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.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

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.

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.

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.

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。

基于色散转折点处的高灵敏度锥形七芯光纤折射率传感器

基于色散转折点的锥形光纤折射率传感器由于依赖色散转折点(Dispersion Turning Point,DTP)的独有特性,可获得超高的传感灵敏度,在生物溶液检测和物质分析等领域展现了广阔的应用前景。提出了一种基于色散转折点处的锥形七芯光纤(Saven-core-fiber,SCF)液体折射率传感器,该传感器通过二次拉锥法制作而成,通过理论和实验证明,该传感器在色散转折点附近具有超高的折射率灵敏度,折射率在1.33附近区域时,折射率灵敏度的最大值为23262.30 nm·RIU^(-1);折射率在1.35附近区域时,折射率灵敏度的最大值为23658.23 nm·RIU^(-1),此外,该传感器具有良好的复现性,使其在微生物溶液检测和血浆检测等领域显示出巨大的潜力。

破碎矿体扇形深孔双点起爆位置优化研究

在采用无底柱分段崩落法开采破碎矿体时,常常面临眉线破坏的问题,这一问题不仅影响后续爆破作业,还严重制约现场的安全高效生产。为解决这一问题,以尖山铁矿1280分段回采进路为工程背景,综合运用现场调研、数值模拟和理论分析等方法,研究双点起爆不同起爆位置下爆轰应力场的分布规律。综合评价不同起爆位置下爆炸能量的空间分布及爆破效果,发现适当调整起爆位置,可以调整爆轰应力场在矿体内部的分布规律,并降低对眉线口处应力作用。现场试验结果表明,当双点起爆时药包布置在装药段1/2~孔底位置,能够加强对顶部矿体的破坏作用,同时减弱对眉线口部位的影响,有效保护眉线。

WPS电子表格在等值电位图绘制中的应用

曲线图通常用于显示检测数据的变化规律,如地基静载试验中的s-lgt曲线和钢筋锈蚀电位检测中的等值电位图。使用WPS sheet能实现编程方法在等值线点坐标的计算、数据分析的应用,同时X-Y散点图可用于等值电位图的绘制。等值电位图上的等值线,本质上是密集的等值电位线点。WPS电子表格,能实现设定的等值线点坐标计算,再绘制密布的等值点即可完成绘制等值电位图。进而,WPS电子表格可用于绘制简单的、二维的图纸。

两点电位滴定法及其应用

提出了只需两组数据即可计算电位滴定计量点的电位滴定数据处理新方法———两点法 ,并在此理论基础上 ,提出了两点电位滴定法。该法只需记录两次电极电位值和相应滴定剂体积 ,利用公式即可计算滴定化学计量点。详细讨论了各因素对方法准确度的影响 ,给出了衡量滴定进行程度的客观指标 ,为两点位置的选择提供了充分的理论依据。实验结果表明 :该法操作方便 ,数据处理简单 ,精密度与准确度均较高 。

基于两点法的掺矿粉新拌混凝土流变性能的试验研究

基于混凝土流变学理论中的"两点法",利用坍落度以及由倒置坍落度筒流出时间来评价不同水胶比和不同矿粉掺量下新拌混凝土的流变性能。试验结果表明:新拌混凝土的屈服应力和黏度系数均随着矿粉掺量的提高而增大,随着水胶比的增大而减小。倒坍落度筒流出时间与公式推导出的黏性系数之间有较好的线性关系。试验结果表明可以用坍落度和倒坍落度筒流出时间来表征掺矿粉新拌混凝土的工作性。