Conservative Means of Orthogonal Series and the Spaces $$L^p [0;1] $$ , $$p \in (1;\infty ) $$

Necessary and sufficient conditions for an orthogonal series to be the Fourier series of a function in the space , , are obtained. In the special case of regular summation methods we recover the classical results of Orlicz and Lomnicki.     

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

Let p>q and let G be the group U(p, q) or Spin₀(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup where

PPCP用固态脉冲电源的实验研究

 介绍了一种采用半导体开关与磁开关、可饱和脉冲变压器相结合技术的固态脉冲电源，此电源可用于脉冲放电等离子体烟气治理。在理论分析的基础上建立了实验模型，通过实验验证了此类电源的可行性，解决了8支晶闸管开关串联的动静态均压及开通同步性问题，并对可饱和脉冲变压器及磁开关的工作特性进行了分析计算。电源在阻性负载上得到峰值电压37.5 kV、前沿101 ns、脉宽1 μs的脉冲，重复频率300 Hz，输出功率10 kW。     

Tchebycheff-Fourier级数的Vallce Poussin平均逼近函数类Lip α

本文考虑用ＴｃｈｅｂｙｃｈｅｆＦｏｕｒｉｅｒ级数的ＶａｌéｅＰｏｕｓｉｎ平均逼近函数类Ｌｉｐα,在ｆ（ｘ）∈Ｃ［－１,１］时获得了逼近阶及逼近误差的表达式,推广并较大地改进了文献［１,２］中的有关结果．     

综合函数与扩展原理

本文首先对合情扩展映射的公理化条件的完备性与独立性进行讨论,之后给出了扩展原理的一般形式及合情扩展映射的等价定义。最后,利用综合函数,特别是变维综合函数列,给出了扩展原理的一些具体形式     

G. Martens′ Dimension Theorem for Curves of Odd Gonality

For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems W _d ^r (C) is d-3r by a result of M. Coppens et al. Furthermore it is known that if the maximum dimension of W(C) for a curve C of odd gonality is attained then C is of very special type of curves by the recent progress made by G. Martens. The purpose of this paper is to chase an extension of the result of G. Martens; if dim W(C)=d-3r-1 for a curve C of odd gonality for some dg-4 and r1, then C must be either a smooth plane sextic, a pentagonal curve of bounded genus or a smooth plane octic.     

On pointwise convergence of Fourier series of radial functions in several variables

We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.

     

Optimizing the performance of single-mode laser diode system using genetic algorithm

In this correspondence, micro-genetic algorithm (MGA) application results for optimizing the performance of electronic feedback of a laser diode are presented. The goal of optimization is to find the maximum bandwidth of the laser diode with electronic feedback used in fiber optic digital communication. A numerical analysis of the system theory of the single-mode laser diode to obtain numerical results of the gain, the pulse response, and the harmonic distortion for electronic feedback is also presented. The dependence of the system gain on the feedback gain and delay is examined. The pulse response is studied and it is shown that a transmission rate over 1 Gbyte/s can be achieved.     

The analysis of correlation integrals in terms of extremal value theory

In this paper we first give an overview of the methods of analysis of time series in terms of correlation integrals, which were developed for time series generated by deterministic systems. From the extremal value theory one obtains asymptotic information on the behaviour of the correlation integrals of time series generated by non-deterministic (mixing) systems. This leads to an analysis in terms of correlation integrals which is complementary to the estimation of dimension and entropy.Dedicated to the memory of Ricardo Mañé     

Correlation integral as a tool for distinguishing between dynamics and statistics in time series data

We propose a new test for time series data for proper choice of processing technique: dynamical or statistical. It is based upon the normalized slope of the correlation integral (, m) = m⁻¹d(ln C()) /d ln , where m is the embedding dimension. It is shown that when does not tend to 0 on the resolved range of scales as m grows, then there will be serious limitations for dynamical methods even if the data are dynamical by nature. In the latter case it means that the length of time series does not allow to resolve small scales, and on large scales the delay reconstruction for any m mixes true and false neighbours of points and therefore restricts the application of dynamical techniques, such as estimating Lyapunov exponents or predicting time series.