关于混合插值样条

本文中我们提出一类特殊的H-B插值问题,即所谓混合插值.我们首先讨论五次样条,它是将Meir和Sharma的缺插值样条中的二阶导数的逐点插值换成一阶导数与二阶导数的交替插值.然后又讨论了三次样条,将[3]中讨论的(p)型插值改成一阶导数及函数值本身在节点处的交替插值.我们研究了这两类样条的存在、唯一性,并得到了它     

奇次样条的渐近展开

渐近展开理论的研究在数值计算中有着广泛的应用,在逼近理论研究中也是一个重要的课题,然而,对于样条的渐近展开的工作,见得还不多.作者在〔1〕中讨论了几类缺插值样条函数的渐近展开,在〔2〕中讨论了五次样条的渐近展开,从上述文章中可以看出,五次样条情形已经相当繁复了,也就是说,单用 Hermite 插值方法很难导出一般n 次样条的渐近展开.本文结合 B-Spline,运用一些技巧可以得到 n 次样条的渐近展开,     

一种 C~2类五次缺插值样条函数

关于 C~2类的五次缺插值样条函数,已有不少讨论.本文讨论一种特殊的 C~2类的五次缺插值样条,它的构造方法和逼近性质与已讨论过的各种均不相同.设 f(x)是[0,1]上的连续函数,Δ:0=x_0相似文献   

关于缺插值样条函数

本文通过Hermite插值样条函数讨论了一类缺插值样条函数,建立了存在性、唯一性及收敛速度估计的定理,并用这类样条函数导数的界限给出某些函数类的特征.     

关于C~k类缺插值样条

文献[1～2]讨论了亏度为2的四次缺插值样条,文献[7～10]讨论了亏度为3的五次缺插值样条,文献[3—6]对很一般的C~1、C~2类缺插值样条作了系统的、深刻的研究。 本文通过运用H-B插值样条的良好结果,讨论一般的C~k[0,1]中的s次缺插值样条,统一并推广了已有的许多成果[1～10]。     

第二类三次样条插值的渐近展开

[1]中详细讨论了一类样条插值的渐近展开问题,并且指出,使用[1]中方法导不出第二类三次样条插值的渐近展开式.本文绘出第二类三次样条插值的一项渐近展开式. 下面引进一些记号:     

二元二次分片多项式插值样条函数

本文在Ⅱ型剖分下,研究一类二元二次分片多项式插值样条函数,采用局部坐标系和本文定理1的拼接技巧,揭示了二元二次样条与一元二次样条之间的紧密联系.只要在垂直网线和水平网线上先构造出一元二次样条并求出它们在节点上的一些数据,就可直接写出二元二次样条的分块解析表示式.利用这种技巧,可以进一步研究各种类型的插值样条,还可用来研究双周期或单周期的插值样条.本文证明了,这类样条函数具有与一元二次样条相同的逼近阶,具体来讲,在不均匀剖分且 f(x,y)∈σ~3[a,b;c,d]时,它的逼近阶是2,在均匀剖分且 f(x,y)∈σ~4[a,b;c,d]时,其逼近阶是3.用本文的方法去研究其他各类插值样条,发现也有这种逼近性质.     

关于缺插值样条函数

在[1,2,3,4]中,我们讨论了几种缺插值样条函数.本文继续研究任意节点的缺插值样条函数,推广[1]中的结果. 在第一节中,我们讨论广义Hermite插值样条函数.通过一系列的恒等式很容易得到收敛速度的估计. 在第二节中,讨论了C~2类缺插值样条函数.建立存在性、唯一性定理,估计收敛速     

二次样条插值的收敛性

<正> 本文讨论一类插值结点与样条结点不重合的二次样条插值.[6]讨论了这类插值的存在性、唯一性和某种变分性质.[1—3],[5]讨论了它的特殊情形——中点插值的收敛性和误差界,本文在一般情况下得出了类似的结果.[4]在一般情况下讨论了收敛性,其条件是 f(x)∈Lipα(0<α≤1).本文给出了当 f(x)∈C~0[a,b]时的收敛性及 f(x)∈C~l[a,b](l=1,2,3)时的余项估计.     

四次插值样条的逐项渐近展式及其叠样条格式

1 引言和辅助引理 关于样条插值的渐近展开,目前已有许多工作,这些工作主要限于周期样条插值和基样条(cardinal spline)插值情形,它们不仅给出了插值误差的渐近展开,而且获得了逐项渐近展开。对于实际中应用最多的有限区间上的样条插值的渐近展开问题,由于受端点条件的影响,呈现十分复杂的局面。目前的工作只是获得了渐近展开结果,并未获得逐项渐近展开,且主要针对二、三次这类低次样条插值情形,考虑高次样条有良好的逼近性质,特别是其中四、五次样条插值在实际应用中被广泛采用,本文致力于研究四次样条插值问题,获得了其误差     

Boundary-Value Problems of the Theory of Thin and Nonthin Orthotropic Shells with Account of Nonlinearly Elastic Properties and Low Shear Rigidity of Composite Materials

The basic geometric and physical relations and resolving equations of the theory of thin and nonthin orthotropic composite shells with account of nonlinear properties and low shear rigidity of their materials are presented. They are derived based on two theories, namely the theory of anisotropic shells employing the Timoshenko or Kirchhoff-Love hypothesis and the nonlinear theory of elasticity and plasticity of anisotropic media in combination with the Lagrange variational principle. The procedure and algorithm for the numerical solution of nonlinear (linear) problems are based on the method of successive approximations, the difference-variational method, and the Lagrange multiplier method. Calculations of the stress-strain state for a spherical shell with a circular opening loaded with internal pressure are presented. The effect of transverse shear strains and physical nonlinearity of the material on the distribution of maximum deflections and circumferential stresses in the shell, obtained according to two variants of the shell theories, is studied. A comparison of the results of the problem solution in linear and nonlinear statements with and without account of the shell shear strains is given. The numerical data obtained for thin and nonthin (medium thick) composite shells are analyzed.     

县域工旅农产业协同度测度研究——以河北省典型县域为例

在全域旅游的背景下,基于产业协同理论,利用工业、旅游业、农业产业系统有序度、协同度模型,从规模、结构、绩效三方面建立其协同度测度指标体系,依据2003-2014年的数据,定性和定量的分析评价了河北典型县域——涞水县、宽城满族自治县、抚宁县、蔚县的工旅农产业协同度.研究表明,县域工旅农产业协同度低,波动明显,且县域工业与旅游业协同变化趋势对其作用显著;县域旅游业与工业或农业普遍处于不协同状态,且前者协同度高于后者.     

Time-linearized,compact methods for the inviscid GRLW equation subject to initial Gaussian conditions

The objective of this paper is three-fold. First, four time-linearization methods that are second- and fourth-order accurate in time and space, respectively, are presented and used to study the dynamics of the modified and generalized regularized-long wave equations (mRLW and GRLW equations, respectively). Two of the methods use the conservation-law form of the equations and treat the wave amplitude and its second-order spatial derivative and the linear and nonlinear advection fluxes as unknowns, whereas the other two employ the non-conservation-law form of the equations and consider the wave amplitude and its first- and second-order spatial derivatives as unknowns. The methods employ three-point fourth-order accurate Padé discretizations for the first- and second-order derivatives, are second-order accurate in time, and yield linear systems of blocktridiagonal matrices. Second, the accuracy of these methods is assessed by comparing their results with those of the exact solution of the mRLW equation. It is reported that the four methods predict nearly the same values of the three invariants and have the same accuracy, and that an accurate prediction of the invariants may not correspond to small errors in space and time. Third, the dynamics of the inviscid GRLW equation is studied first qualitatively in terms of length and time scales and then numerically as a function of the linear advection speed, the exponent of the nonlinear advection flux, the dispersion coefficient and the amplitude and width of the initial bell-shaped or Gaussian conditions. It is shown that wide initial conditions result in wave steepening and breakup and the formation of solitary waves whose amplitude and speed decrease as the time for their formation increases. For narrow initial conditions, it is shown that only a single solitary wave may form. Behind this wave and depending on the parameters that characterized the inviscid GRLW equation, rarefaction or negative amplitude waves that propagate towards the upstream boundary or a train of localized oscillatory waves that do not emerge from the trailing edge of the leading solitary wave may be formed. These oscillatory waves exhibit the characteristics of, but are not dispersive shock waves and their amplitude and frequency increases as the width of the initial conditions is decreased. The results presented here do not only complement previous work by the authors, they also show that the dynamics of the inviscid GRLW equation undergoes new and interesting phenomena as the width of the initial conditions is decreased.     

The application of information and communication technologies in transport

This paper examines the possibilities that are opened today and for the whole decade from the application of Information and Communication Technologies (ICTs), in the field of Transport. The various applications are examined, under the following three headings: operation and management of networks (all modes), information and guidance to the users (of the transport systems), operation and management of freight transport systems.For each of these, a concise and critical review is made of the various technologies that exist today in their final stages of development or at the stage of commercial implementation, and their applications. The review refers to various sub-categories of the above main three.The paper proceeds then to examine the prospects for the future with a medium time horizon of 2010. These prospects show that a number of areas of applications have well established technologies and are secured of commercial viability so that we can predict safely their full scale application in the course of this decade. Examples of such areas of applications are: traffic data information collection and dissemination systems, network control and traffic management strategies, vehicle control and driver assistance, systems for (Electronic or other) fee collection.And specifically for freight: freight resource management; terminal and port information and communication systems, freight and vehicle tracking and tracing, and “front” or “back-office” logistics systems.     

Reliability verification for composite structures of annular cross section

The performance and reliability of tubular composite structures are considered. The suitability of concrete-filled plastic and steel tubes for building structures is discussed. The strength and structural safety of tubular composite members of annular cross section are analyzed, and the criteria of limit states for tubular composite members under concentric and eccentric axial compression are studied. The time-variant functions of efficiency of the members and their components are presented as random processes of variations in their compressive resistance and internal actions. The safety design of the members is based on the conceptions of their conventional resistance, sequences of safety margin, and transformed conditional probabilities.     

基于“动态生成”的大学数学课堂教学

"动态生成"教学观的建立旨在摆脱课堂教学中以教师为中心、强调知识传授的传统教学模式的缺陷,从根本上正确理解课堂教学的复杂性和动态性,构建充满生命活力的大学数学课堂教学生态环境.在用动态生成的视角审视当前大学数学课堂教学中存在的问题的基础上,文章对在课堂教学中如何有效地进行动态生成提出了一些具体的策略:更新教学观念,精心预设弹性化的数学课堂教学方案;根据学生课堂反馈情况及时调整预设,并及时捕捉可利用的动态资源,为学生的生成创造可能的机会;加强教学研究,不断提高课堂教学智慧.     

Complex economic dynamics: Chaotic saddle, crisis and intermittency

Complex economic dynamics is studied by a forced oscillator model of business cycles. The technique of numerical modeling is applied to characterize the fundamental properties of complex economic systems which exhibit multiscale and multistability behaviors, as well as coexistence of order and chaos. In particular, we focus on the dynamics and structure of unstable periodic orbits and chaotic saddles within a periodic window of the bifurcation diagram, at the onset of a saddle-node bifurcation and of an attractor merging crisis, and in the chaotic regions associated with type-I intermittency and crisis-induced intermittency, in non-linear economic cycles. Inside a periodic window, chaotic saddles are responsible for the transient motion preceding convergence to a periodic or a chaotic attractor. The links between chaotic saddles, crisis and intermittency in complex economic dynamics are discussed. We show that a chaotic attractor is composed of chaotic saddles and unstable periodic orbits located in the gap regions of chaotic saddles. Non-linear modeling of economic chaotic saddle, crisis and intermittency can improve our understanding of the dynamics of financial intermittency observed in stock market and foreign exchange market. Characterization of the complex dynamics of economic systems is a powerful tool for pattern recognition and forecasting of business and financial cycles, as well as for optimization of management strategy and decision technology.     

行业结构环境的序参量分析方法研究

行业结构环境分析是发现和掌握行业运行规律与发展状况的必经之路,也是在企业战略管理中的重要组成部分,其结果直接影响着企业战略决策与实施。针对企业战略管理的新价值理念,本文在协同学与竞优理论的基础上,通过对行业内群体结构特性与企业行为的重新考察,建立了行业结构环境分析的一种新方法即序参量分析方法与其应用范例。本文的研究结果,如行业内多层结构、企业群组定位及分布特性、行业基本发展模式、标杆与协同伙伴、企业群组或群组内企业构成与绩效之间的关系等都可为实现符合现代产业发展环境的企业战略管理提供方向性辅助与技术支持。     

Supporting dynamic conceptions of area and its measure

Design research was conducted to investigate the development of dynamic conceptions of area. Students used simple physical instruments, squeegees, and paint, to generate rectangular areas continuously as a sweeping motion of one length through another. Then, they dissected the resulting swept space into discrete units of measure by coordinating measures of the lengths of the sides, including side lengths measured in different units, such as “squeegee” and inch. Analysis of classroom discourse, formative assessments, and flexible interviews conducted 2 months after instruction illustrated that students developed dynamic images and meanings of area and its measure. These expanded their understanding of multiplicative product to include referent-transforming quantity and provided means for re-envisioning the meaning of the commutative and distributive properties of multiplication. Students employed these properties to relate fractional and whole number area products. Dynamic generation and dissection in tandem helped students bridge discrete and continuous conceptions of area and its measure.     

Construction of Teacher Knowledge in Context: Preparing Elementary Teachers to Teach Mathematics and Science

The purpose of this study was to further the understanding of how preservice teachers construct teacher knowledge and pedagogical content knowledge of elementary mathematics and science in a school‐based setting and the extent of knowledge construction. Evidence of knowledge construction (its acquisition, its dimensions, and the social context) was collected through the use of a qualitative methodology. The methods course was content‐specific with instruction in elementary mathematics and science. Learning experiences were based on national standards with a constructivist instructional approach and immediate access to field experiences. Analysis and synthesis of data revealed an extensive acquisition of teacher knowledge and pedagogical content knowledge. Learning venues were discovered to be the conduits of learning in a situated learning context. As in this study, content‐specific, school‐based experiences may afford preservice teachers greater opportunities to focus on content and instructional strategies at deeper levels; to address anxieties typically associated with the teaching of elementary mathematics and science; and to become more confident and competent teachers. Gains in positive attitudes and confidence in teaching mathematics and science were identified as direct results of this experience.