Multilinear Calderón-Zygmund Theory

A systematic treatment of multilinear Calderón-Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, a multilinear T1 theorem, and a variety of results regarding multilinear multiplier operators.     

On G 2 Continuous Spline Interpolation of Curves in ℝ d

In this paper the problem of G ² continuous interpolation of curves in ^d by polynomial splines of degree n is studied. The interpolation of the data points and two tangent directions at the boundary is considered. The case n = r + 2 = d, where r is the number of interior points interpolated by each segment of the spline curve, is studied in detail. It is shown that the problem is uniquely solvable asymptotically, e., when the data points are sampled regularly and sufficiently dense, and lie on a regular, convex parametric curve in ^d . In this case the optimal approximation order is also determined.     

Schif碱药物与细菌作用的热力学研究

在不同温度条件下利用微量热法测定了大肠杆菌以及大肠杆菌在６种Ｓｃｈｉｆ碱药物抑制下的生长热谱，找出了该细菌生长的最佳生长温度，获得了该细菌在不同温度条件及抑制情况下生长代谢的速率常数，并借助化学反应中分子碰撞理论计算了该细菌生长的生长活化能，在此基础上借用化学反应速率的活化络合物理论模型对大肠杆菌生长代谢的生化反应进行了热力学分析     

任意三角形单元上的三次Lagrange型插值逼近

本文推广了文［２］中的结果，对于任意三角形单元的三次Ｌａｇｒａｎｇｅ型插值多项式给出了原函数ｕ与被插函数Ｕ之间的误差估计     

On a class of martingale inequalities

Let Z = {Z₀, Z₁, Z₂,…} be a martingale, with difference sequence X₀ = Z₀, X_i = Z_i ? Z_{i ? 1}, i ≥ 1. The principal purpose of this paper is to prove that the best constant in the inequality λP(sup_i |X_i| ≥ λ) ≤ C sup_iE |Z_i|, for λ > 0, is C = (log 2)^?1. If Z is finite of length n, it is proved that the best constant is $\text{C}{}_{\mathrm{n}}\text{= [n(2}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}\text{? 1)]}{}^{\mathrm{?1}}$. The analogous best constant C_n(z) when Z₀ ≡ z is also determined. For these finite cases, examples of martingales attaining equality are constructed. The results follow from an explicit determination of the quantity G_n(z, E) = sup_zP(max_i=1,…,n |X_i| ≥ 1), the supremum being taken over all martingales Z with Z₀ ≡ z and E|Z_n| = E. The expression for G_n(z,E) is derived by induction, using methods from the theory of moments.     

Parallel Calculation of Accurate Path Lines in Virtual Environments through Exploitation of Multi-Block CFD Data Set Topology

The use of Virtual Reality (VR) techniques for the investigation of complex flow phenomena offers distinct advantages in comparison to conventional visualization techniques. Especially for unsteady flows, VR methodology provides an intuitive approach for the exploration of simulated fluid flows. However, the visualization of Computational Fluid Dynamics (CFD) data is often too time-consuming to be carried out in real-time, and thus violates essential constraints concerning real-time interaction and visualization. To overcome this obstacle, we make use of the fact that typically a multi-block approach is employed for domain decomposition, and we use the corresponding data structures for the computation of path lines and for parallelization. In this paper, we present the synthesis of fragmented multi-block data sets and our implementation of an accurate path line integration scheme in order to speed up path line computations. We report on the results of our efforts and describe a combination of this algorithm with a highly efficient visualization approach of large amounts of particle traces, thus considerably improving interactivity when exploring large scale CFD data sets.Mathematics Subject Classifications (2000) 76Mxx, 76M27, 76M28, 65M55, 65L05, 65L06, 65D05, 65Y05, 68U05.     

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。     

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 .