Radial solution of the Logarithmic Laplacian system

The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.

Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation

This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.

ENTIRE SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS HAVING THE SAME ORDER

In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.

可调频旋转磁场仪的装置设计与磁场测量

在教学演示仪器中利用三相交流电产生旋转磁场的传统方法存在仪器损耗大、安全隐患多、成本昂贵等问题。本论文设计了一种可调频旋转磁场的产生装置,在四个辐射状横放的带铁芯螺线管中通入低压直流电,通过PLC板编程对电流进行换向,同时改变换向时间可使置入装置中心的小磁针的偏转周期发生变化,从而达到可调频的效果。螺线管中通入单相恒定直流电时,小磁针不发生偏转;通入双相矩形脉冲电流时,小磁针以45°角步进旋转。磁场方向的转速取决于电流的换向频率。该装置不仅规避了传统方法的不足,且同时兼具定性演示和定量测量双重功能,可作为一款性能优异的实验教学仪器。

大堤路快速路(二环—三环段)工程总体设计

大堤路作为射线快速路,在加强环线快速路沟通的同时,也要充分发挥环线快速路的分流及屏蔽作用,尽可能减缓快速交通对中心城区的拥堵,因此,工程方案需遵循交通规划“多级分流”的思路。同时考虑上沙地块规划滞后性,方案也需兼顾近远期。

基于线性自抗扰控制的纵向舰载机直接升力全自动着舰控制

舰载机的最终着舰过程受到强烈的舰尾流的干扰,为了抑制舰尾流扰动,本文提出一种基于径向基函数神经网络(radial basis functions neural network,RBFNN)结合线性自抗扰控制(liner active disturbance rejection control,LADRC)的创新设计方法,确保舰载机直接升力控制自动着舰系统的鲁棒性。LADRC将阵风扰动和系统不确定项作为总扰动,通过线性扩展状态观测器(liner extended state observer,LESO)对总扰动进行估计,并通过线性反馈控制律进行补偿,然后根据系统状态利用RBFNN在线调整LADRC控制器的参数,并构建Lyapunov函数以证明闭环系统的稳定性。舰载机跟踪理想下滑道的仿真结果表明,RBF-LADRC的抗干扰性、鲁棒性和跟踪精度均优于与之对比的控制方法。

Application of neural networks for permanent magnet synchronous motor direct torque control

Neural networks require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. The application of neural networks to control interior permanent magnet synchronous motor using direct torque control （DTC） is discussed. A neural network is used to emulate the state selector of the DTC. The neural networks used are the back-propagation and radial basis function. To reduce the training patterns and increase the execution speed of the training process, the inputs of switching table are converted to digital signals, i.e., one bit represent the flux error, one bit the torque error, and three bits the region of stator flux. Computer simulations of the motor and neural-network system using the two approaches are presented and compared. Discussions about the back-propagation and radial basis function as the most promising training techniques are presented, giving its advantages and disadvantages. The system using back-propagation and radial basis function networks controller has quick parallel speed and high torque response.

Electron acceleration by tightly focused radially polarized few-cycle laser pulses

Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. The resulting field distribution is significantly different from that based on the paraxial approximation for pulses with either small or large beam diameters. We compare the electron accelerations obtained with the two solutions and find that the energy gain obtained with our new solution is usually much larger than that with the paraxial approximation solution.

Reversal of radial glow distribution in helicon plasma induced by reversed magnetic field

In this work, the reversal of radial glow distribution induced by reversed magnetic field is reported. Based on the Boswell antenna which is symmetric and insensitive to the magnetic field direction, it seems such a phenomenon in theory appears impossible. However, according to the diagnostic of the helicon waves by magnetic probe, it is found that the direction of magnetic field significantly affects the propagation characteristic of helicon waves, i.e., the interchange of the helicon waves at the upper and the lower half of tube was caused by reversing the direction of magnetic field. It is suggested that the variation of helicon wave against the direction of magnetic field causes the reversed radial glow distribution. The appearance of the traveling wave does not only improve the discharge strength, but also determines the transition of the discharge mode.

结构区间参数反求的DIRECT算法

提出一种基于DIRECT算法的结构区间参数反求方法。对于结构不确定性参数反求问题,一般转化为不确定性传播和模型参数优化的双层求解问题。首先,区间模型用来描述响应和待识别结构参数的不确定性,并建立了相应区间参数反求模型。其次,在迭代反求过程中自适应更新径向基函数用来近似原系统模型,并利用DIRECT算法来求解内层不确定性传播问题。最后,通过遗传算法来求解外层的优化模型,从而识别结构不确定性参数的区间。数值算例用来验证了该方法的正确性和有效性,并将该方法应用来反求车辆乘员约束系统中的不确定性参数。

税收竞争对绿色全要素生产率的影响——基于长江三角洲、长江中游城市群视角

随着长江经济带上升为国家战略,税收等经济力量不断注入的同时,其生态问题也逐渐显露。视角从长江三角洲城市群、长江中游城市群出发,采用非径向方向距离函数构建绿色全要素生产率,以核密度估计对绿色全要素生产率进行演进趋势刻画,对双城市群内的税收竞争利用系统GMM与非对称效应模型进行识别,通过双向固定效应模型与门限模型探究税收竞争对绿色全要素生产率的影响。结果表明在长江三角洲城市群内绿色全要素生产率差异过大,长江中游城市群绿色全要素生产率增长缓慢;双城市群中,存在相互模仿的税收策略互补行为,税收竞争以逐高竞争为主;长江三角洲城市群内的税收竞争对绿色全要素生产率存在抑制作用,长江三角洲城市群内随着税收竞争程度逐渐增大,对绿色全要素生产率存在先促进后抑制的影响效果。

制造业集聚、异质性投资与黄河流域能源环境效率

积极推进多元投融资机制,合理布局制造业集聚区对建设黄河流域生态保护和高质量发展先行区尤为重要。在考虑生态环境承载力的前提下,运用非径向方向距离函数测度2006~2021年黄河流域能源环境效率,通过空间Tobit杜宾模型研究制造业本文集聚对能源环境效率的非线性影响,并探讨异质性投资的作用。结果表明制造业集聚对能源环境效率存在倒U型影响,邻地的制造业集聚对本地的能源环境效率具有正U型溢出效应;机制分析表明在制造业集聚与能源环境效率的关系中,内资存在倒U型影响,港澳台投资发挥着正U型作用,外资存在正向的线性影响;区域异质性分析发现上游制造业集聚与能源环境效率存在正U型关系,中游制造业集聚与能源环境效率存在倒U型关系,下游制造业集聚对能源环境效率不存在显著的影响。

基于面波走时的三维结构面波直接成像:方法综述与应用

利用面波频散数据进行各向同性和各向异性横波速度结构成像是研究全球和区域构造变形、获取地壳上地幔和近地表精细结构的一种非常有效的方法.传统的基于频散数据的面波成像通常采用两步法,即首先反演二维相速度或群速度分布图,然后再基于格点的纯路径频散反演格点下方的一维横波速度模型,之后再拼合成三维速度模型.在本文中我们较为详细地综述新发展的基于面波频散走时的三维面波直接成像方法体系,即面波一步法成像.该方法体系包括通过所有路径、不同频率的面波频散走时直接反演三维各向同性横波速度结构的方法(DSurfTomo)、直接反演三维方位各向异性横波速度结构的方法(DAzimSurfTomo),以及直接反演三维径向各向异性横波速度结构的方法(DRadiSurfTomo).新的面波直接成像方法计算不同周期的面波射线路径,从而更好地考虑复杂结构下面波射线路径弯曲对成像精度的影响.随后我们介绍面波直接成像方法的应用实例,包括地壳上地幔及地壳浅部的多尺度各向同性和各向异性横波速度结构的成像,这些成像研究为认识区域构造演化、孕震构造、断裂带浅部结构、成矿构造、城市地下结构等提供了重要的约束.最后我们讨论面波直接成像方法的频散数据及模型参数化问题,以及基于有限频理论的面波直接成像和面波全波形成像,讨论并展望在面波直接成像方法框架下面波频散数据与其他地震或地球物理数据的联合成像问题.

十字形内置破片定向战斗部破片的飞散特性

针对低附带弹药毁伤需求,设计了一种十字形内置破片定向战斗部,根据目标方位可选择不同起爆模式,进而控制破片的径向飞散特性,在目标区域内形成杀伤破片实现定向毁伤,在非目标区域内实现低附带毁伤。采用数值模拟研究了相邻2点起爆、相邻3点起爆两种模式下定向战斗部起爆时破片的驱动过程,给出了各个位置处破片的飞散速度、径向飞散角度等特征参数;制备了2发单元样弹并开展了地面静爆实验,通过高速摄影及靶板上破片的穿孔分布特征实测出破片的速度及径向飞散角,与数值模拟结果对比,验证了模拟的准确性。在此基础上,通过引入能量分配角建立了破片速度的修正公式,并根据模拟结果对公式参数进行了拟合分析。结果表明:相邻2点起爆、相邻3点起爆模式下,战斗部定向杀伤区破片径向飞散角分别控制在145°、65°以内,且该区域内的破片占破片总数的比例分别达到了50.4%、43%;同时,破片速度呈现梯次分布,介于535~770 m/s之间,对1.5 mm厚的Q235A钢板的穿甲率分别达到了94.4%、84.6%,可实现对轻型车辆类目标的毁伤,其余区域则为低附带安全区;基于能量分配模型求得的破片速度理论计算值与模拟值基本吻合。研究结果可为低附带杀伤战斗部研制提供新的设计思路。

油松不同径向深度与方位树干液流特性研究

为了解油松树干液流与木质部解剖构造的关系,分析树木构造对水分输送功能的影响,利用热扩散探针法(TDP)测定不同径向深度和方位的树干液流速率,采用富兰克林离析法测定相应部位的木材解剖构造特征,进而分析、探讨木质部解剖构造特征与树干液流的响应关系。结果表明,在径向距形成层不同深度处的液流速率顺序为V_(30~50 mm)>V_(20~30 mm)>V_(0~10 mm)>V_(10~20 mm),最大值和最小值分别为0.0097、0.0025 g·cm^(-2)·s^(-1);各深度液流速率之间均呈显著线性相关关系;不同方位间液流速率大小顺序为西侧>东侧>北侧>南侧,西侧最大液流速率为0.0111 g·cm^(-2)·s^(-1),南侧最小液流速率为0.0030 g·cm^(-2)·s^(-1);北侧液流速率与其他方位间液流速率具有高度相关性。不同径向深度管胞长度和长宽比在距形成层40 mm处最大,管胞宽度在距形成层40 mm处最小;不同方位管胞长度和长宽比在西侧最大,管胞宽度在西侧最小,与树干液流变化趋势基本一致;管胞长度和长宽比越大,管胞宽度越小,树干液流速率越快。不同径向深度与方位树干液流速率与解剖构造之间响应程度较高。

Effect of transverse static magnetic field on radial microstructure of hypereutectic aluminum alloy during directional solidification

The effect of different scales thermoelectric magnetic convection(TEMC)on the radial solidification microstructure of hypereutectic Al alloy has been investigated under transverse static magnetic field during directional solidification,focusing on the formation of freckle.Our experimental and numerical simulation results indicate that the TEMC circulation at sample scale under transverse static magnetic field leads to the enrichment of solute Al on one side of the sample.The TEMC and the solute enrichment degree increase with the increase of magnetic field when the magnetic field increases to 0.5 T.The enrichment degree of solute elements under magnetic field is affected by temperature gradient and growth rate.The non-uniform distribution of solute Al in the radial direction of the sample results in the non-uniform distribution of primary dendrite arm spacing(PDAS).Moreover,the applied magnetic field can lead to freckle formation and its number increases with the increase of magnetic field.The change of freckle is consistent with the anisotropy TEMC caused by the anisotropy of primary dendrite or primary dendrite network under magnetic field.Finally,the mechanism of synergism effect of the anisotropy TEMC,the distribution of solute Al and the PDAS on freckle formation and evolution is studied during directional solidification under magnetic field.

Mechanical behaviour of wood compressed in radial direction-part I.New method of determining the yield stress of wood on the stress-strain curve

A test equipment was developed,which allows for real time observation of the deformation behav-ior of wood cellular structure under a compression load applied in radial direction.Compression tests were performed on jack pine(Pinus banksiana)and balsam poplar(Populus balsamifera)spec-imens to explore the relationship between the yield stress and the first failure occurring in wood cell layers during radial compression.The microstructural changes for P.banksiana and P.bal-samifera wood below and above the yield point were analyzed.The study results showed that for P.banksiana the first failure of wood cells occurred at the first earlywood layer,while for P.balsamifera it occurred at the layer with the largest vessels.The first failure of wood cell layer for each species tested was found to correspond to the yield point on the stress-strain curve.A new method of determining the yield stress for wood specimens under radial compression was developed.

Mechanical behaviour of wood compressed in radial direction:Part II.Influence of temperature and moisture content

This study investigated the influence of pressing temperature and moisture content on the me-chanical properties of wood compressed in radial direction.Jack pine(Pinus banksiana)and bal-sam poplar(Populus balsamifera)specimens were tested under a combination of pressing temper-ature(20℃,55℃,90℃,and 125℃)and wood moisture content(2%,7%,12%,and 17%).The yield stress(_(δ)y)and modulus of elasticity(MOE)of the specimens were determined from the stress-strain response.It was found that an increase in either pressing temperature or moisture content of wood generally caused a decrease in the mechanical properties for both species.The t-test results revealed that jack pine specimens are more sensitive to changes in pressing tem-perature and wood moisture content than balsam poplar.For jack pine specimens,at any of the pressing temperatures,the moisture content of 12%was found to be a crucial level to start a significant decrease in𝜎y and MOE,while at any of the moisture content,a change in temper-ature from 55℃to 90℃exhibited a significant change in𝜎y and MOE.The regression models developed can be used to predict𝜎y and MOE as a function of temperature and moisture content.

基于径向基核函数DAG-SVM的变压器故障诊断

本文将有向无环图(Directed Acyclic Graph,DAG)结构和支持向量机(Support Vector Machine,SVM)的分类能力相结合,提出一种基于径向基核函数DAG-SVM的变压器故障诊断方法。通过使用径向基核函数,DAG-SVM能够将非线性特征映射到高维空间,并在该空间中进行分类,从而更好地捕捉变压器故障的复杂模式和特征。数值计算结果表明,基于径向基核函数的故障诊断综合正确率为73.88%,均高于线性核函数、多项式核函数、S型核函数三种方法,所提基于径向基核函数DAG-SVM的变压器故障诊断模型具有较好的诊断效果。