局部凸空间的余逼近

研究了在局部凸空间中的ｆ－余逼近和强ｆ－余逼近的一些性质．     

高维代数多项式逼近与a.e.逼近的一些结果

自Korovkin的文[1]问世以来,有关线性正算子逼近的各种工作一直是颇受逼近论界关注的研究课题,如[2]～[4]等分别考虑了连续函数,L~p空间及随机函数的正算子逼近.然而在一元逼近中,由积分核引出的卷积与形式卷积型算子却占有极为重要的地位,这不仅因为已经有较多具体的积分核能方便地用于误差估计;特别,还有一些如Timan定理那样     

最佳混合范数逼近

本文研究了两变量函数 f(x,y)用单变量函数 g(x)作混合范数逼近问题,即求g~*(x)∈G,G 是一 Haar 子空间,使(?)integral from Y|f(x,y)-g~*(x)|dμ=(?)integral from Y|f((?),y)-g(x)|dμ我们建立了包括交错定理、de la Vallee Poussin 定理、唯一性定理和强唯一性定理在内的 Chebyshev 逼近理论。     

复曲线上的Jackson型定理

令$\Ga$是复平面(z)中的光滑闭Jordan曲线. 作者借助于Hermite插值的基多项式, 引入连续函数插值, 它一致收敛于$f(z)\in C(\Ga)$,且具有和实区间$[-1, 1]$上Jackson定理1中一样的逼近阶, 并证明了这里逼近阶的精确性. 利用和以往工作不同的方法, 研究了同时逼近到函数及其导数, 并得到和实区间$[-1, 1]$上Jackson定理2一样的理想结果.     

同指数函数值有关的有理逼近

本文证明了数∑ｇ∈Ｇｌ（γｇ）ｅβｇ具有指数２＋ε的有理逼近．这里βｇ和γｇ为有限次代数数域ｋ上元素β和γ在ｇ作用下ｋ上共轭元素，Ｇ为ｋ的Ｇａｌｏｉｓ群，ｌ（ｘ）∈ｚ［ｘ］，从而推广了Ｃｈｕｄｎｏｖｓｋｙ的文章［５］的结果．     

有理逼近的一些最新进展

作为非线性逼近的一个重要特殊情形，有理函数逼近（即有理逼近）无论在实践中还是在应用中有都有重要的意义，有理逼近日益成为逼近论的一个重要和具有很强生命力的课题。近年来，在这一方面的研究成果不断涌现，其中许多都是非常有意义的。本文将对此作一个总结，特别对其中涉及我们自己的工作作一个回顾。     

轴对称Stokes流的无限元逼近(Ⅱ)

[1]中讨论了无界区域上轴对称Stokes绕流的无限元方法,我们利用转移矩阵X以及组合刚度矩阵K_z将问题归结为一个有限阶代数方程组。[1]又给出了两种计算K_z的迭代方法,并证明了迭代方法的收敛性。最后证明了无限元解收敛于精确解,估计了误差的阶。这个方法的优点是:无穷远边界条件自然,计算规模小,边界形状不受限制,程序通用,并且理论基础比较完整。 本文是[1]的继续。我们将迭代格式作了一些简化,使之更便于计算;并且利用这种     

论可微函数的共单调逼近和共凸逼近

对有限区间上可微函数借助于代数多项式的共单调逼近和共凸逼近的逼近度估计建立了更为精确的Jackson型不等式,扩充和改进了近期的一些结果。     

关于圆的椭圆逼近显示的最优算法

本给出了一个逼近显示圆的新算法,该算法是通过相交多形而不是内接多边形逼近圆,由于构造构交多连形时其面积等于圆面积,因此新算法的最优逼近,同时还推广到椭圆。     

关于苏联科学院数学研究所在函数逼近论方面的工作（下）

关于苏联科学院数学研究所在函数逼近论方面的工作（下）ＣＡ．捷里亚可夫斯基（原苏联科学院数学研究所）６多元函数逼近多元函数逼近的正逆定理最早是由Ｄ．Ｊａｃｋｓｏｎ［４］和Ｓ．Ｎ．Ｂｅｒｎｓｔｅｉｎ［５］与一元函数的定理同时给出的，对多元函数的系统研究要...     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

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.     

Active control of secondary resonances piezoelectric sandwich beams

Secondary resonances of piezoelectric/elastic/piezoelectric sandwich beams submitted to active control are studied in this paper. The proportional and derivative nonlinear potential feedback controls via piezoelectric sensor and actuator layers are used. The dynamics of the beam is modelled by a highly nonlinear ordinary-differential equation. The method of multiple scales is applied and approximate solutions are obtained for hard excitations. Analytical frequency and phase-amplitude relationships as well as the time response are explicitly given for various super- and subharmonic resonances. Static and dynamic stability criteria are elaborated and critical displacement and excitation amplitudes associated to the resulting unstable zones are analytically given. The feedback parameters effects on the subharmonic and superharmonic resonances and on their stability are investigated.     

Nonlinear and Geometric Programming – Current Status

Great strides have been made in nonlinear programming (NLP) in the last 5 years. In smooth NLP, there are now several reliable and efficient codes capable of solving large problems. Most of these implement GRG or SQP methods, and new software using interior point algorithms is under development. NLP software is now much easier to use, as it is interfaced with many modeling systems, including MSC/NASTRAN, and ANSYS for structural problems, GAMS and AMPL for general optimization, Matlab and Mathcad for general mathematical problems, and the widely used Microsoft Excel spreadsheet. For mixed integer problems, branch and bound and outer approximation codes are now available and are coupled to some of the above modeling systems, while search methods like Tabu Search and Genetic algorithms permit combinatorial, nonsmooth, and nonconvex problems to be attacked.     

A 3D modeling of static and forward smoldering combustion in a packed bed of materials

A three-dimensional (3D) model based on the first principles of mass, momentum and energy was developed that numerically simulates the processes of static and forward smoldering in a porous packed bed of plant materials. The packed bed contains cellulose material or tobacco (cigarette) wrapped in a porous paper and surrounded by an ambient air. Other major characteristics of the model are including the effects of buoyancy forces in the flow field, separate treatment of solid and gas in a thermally non-equilibrium environment, and use of multi-precursor kinetic models for the pyrolysis of staring material and oxidation of char. The changes in porosity due to pyrolysis and char oxidation and the effect of porosity on the bed permeability and gas diffusivity are included. The mass, momentum, energy, and species transport equations are solved in a discretized computational domain using a commercially available computational fluid dynamics (CFD) code. The simulation results show that the model reasonably reproduces the major features of a burning cigarette during smoldering and puffing and are in a good agreement with the existing experimental results for cigarettes. Results include the velocity profiles, gas and solid temperatures, coal shape, burn rates, profile and transport of gas and vapor species throughout the packed bed, dilution through the wrapper paper and ventilation in the filter section, and the mass fraction of some pyrolysis and oxidation products in the mainstream and sidestream flows.     

Some recurrence formulas for box splines and cone splines

A degree elevation formula for multivariate simplex splines was given by Micchelli and extended to hold ]or multivariate Dirichlet splines in [8]. We report similar formulae for multivariate cone splines and box splsplines andines. To this end, we utilize a relation due to Dahmen and Micchelli that connects box cone splines and a degree reduction formulagiven by Cohen, Lyche, and Riesenfeld in [2].     

Financial Risk Modelling and Econometric Inference

In finance, the explicit modelling of uncertainty takes on a particularly important role. The values of financial derivatives increase in the return volatility of the underlying security. This notion requires a concept of volatility and hence uncertainty. In addition, the choice between modelling in discrete and continuous time is not arbitrary, since it corresponds to a distinction between incomplete and complete markets, respectively, and this distinction matters for asset pricing, financial risk modelling, and inference. Risk and volatility are closely connected, and implied volatility, volatility forecasting, volatility in term structure models, stochastic volatility, and portfolio analysis are considered and related to a more general interplay between cross-sectional and dynamic aspects in finance. Stocks, bonds, and options are considered and placed in the context of efficiency and separation in inference.     

CFD modeling of hydrodynamic characteristics of a gas–liquid two-phase stirred tank

A three-dimensional CFD model was developed in this work to simulate hydrodynamic characteristics of a gas–liquid two-phase stirred tank with two six-bladed turbines and four baffles, coupling of the Multiple Size Group model to determine bubble size distribution. Important hydrodynamic parameters of the multi-phase system such as volume-averaged overall and time-averaged local gas holdups and axial liquid velocities along time and transversal courses were simulated and analyzed in detail, under varied operating conditions (inlet air flow rate and impeller rotation speed). Model predictions of local transient gas holdup and liquid velocity distributions on vertical and horizontal sections of the tank were also carried out. The overall flow patterns were discussed in detail to assess the mixing. Bubble size distributions were further predicted to reveal the unique properties of gas phase. Experimental measurements of overall gas holdups and local axial liquid velocities were used to validate the developed model.     

拓扑空间上不动点和具有上下界的变分不等式

ωω根据广义凸空间上的KKM型定理和Fan-Browder型不动点定理, 得到了没有凸和线性结构且没有紧致框架的拓扑空间上的Φ -映射和弱Φ -映射的若干个新的不动点定理. 作为应用, 在非紧致的拓扑空间上讨论了具有上下界的变分不等式解的存在性问题.     

复杂装备研制协调超网络均衡与实现路径

复杂装备研制主体间呈现社会关系、合作关系、协调关系等网络关系,并且相互影响相互作用,其影响复杂装备研制的重要参数。为有效描述在资源环境约束下制造商和供应商的关系,探讨复杂装备研制协调机理与实现路径,本文利用超网络方法,设计了相互影响、相互作用的社会关系网络、协调网络和合作网络的复杂装备研制协调超网络,并将社会关系水平、协调度和合作水平作为超网络的3个决策变量,建立基于关系价值最大、协调成本最低、协调风险最小、合作收益最大、合作风险最小和成本最小等不同偏好下的多目标最优决策模型,构建了复杂装备研制超网络均衡模型,并利用其探讨超网络均衡和实现路径。