Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.

REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.

基于人工鱼群算法的篮球跳投轨迹实时跟踪

篮球运动轨迹跟踪方法由于轨迹特征提取效果差,导致跟踪误差高,提出一种基于人工鱼群算法的篮球跳投轨迹实时跟踪方法。提取三维坐标系下图像中篮球边缘轮廓信息,通过滤波函数消除篮球跳投图像噪声,基于人工鱼群算法提取图像中篮球跳投轨迹特征,寻找篮球运动轨迹的最优解集,改进篮球实时跟踪匹配路径,形成轨迹跟踪函数。实验结果可知,该方法的平均轨迹跟踪误差为18.28mm,与常规方法相比降低了6.22mm以上。因此,该跟踪方法的篮球轨迹跟踪精度更高,并且实时跟踪轨迹与真实轨迹更吻合。

采样控制下的Markov跳变系统稳定性与安全性分析

研究针对连续Markov跳变系统的稳定性和安全性问题通过状态采样控制器保证了其稳定性和安全性。首先,与通常只考虑Markov系统的稳定性不同的是,系统的安全性问题也被考虑了。其次,系统的安全性通过引入控制障碍函数的方法得到解决。因此,系统分析及计算变得极其复杂。最后,通过设计采样控制器保证了系统的稳定性和安全性,并提供了一个有效的数值例子验证了提出方法的有效性。

功能性踝关节不稳男性下蹲跳过程中下肢的生物力学特征

背景:踝关节作为人体的末端承重关节,承受着机体自上而下的压力,这导致踝关节在运动中很容易发生损伤,诱发功能性踝关节不稳,对日常生活造成负面影响。研究功能性踝关节不稳患者在下蹲跳过程中的下肢生物力学表现,对实现科学训练、预防踝关节损伤以及伤后临床康复提供理论参考具有重要意义。目的:探究功能性踝关节不稳患者下蹲跳过程中的下肢运动学与动力学特征。方法:于2023年3-9月在苏州大学招募男性功能性踝关节不稳患者与健康人群各15名,年龄22-28岁,所有受试者均完成下蹲跳试验。采用Vicon红外高速运动捕捉系统和Kistler三维测力台对两组受试者在下蹲跳起跳阶段、离地瞬间时刻、初始着地时刻和垂直地面反作用力峰值时刻的下肢运动学和动力学指标进行同步采集及对比分析。结果与结论:(1)离地瞬间时刻,与健康对照组的匹配侧相比,功能性踝关节不稳组患侧显示出了更小的膝关节内旋力矩(P=0.020)、更小的踝关节内旋力矩(P=0.009)。(2)落地瞬间时刻,与健康对照组的匹配侧相比,功能性踝关节不稳组患侧显示出了更小的髋关节屈曲角度(P=0.039);功能性踝关节不稳组相较于健康对照组显示出了更小的髋关节外展角度(P=0.022)、更小的膝关节内翻角度(P=0.010)、更大的膝关节外旋角度(P=0.021)、更小的踝关节内翻角度(P=0.004)、更小的踝关节外旋角度(P=0.008)。(3)垂直地面反作用力峰值时刻,功能性踝关节不稳组相较于健康对照组显示出了更小的踝关节内翻角度(P=0.044);(4)结果说明,功能性踝关节不稳者在下蹲跳动作中相较于健康人群存在异常的下肢生物力学特征,主要表现为离地与落地瞬间时刻,下肢关节在矢状面和额状面的运动学和动力学指标变化。这些改变反映出功能性踝关节不稳人群在执行下蹲跳时采用了僵硬的起跳与着陆模式,倾向于将患侧踝关节负荷转移至下肢其他关节,并显示出健侧下肢的代偿现象。因此,检测和纠正异常生物力学特征应该成为功能性踝关节不稳者康复训练的一部分。

基于概率函数触发的锂电池模组热失控蔓延建模与分析方法研究

针对现有数值模拟方法难以准确反映锂电池热失控触发温度概率性变化的问题,提出基于概率函数触发的锂电池模组热失控蔓延建模方法。该方法首先通过统计分析实际锂电池热失控温度区间和数量分布,以此计算出各温度区间热失控触发概率,然后基于提出的概率触发模拟器实现仿真过程概率触发,采用实验数据对该方法的有效性进行验证,最后对概率函数触发条件下的热蔓延路径及其概率进行分析。结果表明,存在包括跳跃式热失控现象在内的多种热失控蔓延路径,其中顺序热失控的概率最高,而跳跃式热失控的概率最小。所提出的方法为研究锂电池模组热失控蔓延过程的概率性提供有效的研究工具和分析方法。

基于罚函数的桥式起重机地震跳轨仿真分析

文中基于罚函数建立桥式起重机的大、小车轮与轨道之间的接触耦合关系,模拟桥式起重机在运行中大车车轮与轨道、小车车轮与轨道间的接触关系,使用静力学分析判断起重机有限元模型的正确性。通过增量动力分析法(Incremental Dynamic Analysis,IDA)获取相同地震激励下不同地震加速度的地震动,使用时程分析方法分析起重机在地震中的震动情况并跟踪大小车轮的轮压获取轮压时程曲线图。通过分析轮压数据,提出判断起重机发生跳轨现象的条件,结果表明:基于罚函数的接触耦合能够很好地模拟出地震中起重机的受力情况并获取轮压数据,通过跳轨条件能够快速地捕捉到起重机发生跳轨的时间点以及落下的冲击力。

血流限制下低强度增强式跳跃训练干预功能性踝关节不稳的效果

目的 探讨血流限制下低强度增强式跳跃训练(LI-PJT+BFR)对功能性踝关节不稳(FAI)大学生的下肢动态姿势控制的影响。方法 2023年3月至5月,招募西安体育学院FAI大学生40例,随机分为高强度增强式跳跃训练(HI-PJT, n=14)组、低强度增强式跳跃训练(LI-PJT, n=13)组和LI-PJT+BFR组(n=13),各组完成相应的干预训练,共6周。干预前后,采用无线遥感表面肌电测试仪测量胫骨前肌、腓骨长肌、腓肠肌外侧头、臀大肌、股外侧肌、股二头肌和半腱肌最大自主等长收缩(MVIC)和单腿下落(SLL)时肌电均方根值(RMS),采用Y平衡和坎伯兰踝关节不稳问卷(CAIT)进行评定。结果 干预后,除LI-PJT组腓骨长肌、臀大肌、股二头肌和半腱肌MVIC和RMS,LI-PJT+BFR组腓骨长肌RMS外,各组其余肌肉MVIC和RMS均较干预前提高(t> 2.218, P <0.05);3组中,除腓骨长肌外,LIPJT组各肌肉MVIC和RMS均最低(F> 3.262, P <0.05);各组Y平衡各方向评分和综合分均提高(t> 2.485,P <0.05),3组中LI-PJT组最低(F> 5.042, P <0.05);各组CAIT评分显著改善(t> 5.227, P <0.001),3组中LI-PJT组最低(F=4.640, P <0.05)。结论 LI-PJT+BFR可改善功能恢复期FAI大学生下肢动态姿势控制能力,效果与HI-PJT相似。

On Applications of Generalized Functions in the Discontinuous Beam Bending Differential Equations

This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta function. The governing differential Equation is Euler-Bernoulli beams with jump discontinuities on displacements and rotations. Also, the governing differential Equations of a Timoshenko beam with jump discontinuities in slope, deflection, flexural stiffness, and shear stiffness are obtained in the space of generalized functions. The operator of one of the governing differential Equations changes so that for both Equations the Dirac Delta function and its first distributional derivative appear in the new force terms as we present the same in a Euler-Bernoulli beam. Examples are provided to illustrate the abstract theory. This research is useful to Mechanical Engineering, Ocean Engineering, Civil Engineering, and Aerospace Engineering.

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.

T-Shaped Transmission Line Fault Location Based on Phase-Angle Jump Checking

In order to effectively solve the dead-zone and low-precision of T-shaped transmission line fault location,a new T-shaped transmission line fault location algorithm based on phase-angle jump checking is proposed in this paper.Firstly,the 3-terminal synchronous fundamental positive sequence voltage and current phasors are extracted and substituted into the fault branch distance function to realize the selection of fault branch when the fault occurs;Secondly,use the condition of the fundamental positive sequence voltage phasor at the fault point is equal to calculate all roots(including real root and virtual roots);Finally,the phase-angle jump check function is used for checking calculation,and then the only real root can be determined as the actual fault distance,thereby achieving the purpose of high-precision fault location.MATLAB simulation results show that the proposed new algorithm is feasible and effective with high fault location accuracy and good versatility.

Stochastic Nonlinear Beam Equations with Lévy Jump

In this paper, we study stochastic nonlinear beam equations with Levy jump, and use Lyapunov functions to prove existence of global mild solutions and asymptotic stability of the zero solution.

THE EQUILIBRIUM PROBLEM AND CAPACITY FOR JUMP MARKOV PROCESSES

Let X=(Omega,F,F-t,X(t),theta(t),P-x) be a jump Markov process with q-pair q(x)-q(x, A). In this paper, the equilibrium principle is established and equilibrium functions, energy, capacity and related problems is investigated in terms of the q-pair q(x)-q(x, A).

STOCHASTIC STABILITY OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MARKOVIAN JUMPING PARAMETERS

In this paper, global robust stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters is considered. A novel Linear matrix inequal- ity（LMI） based stability criterion is obtained to guarantee the asymptotic stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters. The results are derived by using the Lyapunov functional technique, Lipchitz condition and S-procuture. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in [31] and [34] to show the effectiveness and conservativeness.

Improved delay-dependent globally asymptotic stability of delayed uncertain recurrent neural networks with Markovian jumping parameters

In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism. In addition, a numerical example is provided to illustrate the applicability of the result using the linear matrix inequality toolbox in MATLAB.

Hyper-exponential jump-diffusion model under the barrier dividend strategy

In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.

THE NUMBERS OF JUMP LAYERS OF BOUNDARY VALUE PROBLEMS IN QUASILINEAR DIFFERENTIAL EQUATIONS

This paper discusses the numbers of jump layers of boundary value problems in quasilinear differential equations. In addition, the paper gives several examples to explain why the original equation must be rediscussed when the determinate function in reference [1 ] is a/ways equal to zero.

New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities

This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems(MJTDSs),whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance,auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function(ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally,numerical examples are given to show the effectiveness and the merits of the proposed method.

Integro-Differential Equations for a Jump-Diffusion Risk Process with Dependence between Claim Sizes and Claim Intervals

The classical Poisson risk model in ruin theory assumed that the interarrival times between two successive claims are mutually independent, and the claim sizes and claim intervals are also mutually independent. In this paper, we modify the classical Poisson risk model to describe the surplus process of an insurance portfolio. We consider a jump-diffusion risk process compounded by a geometric Brownian motion, and assume that the claim sizes and claim intervals are dependent. Using the properties of conditional expectation, we establish integro-differential equations for the Gerber-Shiu function and the ultimate ruin probability.

基于改进JPS的移动机器人路径规划算法

在移动机器人的路径规划技术中,跳点搜索算法(JPS)因具备简单、快速、易实现的特性而被广泛使用。然而,传统的JPS算法由于启发式函数搜寻效率低导致其搜索的节点数量冗余,而且难以有效兼顾规划路径的安全性。针对该问题,本文提出了一种改进的JPS算法。该方法设计了一种由对角线距离和方向信息结合的启发式函数用于提高寻路效率,并且进一步对规划路径进行平滑处理以有效兼顾规划路径的安全可靠性。移动机器人在复杂障碍物环境下的路径规划仿真实验表明,相较于JPS算法,本文改进后的JPS算法平均规划时间减少了13.4%,平均路径长度减少了3.1%,平均危险点数量降低了83.3%。