修正样条小波最小二乘法用于分辨高噪声重叠峰

采用连续样条小波变换确定重叠信号的组分峰的数目和峰位置,将样条小波最小二乘法加以改进,使其成为既能滤出噪声又能分峰的新方法.对信噪比为1的重叠峰进行处理,得到满意结果.该方法只需对信号进行一次处理,处理速度快,且数据点无须为2n(n∈Z).应用于毛细管电泳电导信号的处理,得到满意结果.     

齐型空间中分数次积分交换子的加权端点估计

该文得到齐型空间中分数次积分交换子[b,I_α]的加权端点估计ω({x∈X:|[b,I_α]f(x)|t})≤Cψ(∫_xA(||b||_*(|f(x)|/t)■(ω(x))dμ(x))其中b∈BMO(X,d,μ),A(t)=tlog(e+t),ψ(t)=[tlog(e+t~α)]~(1/(1-α)),■(t)=t~(1-α)log(e+t~(-α)).     

板问题三次样条有限元的超收敛及高精度组合公式

1．引言与问题提出双三次样条有限元是应用比较广泛的矩形板元之一，与其它协调元相比恻双三次Her－mite矩形元），除达到饱和精度O（h‘）外，计算量却小得多［‘］，因而受到人们的重视．目前关于这方面的研究工作已有许多［1，并但关于板弯曲问题的双三次样条有限元的超收敛结果，却尚未见到．本文应用双三次样条插值的逐项渐近展式，通过对有限元的双线性形式进行展开，得到了双三次样条有限元一、二阶偏导数的渐近展式及超收敛结果．考虑如下矩形板弯曲模型问题上述方程对应的双线性形式为对VV，VE”，满足其中，M，。为正常数，11…     

The U~* -property of Orlicz Spaces

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A New Method to Resolve Overlapped Voltammetric Peaks

A new method called spline convolution (SC) for resolving overlapped peaks was proposed in this paper. The differential pulse voltammetric overlapped peaks of mixtures of Pb(Ⅱ） and T1(I) were investigated by this method, and satisfactory results were obtained. The results show excellent correlation between peak areas of the processed signals and the concentrations.     

Some Inequalities in Classical Spaces with Mixed Norms

We consider some inequalities in such classical Banach Function Spaces as Lorentz, Marcinkiewicz, and Orlicz spaces. Our aim is to explore connections between the norm of a function of two variables on the product space and the mixed norm of the same function, where mixed norm is calculated in function spaces on coordinate spaces, first in one variable, then in the other. This issue is motivated by various problems of functional analysis and theory of functions. We will currently mention just geometry of spaces of vector-valued functions and embedding theorems for Sobolev and Besov spaces generated by metrics which differ from L ^p. Our main results are actually counterexamples for Lorentz spaces versus the natural intuition that arises from the easier case of Orlicz spaces (Section 2). In the Appendix we give a proof for the Kolmogorov–Nagumo theorem on change of order of mixed norm calculation in its most general form. This result shows that L ^p is the only space where it is possible to change this order.     

最小能量控制与Lg样条函数

本文考察了一类带有泛函约束的线性系统的最小能量控制问题与Lg样条插值函数的对应关系.得到了求解最优控制——样条函数的递推算法;并建立了最优控制问题解法Ⅱ,指出文献[1]的解法可作为它的特例.     

阶跃伏安法离散数据连续化及导数卷积的方法 Ⅰ.样条插值法

本文对采用样条函数插值法解决阶跃伏安法中离散数据连续化及进一步的导数卷积处理进行了详细讨论。用模拟数据和实验数据进行了该方法的效果测试。结果表明,样条函数插值法处理连续化问题,具有显著的优越性,能成功地解决阶跃伏安法在大阶梯增量(△E)快速扫描时存在的由于采样点不多而造成的波形显示、导数卷积后波形杂散等问题。     

Norm-preserving extensions of functionals and denting points of convex sets

Let W and Z be Banach spaces, and let and be closed subspaces. Let be a subspace of , the Banach space of bounded linear operators from W* to Z**, containing . We describe, for and , all norm-preserving extensions of to the space in terms of convergence of convex combinations. We also characterize denting points of bounded convex subsets of Banach spaces in similar terms. Various applications are presented. Supported by Estonian Science Foundation Grant 5704.