Cyclic BSEC of block size 3

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this note, we discuss constructions of these designs having cyclic automorphisms. We use Langford sequences to construct all possible cyclic BSEC (or CBSEC) with block size 3 and λ = 1,2, which establishes the necessary and sufficient conditions for such designs. Some constructions of the balanced sampling plan avoiding adjacent units, a generalization of BSEC, are also given for fixed λ.     

聚类分析在无回答现象中的应用

对于抽样调查中的无回答现象,本文应用聚类分析方法对辅助变量的数据进行分层,更好地利用了分层后的信息,改进了对无回答变量的估计。将聚类分析与抽样调查结合起来,是一个比较新的尝试,能够更好地解决实际问题中多变量数据的分层问题,进而对提高抽样调查的精度有重要意义。     

Approximation of signals from local averages

This work is concerned with approximation of a signal from local averages. It improves a result of Butzer and Lei [P.L. Butzer, J. Lei, Approximation of signals using measured sampled values and error analysis, Commun. Appl. Anal. 4 (2000) 245–255].     

基于双尺度方程近似解的适合任何连续信号的近似采样定理

提出了一个对任何连续信号,利用双尺度方程的近似解的近似采样定理.采样函数是一个双尺度方程的近似解,是一个逐段线性函数,有明确的计算公式,且精度可以控制.采样函数由双尺度方程的系数唯一决定,可以通过选择双尺度方程的系数而使采样函数具有良好的性质.     

Optimal rates for spectral algorithms with least-squares regression over Hilbert spaces

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regression, principal component regression, and gradient methods. We prove optimal, high-probability convergence results in terms of variants of norms for the studied algorithms, considering a capacity assumption on the hypothesis space and a general source condition on the target function. Consequently, we obtain almost sure convergence results with optimal rates. Our results improve and generalize previous results, filling a theoretical gap for the non-attainable cases.     

Bounded mean oscillation and bandlimited interpolation in the presence of noise

We study some problems related to the effect of bounded, additive sample noise in the bandlimited interpolation given by the Whittaker-Shannon-Kotelnikov (WSK) sampling formula. We establish a generalized form of the WSK series that allows us to consider the bandlimited interpolation of any bounded sequence at the zeros of a sine-type function. The main result of the paper is that if the samples in this series consist of independent, uniformly distributed random variables, then the resulting bandlimited interpolation almost surely has a bounded global average. In this context, we also explore the related notion of a bandlimited function with bounded mean oscillation. We prove some properties of such functions, and in particular, we show that they are either bounded or have unbounded samples at any positive sampling rate. We also discuss a few concrete examples of functions that demonstrate these properties.     

A Sampling Theory for Compact Sets in Euclidean Space

We introduce a parameterized notion of feature size that interpolates between the minimum of the local feature size and the recently introduced weak feature size. Based on this notion of feature size, we propose sampling conditions that apply to noisy samplings of general compact sets in euclidean space. These conditions are sufficient to ensure the topological correctness of a reconstruction given by an offset of the sampling. Our approach also yields new stability results for medial axes, critical points, and critical values of distance functions. The authors were partially supported by DARPA under grant HR0011-05-1-0007 and by ANR under grant “Topologie, Géométrie Différentielle et Algorithmes.”     

计量调整型抽样检验系统GB/T6378-1986与ISO3951 :1989的比较分析

GB/T6378-1986作为计量抽样检验方面的基础性国家标准,是参照国际标准ISO3951:1989而制定的。1989年国际标准化组织ISO/TC69发布了ISO3951的修订版本ISO3951:1989,ISO3951的这一修订版反映了计量抽样检验的最新研究成果,为开展国家标准GB/T6378的修订工作,本文系统地对GB/T6378-86和ISO3951:89进行了比较分析研究。     

Frames arising from irreducible solvable actions I

In this work, we provide a unified method for the construction of reproducing systems arising from unitary irreducible representations of some solvable Lie groups. In contrast to other well-known techniques such as the coorbit theory, the generalized coorbit theory and other discretization schemes, we make no assumption on the integrability or square-integrability of the representations of interest. Moreover, our scheme produces explicit constructions of frames with precise frame bounds. As an illustration of the scope of our results, we highlight that a large class of representations which naturally occur in wavelet theory and time–frequency analysis is handled by our scheme. For example, the affine group, the generalized Heisenberg groups, the shearlet groups, solvable extensions of vector groups and various solvable extensions of non-commutative nilpotent Lie groups are a few examples of groups whose irreducible representations are handled by our method. The class of representations studied in this work is described as follows. Let G be a simply connected, connected, completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}$. Next, let π be an infinite-dimensional unitary irreducible representation of G obtained by inducing a character from a closed normal subgroup $P=\exp ?\mathfrak{p}$ of G. Additionally, we assume that $G=P?M$, $M=\exp ?\mathfrak{m}$ is a closed subgroup of G, $d{\mu }_M$ is a fixed Haar measure on the solvable Lie group M and there exists a linear functional $\lambda \in {\mathfrak{p}}^{?}$ such that the representation $\pi ={\pi }_{\lambda }={\mathrm{ind}}_P^G\left({\chi }_{\lambda }\right)$ is realized as acting in $L^2(M,d{\mu }_M)$. Making no assumption on the integrability of ${\pi }_{\lambda }$, we describe explicitly a discrete subset Γ of G and a vector $\mathbf{f}\in L^2(M,d{\mu }_M)$ such that ${\pi }_{\lambda }\left(\mathrm{\Gamma }\right)\mathbf{f}$ is a tight frame for $L^2(M,d{\mu }_M)$. We also construct compactly supported smooth functions s and discrete subsets $\mathrm{\Gamma }?G$ such that ${\pi }_{\lambda }\left(\mathrm{\Gamma }\right)\mathbf{s}$ is a frame for $L^2(M,d{\mu }_M)$.     

The Development of Appropriate Upscaling Procedures

Permeability upscaling should be carried out with careful attention to the nature of rock heterogeneities. While there are many large-scale features which must be taken into account, there are also important heterogeneities at the small-scale. Many sedimentary structures contain laminae at the mm–cm scale, and beds at the m-scale, which give rise to strong contrasts in permeability. We use a 2D model derived from a photo-panel of an aeolian outcrop, along with permeability measurements from a North Sea oil field, to demonstrate the effects of small-scale heterogeneity. This model is similar in size to a typical cell of a reservoir geological model. We take imaginary probe and core plug measurements from the model, average them, and compare these with the effective permeability for the model computed from a finite difference flow calculation. Although this procedure is standard practice, we show that it can lead to biased estimates of the permeabilities used in flow simulation. As an alternative we suggest using models of representative beds, and performing flow simulation to calculate effective permeabilities for both single-phase and two-phase flow.