Small Ball Probabilities of Fractional Brownian Sheets via Fractional Integration Operators

We investigate the small ball problem for d-dimensional fractional Brownian sheets by functional analytic methods. For this reason we show that integration operators of Riemann–Liouville and Weyl type are very close in the sense of their approximation properties, i.e., the Kolmogorov and entropy numbers of their difference tend to zero exponentially. This allows us to carry over properties of the Weyl operator to the Riemann–Liouville one, leading to sharp small ball estimates for some fractional Brownian sheets. In particular, we extend Talagrand's estimate for the 2-dimensional Brownian sheet to the fractional case. When passing from dimension 1 to dimension d2, we use a quite general estimate for the Kolmogorov numbers of the tensor products of linear operators.     

Linear discriminant analysis in network traffic modelling

It is difficult to give an accurate judgement of whether the traffic model fit the actual traffic. The traditional method is to compare the Hurst parameter, data histogram and autocorrelation function. The method of comparing Hurst parameter cannot give exact results and judgement. The method of comparing data histogram and autocorrelation only gives a qualitative judgement. Based on linear discriminant analysis we proposed a novel arithmetic. Utilizing this arithmetic we analysed some sets of data with large and little differences. We also analysed some sets of data generated by network simulator. The analysis result is accurate. Comparing with traditional method, this arithmetic is useful and can conveniently give an accurate judgement for complex network traffic trace. Copyright © 2005 John Wiley & Sons, Ltd.     

基于FRFT的二维扩频通信方案

介绍了分数阶傅里叶变换的基本概念和原理,分析了线性调频信号在分数阶傅里叶变换中的特点,指出用分数阶傅里叶变换对线性调频信号进行检测和解调的理论依据,并在此基础上,提出了1种基于分数阶傅里叶变换的二维扩频通信方案。该方案的优点在于使通信系统的抗侦收和抗干扰能力更强,提高了战场的频谱使用率。     

Characteristics of high energy interactions II. Production spectra of Gamma-rays in graphite

Twenty high energy nuclear interactions produced in the graphite units of an emulsion chamber were recorded. The emulsion chamber was exposed to cosmic rays at an atmospheric depth of 10 g cm⁻² for about 7 hr over Hyderabad, India. Fourteen interactions which radiated energyΣ E _r⩾1000 GeV in the form ofγ-rays were analysed in detail. The median energy 〈Σ E _r〉 of the interactions was 1600 GeV. Results concerning the multiplicity, the transverse and longitudinal momentum distributions, and the fractional energy distribution ofγ-rays in these interactions are presented. The average transverse momentum ofπ ⁰—mesons <pt _π ⁰> is found to increase very slowly with the primary energyE ₀ and it can be approximated by the function <pt _π ⁰>=0·238E ₀ ^0.06 .     

DSSS系统中基于分数阶傅立叶变换的 扫频干扰抑制算法

本文提出了一种基于分数阶傅立叶变换的DSSS系统中扫频干扰的自适应抑制算法,分析了分数阶傅立叶域中扫频干扰的检测和抑制的基本原理,并给出了相应的干扰抑制接收机的结构,性能分析表明,该方法可获得明显的信噪比改善及较好的误码率性能,和其他基于二维时频分析工具的滤波算法相比,降低了计算的复杂度,其实现更为简便.     

Determination of Squalene Using High-Performance Liquid Chromatography with Diode Array Detection

A high-performance liquid chromatographic method with photodiode array detection has been developed for the determination of squalene. After treated by extraction and fractional crystallization, squalene was analyzed on a C₁₈ column (150 × 3.9 mm, 5 m) with acetonitrile as mobile phase. Excellent linearity of the calibration curve was observed in the range of 100–40000 gL^–1 and the detection limit was 40 gL^–1. The recoveries were from 89.6% to 100.5% and the relative standard deviations were from 0.5% to 1.4%. The method was successfully applied to the determination of squalene in squalene capsules, olive oil, algal lipids and algal cells.     

On the error estimates for the rotational pressure-correction projection methods

In this paper we study the rotational form of the pressure-correction method that was proposed by Timmermans, Minev, and Van De Vosse. We show that the rotational form of the algorithm provides better accuracy in terms of the -norm of the velocity and of the -norm of the pressure than the standard form.

     

Existence of positive solutions of nonlinear fractional differential equations

Existence of positive solutions for the nonlinear fractional differential equation D^su(x)=f(x,u(x)), 0<s<1, has been studied (S. Zhang, J. Math. Anal. Appl. 252 (2000) 804-812), where D^s denotes Riemann-Liouville fractional derivative. In the present work we study existence of positive solutions in case of the nonlinear fractional differential equation:

L(D)u=f(x,u),u(0)=0,0<x<1,     

On support points of univalent functions and a disproof of a conjecture of Bombieri

We consider the linear functional for on the set of normalized univalent functions in the unit disk and use the result to disprove a conjecture of Bombieri.