On interpolation by radial polynomials

A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning interpolation by radial polynomials. Schaback's interpolant is explored. Happy 60th and beyond, Charlie! Mathematics subject classifications (2000) 41A05, 41A6.     

（0,1;0）-INTERPOLATION ON INFINITE INTERVAL （-∞, ＋∞）

In this paper, we study the explicit representation and convergence of （0, 1;0）-interpolation on infisite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values areprescribed at two set of points namely the zeros of Hn（x） and H′n （x） and the first derivatives at the zerosof H′n（x）.     

系统动力学模型结构分析中表函数的改进方法

分析了非线性系统动力学(SD)模型中表函数环节的传统表示方法,指出该方法对于进行SD模型的结构分析所造成的障碍,并提出了用牛顿插值的承袭性算法来改进表函数环节的表示方法的思路.接着分别介绍了用差商和差分牛顿插值法改进表函数的过程.最后,通过一个实例说明了表函数改进的方法,并展示了以此为基础进行结构分析的思路.     

C~k连续的保形分段2k次多项式插值

1．引言在每个子区间上，通过插入至多一个内结点，Brodlie和Butt［1］给出了分段三次多项式保形插值算法，Randal［2］等讨论了分段五次多项式插值，作者［31讨论了一般分段奇次多项式的保形插值，并且给1了内结点的位置范围公式．这种插值方法完全解决了一般的分段奇次多项式的保形插值问题．关于分段偶次多项式的保形插值，大多数文献只讨论分段二次保形插值，这里要特别指出的是Shumake［4j导出了二次样条保凸的充要条件，并且给出了一个二次样条保形插值的方法．在每一个子区间上至多插入一个内结点，则一个二次插值样条就可得到．作…     

Upward and downward heat and mass transfer with miniature periodically operating loop thermosyphons

Upward and downward two-phase heat and mass transfer has been considered in the present paper. The heat and mass transfer with the condenser located below the evaporator has been obtained by inserting an accumulator tank in the liquid line of a loop thermosyphon and enforcing a pressure pulsation. In previous papers these heat transfer devices have been called pulsated two phase thermosyphons (PTPT). A mini PTPT has been experimentally investigated. It has shown a stable periodic heat transfer regime weakly influenced by the position of the condenser with respect to the evaporator. In contrast a classical loop mini thermosyphon (diameter of connecting pipes 4 mm) did not achieve a stable functioning for the investigated level differences between evaporator and condenser lower than 0.37 m. The present study shows that the functioning of a PTPT device does not directly depend on the level difference or the presence of noncondensable gas. In order to obtain a natural circulation in mini or micro loops, a periodically operating heat transfer regime should therefore be considered.     

A Sufficient Condition for Interolation by Functions in A~P(φ) (1

肖杰  赵大蕻 《数学季刊》1992,(4)

关于Fejer点上的一种复有理型插值的一致逼近阶

设D是一个Jordan,Г为其边界，并设Г满足Aльпер条件。本文得到了一种基于Fejer点的有理型插值算子对于f(z)∈C（Г）的一致逼近阶。     

Effect of biotransformation on multispecies plume evolution and natural attenuation

Biological transformation of volatile organic compounds is one of the key factors that influence contaminant-plume evolution and thus natural attenuation. In this study we investigate the effect of biological transformation on the transport of contaminants in the aqueous and gaseous phases. The analysis includes the study of the effect of density-driven advection of contaminants in the gaseous phase on multiphase and multispecies flow, fate and transport modeling in the subsurface. Trichloroethylene (TCE) and its two byproducts, dichloroethylene and vinyl chloride, are analyzed as the target contaminants. Our results indicate that density-driven advection of the gaseous phase, which is initiated by evaporation of TCE as a nonaqueous phase liquid, increases the downward and also the lateral migration of TCE within the unsaturated zone. This process also influences the location of high-concentration zones of the byproducts of TCE in the unsaturated and the saturated zones. Biotransformation of TCE contributes to the reduction of dissolved TCE plume development as expected. The daughter byproducts, which are introduced into the subsurface system, show distinct transport patterns as they are affected by their independent degradation kinetics and density-driven advection. These observations, which are based on our simulation results for biotransformation and transport of TCE and its byproducts, are useful in evaluating the natural attenuation processes, its potential health hazards and also the evaluation of potential plume development at contaminated sites.     

Discrete Sturm–Liouville problems, Jacobi matrices and Lagrange interpolation series

The close relationship between discrete Sturm–Liouville problems belonging to the so-called limit-circle case, the indeterminate Hamburger moment problem and the search of self-adjoint extensions of the associated semi-infinite Jacobi matrix is well known. In this paper, all these important topics are also related with associated sampling expansions involving analytic Lagrange-type interpolation series.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.