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英文中文

Some new results for $ B_1 $-matrices 关于$ B_1 $-矩阵的一些新结果

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023244

Yan Li, Yaqiang Wang

The class of $ B_1 $-matrices is a subclass of $ P $-matrices and introduced as a generalization of $ B $-matrices. In this paper, we present several properties for $ B_1 $-matrices. Then, the infinity norm upper bound for the inverse of $ B_1 $-matrices is obtained. Furthermore, the error bound for the linear complementarity problem of $ B_1 $-matrices is presented. Finally, some numerical examples are given to illustrate our results.

$ B_1 $-矩阵是$ P $-矩阵的一个子类，是作为$ B $-矩阵的推广引入的。本文给出了$ B_1 $-矩阵的几个性质。然后，得到了$ B_1 $-矩阵逆的无穷范数上界。进一步给出了$ B_1 $-矩阵线性互补问题的误差界。最后，给出了一些数值算例来说明我们的结果。

引用次数: 0

Application of Improved Jellyfish Search algorithm in Rotate Vector reducer fault diagnosis 改进水母搜索算法在旋转矢量减速器故障诊断中的应用

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023250

Xiaoyan Wu, Guowen Ye, Yongming Liu, Zhuanzhe Zhao, Zhibo Liu, Yu Chen

In order to overcome the low accuracy of traditional Extreme Learning Machine (ELM) network in the performance evaluation of Rotate Vector (RV) reducer, a pattern recognition model of ELM based on Ensemble Empirical Mode Decomposition (EEMD) fusion and Improved artificial Jellyfish Search (IJS) algorithm was proposed for RV reducer fault diagnosis. Firstly, it is theoretically proved that the torque transmission of RV reducer has periodicity during normal operation. The characteristics of data periodicity can be effectively reflected by using the test signal periodicity characteristics of rotating machinery and EEMD. Secondly, the Logistic chaotic mapping of population initialization in JS algorithm is replaced by tent mapping. At the same time, the competition mechanism is introduced to form a new IJS. The simulation results of standard test function show that the new algorithm has the characteristics of faster convergence and higher accuracy. The new algorithm was used to optimize the input layer weight of the ELM, and the pattern recognition model of IJS-ELM was established. The model performance was tested by XJTU-SY bearing experimental data set of Xi'an Jiaotong University. The results show that the new model is superior to JS-ELM and ELM in multi-classification performance. Finally, the new model is applied to the fault diagnosis of RV reducer. The results show that the proposed EEMD-IJS-ELM fault diagnosis model has higher accuracy and stability than other models.

针对传统极限学习机(ELM)网络在RV减速器性能评估中准确率较低的问题，提出了一种基于集成经验模态分解(EEMD)融合和改进人工水母搜索(IJS)算法的ELM模式识别模型，用于RV减速器故障诊断。首先，从理论上证明了RV减速器在正常运行时的转矩传递具有周期性。利用旋转机械和EEMD测试信号的周期性特征，可以有效地反映数据的周期性特征。其次，将JS算法中人口初始化的Logistic混沌映射替换为帐篷映射。同时引入竞争机制，形成新的IJS。标准测试函数的仿真结果表明，新算法具有收敛速度快、精度高等特点。利用该算法对ELM的输入层权值进行优化，建立了IJS-ELM的模式识别模型。利用西安交通大学的XJTU-SY轴承实验数据集对模型的性能进行了测试。结果表明，新模型在多分类性能上优于JS-ELM和ELM。最后，将该模型应用于RV减速器的故障诊断。结果表明，所建立的EEMD-IJS-ELM故障诊断模型具有较高的准确性和稳定性。

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引用次数: 0

Elliptic and multiple-valued solutions of some higher order ordinary differential equations 若干高阶常微分方程的椭圆解和多值解

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023302

Guoqiang Dang

In the present paper, by the complex method, the meromorphic solutions of the higher order ordinary differential equation $ w^{(5)}+aw^{''}+bw^2-cw+d = 0 $ are investigated, where $ a, b, c, d $ are constant complex numbers, and $ b neq0 $. Furthermore, by Theorem 1.1, we built elliptic and multiple-valued solutions for the higher order ordinary differential equations $ u^{(6)}-u^{(5)}+u'^2-2u'u+u^2+2u'-2u+1 = 0 $ and $ u^{(6)}-u^{(5)}+au^{'''}-au''+bu'^2-2bu'u+bu^2-cu'+cu+d = 0 $. At the end, we give some new meromorphic solutions for two higher-order KdV-like equations.

本文用复形方法研究了一类高阶常微分方程$ w^{(5)}+aw^{"}+bw^2-cw+d = 0 $的亚纯解，其中$ a, b, c, d $为常复数，$ b neq0 $。进一步，利用1.1定理，构造了高阶常微分方程$ u^{(6)}-u^{(5)}+u'^2-2u'u+u^2+2u'-2u+1 = 0 $和$ u^{(6)}-u^{(5)}+au^{'}-au' +bu'^2-2bu'u+bu^2-cu'+cu+d = 0 $的椭圆解和多值解。最后给出了两个高阶类kdv方程的一些新的亚纯解。

引用次数: 2

Multi-features combinatorial optimization for keyframe extraction 关键帧提取的多特征组合优化

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023304

Lei Ma, Weiyu Wang, Yaozong Zhang, Yu Shi, Zhenghua Huang, Hanyu Hong

Recent advancements in network and multimedia technologies have facilitated the distribution and sharing of digital videos over the Internet. These long videos contain very complex contents. Additionally, it is very challenging to use as few frames as possible to cover the video contents without missing too much information. There are at least two ways to describe these complex videos contents with minimal frames: the keyframes extracted from the video or the video summary. The former lays stress on covering the whole video contents as much as possible. The latter emphasizes covering the video contents of interest. As a consequence, keyframes are widely used in many areas such as video segmentation and object tracking. In this paper, we propose a keyframe extraction method based on multiple features via a novel combinatorial optimization algorithm. The key frame extraction is modeled as a combinatorial optimization problem. A fast dynamic programming algorithm based on a forward non-overlapping transfer matrix in polynomial time and a 0-1 integer linear programming algorithm based on an overlapping matrix is proposed to solve our maximization problem. In order to quantitatively evaluate our approach, a long video dataset named 'Animal world' is self-constructed, and the segmentation evaluation criterions are introduced. A good result is achieved on 'Animal world' dataset and a public available Keyframe-Sydney KFSYD dataset [1].

网络和多媒体技术的最新进展促进了数字视频在互联网上的分发和共享。这些长视频包含非常复杂的内容。此外，使用尽可能少的帧来覆盖视频内容而不丢失太多信息是非常具有挑战性的。用最少的帧来描述这些复杂的视频内容，至少有两种方法:从视频中提取关键帧或视频摘要。前者强调尽可能覆盖整个视频内容。后者强调覆盖感兴趣的视频内容。因此，关键帧在视频分割和目标跟踪等领域得到了广泛的应用。本文通过一种新的组合优化算法，提出了一种基于多特征的关键帧提取方法。关键帧提取是一个组合优化问题。提出了一种基于多项式时间前向无重叠传递矩阵的快速动态规划算法和一种基于重叠矩阵的0-1整数线性规划算法来解决最大化问题。为了定量评价我们的方法，我们构建了一个名为“动物世界”的长视频数据集，并引入了分割评价标准。在“动物世界”数据集和公开可用的关键帧-悉尼KFSYD数据集[1]上取得了很好的结果。

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引用次数: 0

Dynamic analysis of reaction-diffusion dual carbon model considering economic development in China 考虑中国经济发展的反应-扩散双碳模型动态分析

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023126

Yanchuang Hou, Chunyue Wei, Yuting Ding

In this paper, a reaction-diffusion dual carbon model associated with Dirichlet boundary condition is proposed under the influence of economic development in China. First, we enumerate and analyse some influencing factors of carbon emission and carbon absorption, and select economic development as the influence factor of carbon emission. Second, we establish a model associated with dual carbon and analyse the existence and stability of equilibrium and the existence of bifurcations. Finally, we analyse and predict for the value of parameters. Numerical simulations are presented to support our theory results. Combined with theoretical analysis and numerical simulations, we obtain that China can achieve carbon peak before 2030. If we want to achieve carbon neutral before 2060, it requires efforts from all of parts of society. Therefore, we put forward some practical suggestions to achieve carbon neutrality and carbon peak on schedule in China for the next few decades.

本文在中国经济发展的影响下，提出了一个与Dirichlet边界条件相关的反应-扩散双碳模型。首先，我们列举和分析了碳排放和碳吸收的影响因素，并选择经济发展作为碳排放的影响因素。其次，我们建立了一个与双碳相关的模型，并分析了平衡的存在性和稳定性以及分岔的存在性。最后，对各参数的取值进行了分析和预测。数值模拟支持了我们的理论结果。结合理论分析和数值模拟，得出中国可以在2030年前达到碳峰值。如果我们想在2060年之前实现碳中和，就需要社会各方面的努力。因此，我们提出了中国未来几十年如期实现碳中和和碳峰值的一些切实可行的建议。

引用次数: 1

Local well-posedness of perturbed Navier-Stokes system around Landau solutions 朗道解周围摄动Navier-Stokes系统的局部适定性

IF 0.8 4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/ERA.2021010

Jingjing Zhang, Ting Zhang

In this paper, we consider the perturbed Navier–Stokes equations around the Landau solution and investigate the global well-posedness results of the perturbed system with the small initial data in the [Formula: see text] space, where [Formula: see text].

本文考虑围绕Landau解的摄动Navier-Stokes方程，在[公式:见文]空间中研究初始数据较小的摄动系统的全局适定性结果，其中[公式:见文]。

引用次数: 3

Dynamical behavior of Benjamin-Bona-Mahony system with finite distributed delay in 3D 三维有限分布时滞Benjamin-Bona-Mahony系统的动力学行为

4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.20233348

Lingrui Zhang, Xue-zhi Li, Keqin Su

We study the Benjamin-Bona-Mahony model with finite distributed delay in 3D, which depicts the dispersive impact of long waves. Based on the well-posedness of model, the family of pullback attractors for the evolutionary processes generated by a global weak solution has been obtained, which is unique and minimal, via verifying asymptotic compactness in functional space with delay $ C_V $ and topological space $ Vtimes C_V $, where the energy equation method and a retarded Gronwall inequality are utilized.

< >< >我们研究了三维有限分布延迟的Benjamin-Bona-Mahony模型，该模型描述了长波的色散影响。在模型适定性的基础上，利用能量方程法和延迟Gronwall不等式，验证了具有延迟C_V $的泛函空间和拓扑空间V乘以C_V $上的渐近紧性，得到了由全局弱解生成的演化过程的拉回吸引子族的唯一性和极小性。

引用次数: 0

Transition characteristics of the dynamic behavior of a vehicle wheel-rail vibro-impact system 车辆轮轨振动冲击系统动力学特性的过渡特性

4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023357

Yang Jin, Wanxiang Li, Hongbing Zhang

A two-degree-of-freedom vehicle wheel-rail impact vibration system model is developed, and the equivalent impact stiffness and damping of the rail are fitted applying ABAQUS, taking into account the high and low irregularity generated by the welded joints of the rail. A wheel-rail periodic interface with fixed impact was selected as the Poincaré map, and the fourth-order Runge-Kutta numerical method with variable step size was used to solve the system response. The dynamic characteristics of the system are investigated using a combination of the Bifurcation diagram, Phase plane diagram, the Poincaré map, the Time-domain diagram and the Frequency-domain diagram. It is verified that the vehicle wheel-rail impact vibration system has Hopf bifurcation, Neimark-Sacker bifurcation, Period-doubling bifurcation and Boundary crisis, and there are rich and complex nonlinear dynamic behavior changes. The research on the bifurcation and chaos characteristics of vehicle wheel-rail impact vibration systems can provide a reference for improving the stability of vehicle operation in engineering practice as well as the prediction and control of chaos in vehicle vibration reduction design.

& lt; abstract>建立了二自由度车辆轮轨冲击振动系统模型，考虑钢轨焊接接头产生的高低不规则性，应用ABAQUS拟合了钢轨的等效冲击刚度和阻尼;选取固定碰撞的轮轨周期界面作为庞卡罗图，采用变步长四阶龙格-库塔数值方法求解系统响应。采用分岔图、相平面图、庞卡罗图、时域图和频域图相结合的方法研究了系统的动态特性。验证了车辆轮轨碰撞振动系统存在Hopf分岔、neimmark - sacker分岔、倍周期分岔和边界危机，存在丰富而复杂的非线性动力学行为变化。研究车辆轮轨碰撞振动系统的分岔与混沌特性，可为工程实践中提高车辆运行的稳定性以及车辆减振设计中的混沌预测与控制提供参考。& lt; / abstract>

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引用次数: 0

Investigation of the global dynamics of two exponential-form difference equations systems 两个指数型差分方程组的全局动力学研究

4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023338

Merve Kara

In this study, we investigate the boundedness, persistence of positive solutions, local and global stability of the unique positive equilibrium point and rate of convergence of positive solutions of the following difference equations systems of exponential forms:

begin{document}$ begin{equation*} Upsilon_{n+1} = frac{Gamma_{1}+delta_{1}e^{-Psi_{n-1}}}{Theta_{1}+Psi_{n}}, Psi_{n+1} = frac{Gamma_{2}+delta_{2}e^{-Omega_{n-1}}}{Theta_{2}+Omega_{n}}, Omega_{n+1} = frac{Gamma_{3}+delta_{3}e^{-Upsilon_{n-1}}}{Theta_{3}+Upsilon_{n}}, end{equation*} $end{document}

begin{document}$ begin{equation*} Upsilon_{n+1} = frac{Gamma_{1}+delta_{1}e^{-Psi_{n-1}}}{Theta_{1}+Upsilon_{n}}, Psi_{n+1} = frac{Gamma_{2}+delta_{2}e^{-Omega_{n-1}}}{Theta_{2}+Psi_{n}}, Omega_{n+1} = frac{Gamma_{3}+delta_{3}e^{-Upsilon_{n-1}}}{Theta_{3}+Omega_{n}}, end{equation*} $end{document}

for $ nin mathbb{N}_{0} $, where the initial conditions $ Upsilon_{-j} $, $ Psi_{-j} $, $ Omega_{-j} $, for $ jin{0, 1} $ and the parameters $ Gamma_{i} $, $ delta_{i} $, $ Theta_{i} $ for $ iin{1, 2, 3} $ are positive constants.

<abstract>In this study, we investigate the boundedness, persistence of positive solutions, local and global stability of the unique positive equilibrium point and rate of convergence of positive solutions of the following difference equations systems of exponential forms: <disp-formula> <label/> <tex-math id="FE1"> begin{document}$ begin{equation*} Upsilon_{n+1} = frac{Gamma_{1}+delta_{1}e^{-Psi_{n-1}}}{Theta_{1}+Psi_{n}}, Psi_{n+1} = frac{Gamma_{2}+delta_{2}e^{-Omega_{n-1}}}{Theta_{2}+Omega_{n}}, Omega_{n+1} = frac{Gamma_{3}+delta_{3}e^{-Upsilon_{n-1}}}{Theta_{3}+Upsilon_{n}}, end{equation*} $end{document} </tex-math></disp-formula> <disp-formula> <label/> <tex-math id="FE2"> begin{document}$ begin{equation*} Upsilon_{n+1} = frac{Gamma_{1}+delta_{1}e^{-Psi_{n-1}}}{Theta_{1}+Upsilon_{n}}, Psi_{n+1} = frac{Gamma_{2}+delta_{2}e^{-Omega_{n-1}}}{Theta_{2}+Psi_{n}}, Omega_{n+1} = frac{Gamma_{3}+delta_{3}e^{-Upsilon_{n-1}}}{Theta_{3}+Omega_{n}}, end{equation*} $end{document} </tex-math></disp-formula> for $ nin mathbb{N}_{0} $, where the initial conditions $ Upsilon_{-j} $, $ Psi_{-j} $, $ Omega_{-j} $, for $ jin{0, 1} $ and the parameters $ Gamma_{i} $, $ delta_{i} $, $ Theta_{i} $ for $ iin{1, 2, 3} $ are positive constants.</abstract>

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引用次数: 0

The Riccati-Bernoulli subsidiary ordinary differential equation method to the coupled Higgs field equation 耦合希格斯场方程的里卡蒂-伯努利辅助常微分方程解法

4区数学 Q1 MATHEMATICS

Electronic Research Archive

Pub Date : 2023-01-01 DOI: 10.3934/era.2023342

Yi Wei

By using the Riccati-Bernoulli (RB) subsidiary ordinary differential equation method, we proposed to solve kink-type envelope solitary solutions, periodical wave solutions and exact traveling wave solutions for the coupled Higgs field (CHF) equation. We get many solutions by applying the Bäcklund transformations of the CHF equation. The proposed method is simple and efficient. In fact, we can deal with some other classes of nonlinear partial differential equations (NLPDEs) in this manner.

利用riccti - bernoulli (RB)辅助常微分方程方法，提出了求解耦合希格斯场(CHF)方程的扭结型包络孤立解、周期波解和精确行波解的方法。通过对CHF方程进行Bäcklund变换，我们得到了许多解。该方法简单、高效。事实上，我们可以用这种方法处理其他一些类型的非线性偏微分方程(NLPDEs)。</ </abstract>

引用次数: 0

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