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1.
研究了一个具有三次非线性项的可积的两分量Camassa-Holm系统Cauchy问题解的持久性.通过用权函数估计的方法证明:如果两分量Camassa-Holm系统的初值以及初值的空间导数都以指数形式衰减,则两分量Camassa-Holm系统的强解也在无穷远处以指数形式衰减,进一步,给出了动量的最优衰减估计. 相似文献
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3.
Christina Petschnigg Markus Spitzner Lucas Weitzendorf Jürgen Pilz 《Entropy (Basel, Switzerland)》2021,23(3)
The 3D modelling of indoor environments and the generation of process simulations play an important role in factory and assembly planning. In brownfield planning cases, existing data are often outdated and incomplete especially for older plants, which were mostly planned in 2D. Thus, current environment models cannot be generated directly on the basis of existing data and a holistic approach on how to build such a factory model in a highly automated fashion is mostly non-existent. Major steps in generating an environment model of a production plant include data collection, data pre-processing and object identification as well as pose estimation. In this work, we elaborate on a methodical modelling approach, which starts with the digitalization of large-scale indoor environments and ends with the generation of a static environment or simulation model. The object identification step is realized using a Bayesian neural network capable of point cloud segmentation. We elaborate on the impact of the uncertainty information estimated by a Bayesian segmentation framework on the accuracy of the generated environment model. The steps of data collection and point cloud segmentation as well as the resulting model accuracy are evaluated on a real-world data set collected at the assembly line of a large-scale automotive production plant. The Bayesian segmentation network clearly surpasses the performance of the frequentist baseline and allows us to considerably increase the accuracy of the model placement in a simulation scene. 相似文献
4.
Yongtao LIU 《Frontiers of Mathematics in China》2021,16(3):783
By using the perpetual cutoff method, we prove two discrete versions of gradient estimates for bounded Laplacian on locally finite graphs with exception sets under the condition of (K,N). This generalizes a main result of F. Münch who considers the case of CD(K, ) curvature. Hence, we answer a question raised by Münch. For that purpose, we characterize some basic properties of radical form of the perpetual cutoff semigroup and give a weak commutation relation between bounded Laplacian and perpetual cutoff semigroup in our setting. 相似文献
5.
This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurrence of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap is needed. The main tool used here is a crucial Lemma which reveals to be needed because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions’ regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients. 相似文献
6.
对船舶柴油机而言,润滑油常受到冷却液的污染,引起润滑油劣化变质,从而导致其功能失效。冷却液的主要成分是水、乙二醇及少量的防腐蚀、抗穴蚀、消泡沫等添加剂。将拉曼光谱用于检测润滑油被冷却液污染的浓度,是一种针对复杂混合物的拉曼光谱检测问题,单个拉曼峰强度的定量分析方法无法满足浓度的定量检测。为此,将拉曼光谱分析和LSTM神经网络数据挖掘方法应用于检测润滑油冷却液污染的浓度。在实验室条件下,配制了冷却液污染浓度为2%,1.5%,1%,0.5%,0.25%和0%的柴油机润滑油油样,对每个油样取样50次,并进行拉曼光谱分析,共获得300个拉曼光谱数据,随机抽取其中80%的数据作为神经网络训练样本,剩余20%的数据作为测试样本,拉曼光谱样本数据的光谱范围为300~2 000 cm-1;对数据进行预处理,包括采样、拟合、离散点平均梯度估计等;构建训练样本集,将LSTM神经网络和多层全连接层(FC)结合,建立4种不同的神经网络模型结构;得到其在训练集和测试集上的平均误差曲线、测试集上的检测准确率曲线。分析结果表明,FCs,LSTM-FCs-1,LSTM-FCs-2和LSTM-FCs-3等4种神经网络模型,检测准确率分别为96.7%,93.3%,98.3%和83.3%。选取任意1%的波数点,加入幅值随机正负变化1%的噪声之后,4种神经网络模型的检测准确率分别为88.3%,90.0%,96.7%和78.3%。可见,相比于其他3种神经网络结构模型,LSTM-FCs-2模型更适用于进行润滑油冷却液污染的定量估计,加噪后最高准确率仍可以达到96.7%,鲁棒性优于其他三种模型。拉曼光谱结合LSTM网络中的LSTM-FCs-2模型,应用于冷却液污染浓度分别为0.2%和0.4%的实际油样检测,相对误差分别为5.0%和7.5%,结果表明该方法可用于在用润滑油冷却液污染浓度的检测。 相似文献
7.
Boniface Nkemzi Michael Jung 《Numerical Methods for Partial Differential Equations》2021,37(1):836-853
Solutions of boundary value problems in three‐dimensional domains with edges may exhibit singularities which are known to influence both the accuracy of the finite element solutions and the rate of convergence in the error estimates. This paper considers boundary value problems for the Poisson equation on typical domains Ω ? ?3 with edge singularities and presents, on the one hand, explicit computational formulas for the flux intensity functions. On the other hand, it proposes and analyzes a nonconforming finite element method on regular meshes for the efficient treatment of the singularities. The novelty of the present method is the use of the explicit formulas for the flux intensity functions in defining a postprocessing procedure in the finite element approximation of the solution. A priori error estimates in H1(Ω) show that the present algorithm exhibits the same rate of convergence as it is known for problems with regular solutions. 相似文献
8.
Taking flood catastrophe risk in China as the research background, aiming at the characteristics of flood loss ``low frequency and high loss', Bayesian inference method is used to fit the loss distribution, and Bayesian inference is used to obtain the loss frequency distribution and loss quota distribution of flood in China.
On this basis, Monte Carlo simulation method is used to calculate the probability distribution of annual flood loss in China under different trigger conditions, and then CAPM is used to study the pricing of flood catastrophe bonds in China. It is concluded that under different trigger conditions, as the trigger value increases gradually, the corresponding trigger is triggered. Comparing the three types of bonds, it can be found that the price of bonds decreases with the decrease of principal guarantee ratio and the increase of principal loss ratio, that is, the investment risk is directly proportional to the return, which provides reference for
issuing flood catastrophe bonds in China. 相似文献
9.
当初值不光滑时,时间分数阶齐次扩散方程数值方法的精度会下降.为了得到高阶时间收敛格式,提出加权移位的Grünwald-Letnikov的修正格式,运用Lubich的修正方法,得到非光滑时间分数阶齐次扩散方程的收敛阶仍为O(k2).最后,通过数值算例验证了数值计算结果与理论计算结果一致. 相似文献
10.