法具有两个主要优点:1) 使用任意单调通量和重新表述源项的方法获得了良好平衡特性。2) 采用Lax-Friedrichs (LF)通量的一阶方案在适当的时间步长内保持了水高保正性。通过大量的数值算例验证了该格式具有高阶精度和良好平衡特性,所有算例的数值结果与解析解一致。In this paper, we propose a higher-order well-balanced and positivity-preserving finite-difference AWENO scheme for solving the one-dimensional porous shallow water equation with discontinuous porosity and bottom topography. The proposed format maintains the well-balanced property of the hydrostatic steady state. In this numerical framework, the hydrostatic reconstruction (HR) method is employed with two main advantages: 1) The method using arbitrary monotone fluxes and reformulated source terms obtains the well-balanced property. 2) The first-order scheme using Lax-Friedrichs (LF) fluxes and the HR method maintains the water height preserving properties with an appropriate time step. We verify that the scheme has high-order accuracy and well-balanced properties through a large number of numerical examples, and the numerical results of all cases agree with the analytical solutions.
