Singular Perturbation of Linear Systems with a Regular Singularity

We study singularly perturbed inhomogeneous linear systems which have a regular singularity at the origin. Under some extra assumption, this system has a unique formal solution which is a power series in the variable z and the perturbation parameter . Here we investigate its summability properties. In particular, we show that the series, regarded as a power series in with coefficients depending on z, is 1-summable under some eigenvalue condition. Moreover, we show that this condition in general is sharp.     

Regular Linear Systems Governed by a Boundary Controlled Heat Equation

In this paper we consider a class of distributed parameter systems governed by the heat equation on bounded domains in ⁿ . We consider two types of boundary inputs (actuators) and two types of boundary outputs (sensors). Allowing for any possible pairing of these, we consider a totality of four possible arrangements of our system. The first type of input (control) is through the Neumann boundary condition on a part of the boundary, together with a homogenous Neumann boundary condition on the remaining part of the boundary. For this type of input, the input space is infinite-dimensional. The second type of input (with a finite-dimensional input space) is obtained by imposing constant normal derivatives on each element of a finite partition of the boundary. The first type of output (observation) is given by evaluation (trace) of the state of the system on a part of the boundary, so that the output space is infinite-dimensional. For the second type of output (with a finite-dimensional output space), we again consider a partition of the boundary of the spatial domain (which can be different from the one considered for the inputs) and each output channel contains the average of the values of the state of the plant on one element of this partition. Our main result is that any possible combination of the aforementioned inputs and outputs provides a regular linear system.     

Singular Trajectories in Multi-Input Time-Optimal Problems: Application to Controlled Mechanical Systems

This paper deals with the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems have certain special properties. These properties are explored and used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated by an application to a time-optimal problem for a class of underwater vehicles.     

Nonoscillating Projections for Trajectories of Vector Fields

The properties of oscillation for trajectories of three-dimensional vector fields are “visible” in the sense that they can be detected by means of plane projections. We also recover a three-dimensional version of the classical dichotomy “nonoscillation” versus “spiralling” for plane vector fields.      

Coalescence of Two Regular Singularities into One Regular Singularity for the Linear Ordinary Differential Equation

The process of coalescence of two regular singular points of linear ODE into a single regular singularity is studied. This problem is examined in terms of connection matrices and solutions of the corresponding equations.     

五级导叶式离心泵轴心轨迹的试验测量

鉴于多级离心泵轴心轨迹研究较少的问题,对五级导叶式离心泵的能量性能和轴心轨迹进行了试验测量。结果表明,设计工况下五级导叶式离心泵的扬程为165.40m、效率为72.84%;测点的轴心轨迹时域在x向呈现周期性的畸形正弦波,在y向呈现周期性的畸形余弦波;前轴承测点A1的轴振变化幅度大于后轴承测点A2的轴振变化幅度,前轴承B2的振动比后轴承B1的振动更强;设计工况下,前轴承测点A1的轴心轨迹呈现近似八字形分布,后轴承测点A2的轴心轨迹呈现近似椭圆分布。研究成果可为多级离心泵的振动特性分析提供参考。     

Modeling and CFD Simulation of a Mixed‐Convection Flow of Regular Fluids and Nanofluids in Vertical Porous and Regular Channels

In this article, the problem of combined forced and free convection in vertical porous and regular channels for both regular fluids and nanofluids has been solved using the CFD technique in the entrance regions of momentum and heat transfer taking into account the influences of viscous heating and inertial force. In this regard, various types of viscous dissipation models reported in the literature such as the Darcy model, the power of the drag force model, and the clear fluid‐compatible model were applied. In the case of nanofluid flow, both the Brownian and thermophoresis molecular transfer mechanisms were considered. The dimensionless distributions of velocity, temperature, and the volume fraction of nanoparticles were determined in terms of corresponding dimensionless numbers such as the Grashof, Reynolds, Forchheimer, Brinkman, and Darcy numbers. The predicted results were validated using fully‐developed distributions of velocity and temperature. In addition, the influences of the Grashof number value on the temperature and velocity distributions in the entrance and fully‐developed regions were examined carefully. In addition, temperature and velocity distributions of nanofluids and regular fluids in porous and regular channels were compared. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 243–269, 2014; Published online 30 September 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21079     

Local Regularity of Optimal Trajectories for Control Problems with General Boundary Conditions

Let f and g be two smooth vector fields on a manifold M. Given a submanifold S of M, we study the local structure of time-optimal trajectories for the single-input control-affine system ̇q = f(q) + ug(q) with the initial condition q(0) S. When the codimension s of S in M is small (s 4) and the system has a small codimension singularity at a point q₀ S, we prove that all time-optimal trajectories contained in a sufficiently small neighborhood of q₀ are finite concatenations of bang and singular arcs. The proof is based on an extension of the index theory to the case of general boundary conditions.2000 Mathematics Subject Classification. 49K15, 49K30.     

气固两相流中颗粒轨道运动方程的一组分析解

在气固两相流场的单元体内建立了描述颗粒沿轨道运动的控制方程,针对不同Ｒｅｙｎｏｌｄｓ数范围内的气体－颗粒阻力系数表达式,导出了颗粒运动方程的一组分析解,在采用颗粒轨道或随机轨道模型时,它们可用于计算流场网格单元控制体或湍流随机涡团内颗粒运动的速度和轨迹。     

Tangent, Quasitangent, and Peritangent Directions to the Trajectories of Differential Inclusions

We introduce several new types of tangent and generalized tangent directions to the trajectories of autonomous differential inclusions and prove some refinements of the existing results on lower estimates and even exact characterizations of these sets in the case where the differential inclusion is either locally Lipschitz or continuously parametrized.     

浅谈全面深入开展大气微生物污染监测的必要性

由于传染病控制非常迫切,全面深入地开展大气微生物监测就显得非常重要。介绍了大气微生物污染的特点及监测研究现状,给出了大气微生物污染监测实施的方法及措施。     

Confluence of Several Regular Singular Points into an Irregular Singular One

Consider the systems and , where s and t are variables, is a parameter, and A and B = diag(₁,..., _n ) are n by n matrices. (1) has only regular singular points, and (2) has an irregular singular point at t = . Several kinds of special solutions having particular behavior near singular points were selected in previous papers. In the present paper, the author shows how (2) results from (1) in a process of confluence as . It is analyzed how the special solutions of (1) converge to those of (2) in that process. As a consequence new proofs of earlier results about connection problems are obtained.     

Extremal Trajectories and Maxwell Strata in Sub-Riemannian Problem on Group of Motions of Pseudo-Euclidean Plane

We consider the sub-Riemannian length minimization problem on the group of motions of pseudo-Euclidean plane that form the special hyperbolic group SH(2). The system comprises of left invariant vector fields with 2-dimensional linear control input and energy cost functional. We apply the Pontryagin maximum principle to obtain the extremal control input and the sub-Riemannian geodesics. A change of coordinates transforms the vertical subsystem of the normal Hamiltonian system into the mathematical pendulum. In suitable elliptic coordinates, the vertical and the horizontal subsystems are integrated such that the resulting extremal trajectories are parametrized by the Jacobi elliptic functions. Qualitative analysis reveals that the projections of normal extremal trajectories on the xy-plane have cusps and inflection points. The vertical subsystem being a generalized pendulum admits reflection symmetries that are used to obtain a characterization of the Maxwell strata.     

车用柴油发动机常见故障诊断

详细阐述了车用柴油机在使用中的常见故障现象:异响噪声,油、气渗漏,起动困难,油路堵塞,周期性“游车”,飞车等。分析引起这些故障的原因,重点介绍这些故障的诊断和排除方法,为使用维修提供指导。     

钻机柴油机的配套、使用习惯作法浅释

本文就钻机柴油机在实际配套使用中的不合理习惯作法进行了分析,并提出解决方法.     

点检定修在实际应用中的初步探讨

介绍点检定修在发电厂中的应用，根据十里泉发电厂设备维修的经验提出点检定修向状态检修过渡的方法。     

基于加权正则极限学习机的短期风速预测

精确的风速预测是风电功率预测的基础,对保障风电场并网运行和维护电力系统的安全、稳定具有重要意义。针对风速时间序列强烈的波动性、随机性,难以预测的特点,建立了一种基于加权正则极限学习机(WRELM)的短期风速预测新方法。首先,采用与风速相关性大的历史风速、风向以及温度、气压、湿度等气象因素构成候选特征集;采用最大相关最小冗余(mRMR)准则选取与风速序列相关性最大的特征集作为预测输入,由此确定预测网络的训练集和测试集,建立WRELM;采用训练集数据训练网络参数,构建WRELM预测模型;最后,采用WRELM网络预测短期风速。通过风电场实测风速数据试验,验证了该方法的有效性,可用于短期风速预测实践。     

盐锅峡水电站大坝首次安全定期检查

简要介绍盐锅峡大坝首次安全定期检查工作情况，阐述首次定检的意义、成效和主要结论，指出首次定检遗留的问题，提出对搞好第二次定期检查的建议。     

Analytic Solutions of Systems

In this paper, functional series solutions of the nonlinear analytic system for the unknown state variable x(t), and functional series solutions of the analytic infinite-dimension