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.     

Multiple dependent state sampling plans for lot acceptance based on measurement data

This paper proposes a multiple dependent (or deferred) state sampling plan by variables for the inspection of normally distributed quality characteristics. The decision upon the acceptance of the lot is based on the states of the preceding lots (dependent state plan) or on the states of the forthcoming lots (deferred state plan). The lot acceptance probability is derived and the two-point approach to determining the plan parameters is described. The advantages of this new variables plan over conventional sampling plans are discussed. Tables are constructed for the selection of parameters of this plan under the specific values of the producer’s and consumer’s risks, indexed by acceptable quality level and limiting quality level, when the standard deviation is known or unknown.     

GC analysis of gas in halogen lamps using a new sampling device

Summary A new type of gas sampling device was constructed to improve the analysis of the gas in halogen lamps. Low levels of gases such as O₂, CH₄, C₂H₄ and CH₃Br could be determined by the techniques worked out.     

流动注射氢化物发生-蒸气贮存脉冲进样原子荧光法测定地质样品中的痕量砷

本文研究了流动注射氢化物发生－蒸气贮存脉冲进样原子荧光法测定地质样品中痕量砷的方法，砷的灵敏度提高17.6倍，精密度(RSD)为2.1%，检出限为0.32ng/mL。用于地质标准样的测定，结果满意。     

抽样调查的设计与分析(Ⅱ)

本文讨论抽样调查实践中有关设计和数据分析中的若干问题．第二部分主要涉及数据处理与统计分析问题．     

Head space gas chromatography with glass capillaries using an automatic electropneumatic dosing system

Head space GC using a special electropneumatic sampling system works well in combination with glass capillaries. Because a homogenous gas mixture is already present most problems inherent with inlet splitters are thus avoided. In cases where the high vapor pressure of the sample can cause problems with the pressure controlled sampling system, the use of narrow bore glass capillaries provides the necessary inlet pressure. The use of this powerful and convenient analytical tool for water pollution analysis, flavour analysis and the analysis of volatiles in crude oil samples is shown by examples.     

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 $L^2(M,d{\mu }_M)$.     

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.     

Sampling and recovery of multidimensional bandlimited functions via frames

In this paper, we investigate frames for L₂d[−π,π] consisting of exponential functions in connection to oversampling and nonuniform sampling of bandlimited functions. We derive a multidimensional nonuniform oversampling formula for bandlimited functions with a fairly general frequency domain. The stability of said formula under various perturbations in the sampled data is investigated, and a computationally manageable simplification of the main oversampling theorem is given. Also, a generalization of Kadec's 1/4 theorem to higher dimensions is considered. Finally, the developed techniques are used to approximate biorthogonal functions of particular exponential Riesz bases for L₂[−π,π], and a well-known theorem of Levinson is recovered as a corollary.     

Weighted sampling and reconstruction in weighted reproducing kernel spaces

In this paper, we discuss sampling and reconstruction of signals in the weighted reproducing kernel space associated with an idempotent integral operator. We show that any signal in that space can be stably reconstructed from its weighted samples taken on a relatively-separated set with sufficiently small gap. We also develop an iterative reconstruction algorithm for the reconstruction of a signal from its weighted samples taken on a relatively-separated set with sufficiently small gap.