A Two-Point Boundary Value Problem by Using a Mixed Finite Element Method

This paper describes a numerical solution for a two-point boundary value problem. It includes an algorithm for discretization by mixed finite element method. The discrete scheme allows the utilization a finite element method based on piecewise linear approximating functions and we also use the barycentric quadrature rule to compute the stiffness matrix and the L2-norm.

Clinical Observation on Brachial Plexus Block with “One Injection Two Points” Method Guiding by Ultrasound

OBJECTIVE: To compare the clinical effect of brachial plexus block with "One Injection Two Points" guided under ultrasound and the conventional method guiding by ultrasound. METHODS: 70 patients were randomized evenly into 2 groups, with 35 patients in each group, while the Experiment Group(Group B) received One Injection Two Points" method, the Control Group(Group A) received the conventional method.The nerve block every 5 s, the success rate of anesthesia, the dosage of local anesthetics, second remedial anesthesia, adverse reactions, etc.were recorded. RESULTS: Group B was superior to group A in the success rate of anesthesia; There were 6 patients in group A who required constant pump injection of Remifentanil to remedy, while no patients in Group B needed remedy treatment. There were no serious adverse reactions in both groups.CONCLUSIONS: The clinical effect of brachial plexus block with "One Injection Two Points" method guided under ultrasoundguiding by ultrasound was superior to that of the conventional method.

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.

Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

基于云计算的优化配网调度执行系统研究

为了优化配网调度执行工作,对配网调度进行了研究。设计了基于云计算的优化配网调度执行系统。在硬件设计中采用分布式结构执行配网调度。在系统软件部分,使用云计算技术,设计了主动配网云边协同计算体系。该体系实现了配电调度边缘计算节点的远程操作,提高了配网调度执行优化的能力。采用客户端/服务端(C/S)、浏览器/服务器(B/S)混合架构,实现了配网调度的人机可视化执行。利用两点估计法以提高配网调度模型的优化计算能力,进而实现配网调度的控制,提升了配网调度运行的稳定性与经济性。试验结果表明,在对配网调度执行的可靠性进行测试时,该系统的可靠性达到了96%。该系统可使配网始终处于安全、可靠、优质、经济、高效的运行状态,为配网调度执行提供了一种可行的方案。

足踝复合体本体感觉的测量与评价

背景:足踝本体感觉的研究对于慢性踝关节不稳、老年疾病的康复治疗以及身体姿势控制、运动表现的提高至关重要。前期的相关研究经常把足部和踝关节的感觉评价分开研究,对全面且综合地了解其感觉功能存在一定的局限。目的:足踝复合体是唯一与支撑面直接接触的部位,在收集体感反馈和调节平衡控制中起重要作用。文章通过汇总现有关于足部和踝关节本体感觉的调查研究,梳理足踝复合体感觉的测量与评价方法,以期为日后的相关研究做出铺垫并提供理论依据。方法:中文检索词为“(足OR足踝关节OR踝关节)AND(感觉OR本体感觉)”、英文检索词为“(foot OR ankle)AND(feel OR proprioception)”,在Web of Science、PubMed和中国知网数据库检索相关文献,了解关于足踝基本概念、研究现状与范畴,总结并评价足踝的本体感觉评价方法,最终纳入57篇文献进行综述分析。结果与结论:①足踝复合体感觉的评价主要分为对足部的感觉评价和踝关节的本体感觉评价。②足部的感觉评价主要描述其皮肤的感觉以及干预条件下的感觉反馈,方法主要包括:压力感觉阈值测试、足(底侧和跖侧)两点辨别能力测试、皮肤振动感觉持续时间测试。③踝关节本体感觉评价着重描述关节位置、运动范围、力值及功能表现,方法主要分为静态的关节角度重置测试、运动最小阈值测试、力觉重现测试以及动静态的平衡、速度及行走能力的测试。④对量化结果的报道一般以“误差”来表示,根据报道的需要一般分为:绝对误差、相对误差和恒定误差等。⑤结果证实,足踝复合体具备特殊的感觉能力,包括足部感觉和踝关节的本体感觉,影响人类的生活质量以及运动表现;足部感觉与踝关节本体感觉的弱化均与人体平衡能力下降相关,二者联合测量可以全面有效地评价足踝功能;根据不同的研究需求,需要选择足部与踝关节的感觉测量方法的组合形式,并充分考虑环境、情绪以及报道方式等多种影响因素,提高测量与评价的有效性。

高精度微球半径测量模型及圆度评定方法比较

提出了一种基于回转轴法和两点法原理的高精度微球半径测量模型,实现了基于半径变化量的微球圆度评定。建立了可以分离主轴跳动误差和计算各测量点对应半径的模型。利用团队开发的基于高精度气浮转台和两个迈克尔逊干涉仪的微球圆度测量系统,对标称直径为300μm、圆度为250 nm的红宝石球的赤道圆截面进行了扫描测量。将采用所建模型测得的微球半径与采用直径算得的半径进行对比,并通过最小区域法对所测微球圆度进行评定,结果表明:所建模型与传统直径评定方法得到的微球圆度分别为280 nm和403 nm,标准差分别为2 nm和23 nm,所建微球半径测量模型准确可靠,利用所建模型和最小区域法评定出的微球圆度更加准确可靠。所建模型可以方便准确地获得被测微球的半径,可应用于微球圆度准确评定。

A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension

In this paper,a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems.The key idea is to postprocess the Galerkin approximation,and the analysis shows that the postprocess improves the order of convergence.Consequently,we obtain asymptotically exact aposteriori error estimators based on the postprocessing results.Numerical examples are included to illustrate the theoretical analysis.

Precise integration method for solving singular perturbation problems

This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.

High order multiplication perturbation method for singular perturbation problems

This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.

Inversion of two-dimensional tidal open boundary conditions of M_2 constituent in the Bohai and Yellow Seas

Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE) after assimilation,the cost function may reach 1% or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.

Numerical solutions for point masses sliding over analytical surfaces: Part 1

In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge–Kutta(RK4) scheme. The forces acting on the masses are gravity, the reaction force of the surface, friction, and, in case of two masses, their mutual interaction force. This latter is introduced by imposing that the geometrical distance between the coupled masses is constant. The solution is computed under the assumption that the point masses strictly slide on the surface, without leaping or rolling. To avoid complications stemming from numerical errors related to real topographies that are only known over discrete grids, we restrict our attention to simulations on analytical continuous surfaces. This study sets the basis for a generalization to more complex systems of masses, such as chains or matrices of blocks that are often used to model complex processes such as landslides and rockfalls. The results shown in this paper provide a background for a companion paper in which the system of equations is generalized, and different geometries are presented.

Mathematical analysis of EEP method for one-dimensional finite element postprocessing

For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan＇s element energy projection （EEP） method has the accuracy O（h^min{2k,k＋4}） The theoretical analysis coincides the reported numerical results.

南昌核心城区核酸采样点可达性研究

通过分析核酸采样点的空间分布和资源配置情况,探索中心城市社区核酸采样点的可达性和公平性,旨在缓解日益增长的核酸采样需求与核酸采样点设施供给之间的矛盾,提高核酸采样服务的效率和公平性。以南昌市中心城区为研究区域,提出了基于多出行模式两步移动搜索法分析核酸采样点与人口的匹配性的研究方法来探索各种出行方式下核酸采样点的综合可达性,并基于洛伦兹曲线、基尼系数等非空间分析指标,对南昌市核酸采样点与人口的匹配性核酸检测点均等化水平进行评价。结果表明,南昌市整体的核酸采样点可达性较好,但仍处于不公平状态。

Coupling of high order multiplication perturbation method and reduction method for variable coefcient singular perturbation problems

Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.

基于Tsallis熵的两点法确定明渠断面流速分布及数值模拟验证

在现代农业灌溉中,为了得到明渠断面的流量,首先需要确定明渠断面的流速分布,然而以往的流速分布公式大都不够准确,无法满足精准灌溉的需求,针对这一难题,在基于Tsallis熵推导流速分布的基础上,对熵参数重新推导,提出新的熵参数,进一步简化了流速分布公式,提出两点法确定断面流速分布的研究方法,并结合实测资料和数值模拟软件进行验证。结果表明:通过测量水面下断面中心线上一点流速值u_(c)与相同水深下另一点的流速值u_(z),可计算出流速分布公式中两个未知参数G_(p)、m_(p),确定该水深位置横向流速分布公式,再通过已知参数计算出断面最大流速u_(max),并确定断面中心线流速分布公式。与以往的流速分布公式相比,两点法更加简便,能够较好的应用在工程实际中,具有较高的理论意义和实用价值。

双面阵CCD实时测量激光发散角的系统

针对目前激光光束发散角测试速度慢,实时性差的问题,提出采用两个面阵CCD同时测量激光远场区域两个不同位置的光束宽度,用两点拟合的方法计算激光光束发散角的方法。该方法装置简单,可快速实时准确地测量激光光束发散角。测试结果表明,系统测量误差<0.1 mrad,重复测量误差均±1%之内。该测量方法研制的仪器成本低、测试效率高、便于携带,适合设备生产现场和空间有限的快速实时检测需求。