三组谱的Sturm-Liouville反问题

考虑与三组谱关联的逆Sturm-Liouville问题,证明了若对于给定的两组数列,在一定条件下,可划分为三组数列,使其分别为区间[0,a]上三个Sturm-Liouville问题的部分特征值,则通过三组谱的部分特征值能唯一确定区间[0,a]上的势函数q(x).     

利用近似能量极小构造平面C1三次Hermite插值曲线

研究了利用近似能量极小构造平面$C^1$三次Hermite插值曲线的方法.该方法的主要的目是求出$C^1$三次Hermite插值曲线的最佳切矢.通过将应变能、曲率变化能和组合能的近似函数极小化,得到了求解最佳切矢的线性方程组.通过求解发现,近似曲率变化能极小不存在唯一解, 而近似应变能极小和近似组合能极小由于方程系统的系数矩阵为严格对角占优故都存在唯一解.最后, 通过实例表明了本文方法构造平面$C^1$三次Hermite插值曲线的有效性.     

Disjointly homogeneous rearrangement invariant spaces via interpolation

A Banach lattice E is called p-disjointly homogeneous  , 1≤p≤∞$1\le p\le \infty$, when every sequence of pairwise disjoint normalized elements in E   has a subsequence equivalent to the unit vector basis of _?p${?}_p$. Employing methods from interpolation theory, we clarify which r.i. spaces on [0,1]$[0,1]$ are p  -disjointly homogeneous. In particular, for every 1<p<∞$1<p<\infty$ and any increasing concave function φ   on [0,1]$[0,1]$, which is not equivalent to neither 1 nor t, there exists a p-disjointly homogeneous r.i. space with the fundamental function φ  . Moreover, it is shown that given 1<p<∞$1<p<\infty$ and an increasing concave function φ with non-trivial dilation indices, there is a unique p-disjointly homogeneous space among all interpolation spaces between the Lorentz and Marcinkiewicz spaces associated with φ.     

Limit cases of reiteration theorems

We consider real interpolation methods defined by means of slowly varying functions and rearrangement invariant spaces, for which we present a collection of reiteration theorems for interpolation and extrapolation spaces. As an application we obtain interpolation formulas for Lorentz‐Karamata type spaces, for Zygmund spaces , and for the grand and small Lebesgue spaces.     

基于STM32F4的时栅位移传感器信号处理系统设计

为了提高时栅位移传感器的测量精度及分辨率,提出了一种基于STM32F4的时栅位移传感器信号处理系统。系统包括硬件电路和软件设计,运用STM32F4处理器产生的高频时钟脉冲插补感应信号和参考信号的相位差,实现了相位检测。经实验验证,采用系统后,时栅位移传感器的角度误差峰峰值为2.4＂,实现了高精度、高分辨率的时栅角位移测量。     

Representation of discrete sequences with N-dimensional iterated function systems in tensor form

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine or piecewise self-affine in R ² or R ³ (R is the set of real numbers). In this paper, the piecewise hidden-variable fractal model is extended from R ³ to R ⁿ (n is an integer greater than 3), which is called the multi-dimensional piecewise hidden variable fractal model. This new model uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the hidden variables. Therefore the result is very general. Moreover, the piecewise hidden-variable fractal model in tensor form is more terse than in the usual matrix form.     

A Family of Approximation Formulas and some Applications

The general scheme, suggested in [1] using a basis of an infinite-dimensional space and allowing to construct finite-dimensional orthogonal systems and interpolation formulas, is improved in the paper. This results particularly in a generalization of the well-known scheme by which periodic interpolatory wavelets are constructed. A number of systems which do not satisfy all the conditions for multiresolution analysis but have some useful properties are introduced and investigated.

Starting with general constructions in Hilbert spaces, we give a more careful consideration to the case connected with the classic Fourier basis.

Convergence of expansions which are similar to partial sums of the summation method of Fourier series, as well as convergence of interpolation formulas are considered.

Some applications to fast calculation of Fourier coefficients and to solution of integrodifferential equations are given. The corresponding numerical results have been obtained by means of MATHEMATICA 3.0 system.