With the development of digital economy, metaverse and blockchain, the inherent economic form changes. In the era of digital economy, changes in value have new characteristics. This paper uses the method of political ...With the development of digital economy, metaverse and blockchain, the inherent economic form changes. In the era of digital economy, changes in value have new characteristics. This paper uses the method of political economy to analyze and demonstrate the composition of value. Then it analyzes the economic reasons for the economic depression, insufficient consumption power and unsalable commodities in the digital economy period. And the article gives a specific solution. It has specific application value for all countries to deal with and pass through the economic depression. It has a theoretical guiding role in the stable development of macro economy in the digital economy period.展开更多
On one hand,to find the sparsest solution to the system of linear equations has been a major focus since it has a large number of applications in many areas;and on the other hand,the system of absolute value equations...On one hand,to find the sparsest solution to the system of linear equations has been a major focus since it has a large number of applications in many areas;and on the other hand,the system of absolute value equations(AVEs)has attracted a lot of attention since many practical problems can be equivalently transformed as a system of AVEs.Motivated by the development of these two aspects,we consider the problem to find the sparsest solution to the system of AVEs in this paper.We first propose the model of the concerned problem,i.e.,to find the solution to the system of AVEs with the minimum l0-norm.Since l0-norm is difficult to handle,we relax the problem into a convex optimization problem and discuss the necessary and sufficient conditions to guarantee the existence of the unique solution to the convex relaxation problem.Then,we prove that under such conditions the unique solution to the convex relaxation is exactly the sparsest solution to the system of AVEs.When the concerned system of AVEs reduces to the system of linear equations,the obtained results reduce to those given in the literature.The theoretical results obtained in this paper provide an important basis for designing numerical method to find the sparsest solution to the system of AVEs.展开更多
Scott formulated his version of Boolean-valued models in 1967, He proved that the V<sup>（B）</sup> is a Boolean-valued model of ZFC, i. e. every axiom of ZFC has Boolean value 1, and assumed the GCH. Then...Scott formulated his version of Boolean-valued models in 1967, He proved that the V<sup>（B）</sup> is a Boolean-valued model of ZFC, i. e. every axiom of ZFC has Boolean value 1, and assumed the GCH. Then, if B satisfies ccc and |B|=2<sup>No</sup>, V<sup>（B）</sup> GCH （see [1]）. In this note we construct the model △<sup>（B）</sup> on the basis of V<sup>（B）</sup>. Our main results are:（1）△<sup>（B）</sup>) is a Booleanvalued model of GB. （2） Assume the GCH. Then, if B satisfies ccc and |B|=2<sup>No</sup>, △<sup>（B）</sup> GCH. （3） The maximum and minimum principle is true in △<sup>（B）</sup>. （4） △<sup>（B）</sup>（B≠{0, 1}） is a Boolean-valued model of QM.展开更多
当移动机器人在行进过程中使用传统人工势场法(artificial potential field method, APF)进行路径规划时,通常会陷入局部最优困境,无法顺利到达目标点。为解决这一问题,首先,对APF算法规划路径失败原因进行分析,其次设置情况判断条件,...当移动机器人在行进过程中使用传统人工势场法(artificial potential field method, APF)进行路径规划时,通常会陷入局部最优困境,无法顺利到达目标点。为解决这一问题,首先,对APF算法规划路径失败原因进行分析,其次设置情况判断条件,判断当机器人陷入局部最小值时,通过在合适位置增加临时引导点的方法,引导其跳出局部极小值点;其次,引入分数阶微积分思想方法结合APF算法,提出混合阶次的分数阶梯度下降法进行位置信息迭代,优化算法的收敛速度和收敛精度;最后,用MATLAB软件对该方法进行仿真,实验结果表明提出的方法可以有效解决局部最小值问题,而且在速度、精度上都有明显的提高,且能适应较为复杂的多障碍物环境,验证了改进方法的有效性、正确性。展开更多
针对滚动轴承振动信号易受噪声影响,难以提取故障特征信息的问题,提出一种奇异值分解(singular value decomposition,SVD)重构结合最小熵反卷积(minimum entropy deconvolution,MED)增强的滚动轴承故障特征提取方法。首先,对振动信号进...针对滚动轴承振动信号易受噪声影响,难以提取故障特征信息的问题,提出一种奇异值分解(singular value decomposition,SVD)重构结合最小熵反卷积(minimum entropy deconvolution,MED)增强的滚动轴承故障特征提取方法。首先,对振动信号进行SVD分解,并计算奇异分量(singular component,SC)对应线性峭度(L-kurtosis)值;其次,根据线性峭度值结合设定阈值筛选SC,叠加得到重构信号;随后,对重构信号利用MED进行增强,凸出信号中周期冲击成分;最后,结合包络解调提取故障特征频率。仿真信号及实测信号分析结果表明,该方法可以降低噪声对振动信号的影响且凸显故障的特征信息,实现故障诊断。展开更多
文摘With the development of digital economy, metaverse and blockchain, the inherent economic form changes. In the era of digital economy, changes in value have new characteristics. This paper uses the method of political economy to analyze and demonstrate the composition of value. Then it analyzes the economic reasons for the economic depression, insufficient consumption power and unsalable commodities in the digital economy period. And the article gives a specific solution. It has specific application value for all countries to deal with and pass through the economic depression. It has a theoretical guiding role in the stable development of macro economy in the digital economy period.
基金This work was supported in part by the National Natural Science Foundation of China(Nos.11171252,11201332 and 11431002).
文摘On one hand,to find the sparsest solution to the system of linear equations has been a major focus since it has a large number of applications in many areas;and on the other hand,the system of absolute value equations(AVEs)has attracted a lot of attention since many practical problems can be equivalently transformed as a system of AVEs.Motivated by the development of these two aspects,we consider the problem to find the sparsest solution to the system of AVEs in this paper.We first propose the model of the concerned problem,i.e.,to find the solution to the system of AVEs with the minimum l0-norm.Since l0-norm is difficult to handle,we relax the problem into a convex optimization problem and discuss the necessary and sufficient conditions to guarantee the existence of the unique solution to the convex relaxation problem.Then,we prove that under such conditions the unique solution to the convex relaxation is exactly the sparsest solution to the system of AVEs.When the concerned system of AVEs reduces to the system of linear equations,the obtained results reduce to those given in the literature.The theoretical results obtained in this paper provide an important basis for designing numerical method to find the sparsest solution to the system of AVEs.
文摘Scott formulated his version of Boolean-valued models in 1967, He proved that the V<sup>（B）</sup> is a Boolean-valued model of ZFC, i. e. every axiom of ZFC has Boolean value 1, and assumed the GCH. Then, if B satisfies ccc and |B|=2<sup>No</sup>, V<sup>（B）</sup> GCH （see [1]）. In this note we construct the model △<sup>（B）</sup> on the basis of V<sup>（B）</sup>. Our main results are:（1）△<sup>（B）</sup>) is a Booleanvalued model of GB. （2） Assume the GCH. Then, if B satisfies ccc and |B|=2<sup>No</sup>, △<sup>（B）</sup> GCH. （3） The maximum and minimum principle is true in △<sup>（B）</sup>. （4） △<sup>（B）</sup>（B≠{0, 1}） is a Boolean-valued model of QM.
文摘当移动机器人在行进过程中使用传统人工势场法(artificial potential field method, APF)进行路径规划时,通常会陷入局部最优困境,无法顺利到达目标点。为解决这一问题,首先,对APF算法规划路径失败原因进行分析,其次设置情况判断条件,判断当机器人陷入局部最小值时,通过在合适位置增加临时引导点的方法,引导其跳出局部极小值点;其次,引入分数阶微积分思想方法结合APF算法,提出混合阶次的分数阶梯度下降法进行位置信息迭代,优化算法的收敛速度和收敛精度;最后,用MATLAB软件对该方法进行仿真,实验结果表明提出的方法可以有效解决局部最小值问题,而且在速度、精度上都有明显的提高,且能适应较为复杂的多障碍物环境,验证了改进方法的有效性、正确性。
