Quasilinear evolutionary equations and continuous interpolation spaces

In this paper we analyze the abstract parabolic evolutionary equations

     

On theorems of Gelfond and Selberg concerning integral-valued entire functions

For each sN define the constant θ_s with the following properties: if an entire function g(z) of type t(g)<θ_s satisfies then g is a polynomial; conversely, for any δ>0 there exists an entire transcendental function g(z) satisfying the display conditin and t(g)<θ_s+δ. The result θ₁=log2 is known due to Hardy and Pólya. We provide the upper bound θ_sπs/3 and improve earlier lower bounds due to Gelfond (1929) and Selberg (1941).     

小波双线性插值搜索算法及其在光学遥感图像中的应用

详细分析了在小波双线性插值中高频外推阈值门限与峰值信噪比的变化关系,提出了基于峰值信噪比最大的小波双线性插值搜索算法。提出的算法能够自动搜索到峰值信噪比最大的高频外推最佳阈值门限,实现了在不破坏光学遥感图像原始信息的情况下,提高了图像的空间分辨率,有利于对图像的细节信息进行观察分析。实验结果表明:该算法能够得到比双线性插值和全小波插值更高的峰值信噪比、熵值和更好的图像细节效果,是一种适合提高光学遥感图像分辨率的有效算法。     

Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes

In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition _K/h_K c₀ > 0 is not satisfied, whereh_K is the diameter of the element K and _K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L²-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek.     

Interpolation between and

We show that if is a rearrangement invariant space on that is an interpolation space between and and for which we have only a one-sided estimate of the Boyd index 1/p, 1 < p < \infty$">, then is an interpolation space between and . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type .

     

Local behaviour of polynomials

In this paper we study the local behaviour of a trigonometric polynomial around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in . The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form are also proved.

     

Trust-region algorithms for derivative-free optimization and nonlinear bilevel programming

We briefly describe the contents of the authors PhD thesis (see Colson 2003) discussed on July 2003 at the University of Namur (Belgium) and supervised by Philippe L. Toint. The contributions presented in this thesis are the development of trust-region methods for solving two particular classes of mathematical programs, namely derivative-free optimization (DFO) problems and nonlinear bilevel programming problems. The thesis is written in English and is available via the author.Received: July 2003, AMS classification: 65D05, 90C30, 90C56, 90C59     

Implementation of the Sparr Interpolation Method in Classes of Spaces of Smooth Functions

The multidimensional Sparr interpolation method is implemented in the Besov spaces and the Lizorkin--Triebel spaces . It is shown that this results in Besov spaces of type . An interpolation theorem for Besov spaces using weak conditions of the form is formulated.     

On an Embedding Criterion for Interpolation Spaces and Application to Indefinite Spectral Problems

An embedding criterion for interpolation spaces is formulated and applied to the study of the Riesz basis property in the L _2,g space of eigenfunctions of an indefinite Sturm–Liouville problem u=gu on the interval (-1,1) with the Dirichlet boundary conditions, provided that the function g(x) changes sign at the origin. In particular, the basis property criterion is established for an odd g(x). Some connections with stability in interpolation scales are discussed.     

Approximation Constants in Equidistant Lagrange Interpolation

In this paper we present a new limit relation for the equidistant Lagrange interpolation polynomials to |x|, (0, 1] on the internal [–1, 1]. The result extends a well-known result of D. L. Berman and S. M. Losinskii. Furthermore, we briefly discuss on a possible connection of the limit relation to another prominent constant in best uniform polynomial approximation for |x| - the so-called Bernstein constant.