Estimation of the Multivariate Normal Precision Matrix under the Entropy Loss

Let X ₁, , X _n (n > p) be a random sample from multivariate normal distribution N _p (, ), where R ^p and is a positive definite matrix, both and being unknown. We consider the problem of estimating the precision matrix ^–1. In this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of ^–1 is inadmissible and an improved estimator is explicitly constructed. Note that our improved estimator is obtained from the class of lower-triangular scale equivariant estimators.     

Electroweak precision data and gravitino dark matter

Electroweak precision measurements can provide indirect information about the possible scale of supersymmetry already at the present level of accuracy. We review present day sensitivities of precision data in mSUGRA-type models with the gravitino as the lightest supersymmetric particle (LSP). The χ ² fit is based on M _W , sin² θ _eff, (g−2) _μ , BR(b → sγ) and the lightest MSSM Higgs boson mass, M _h . We find indications for relatively light soft supersymmetry-breaking masses, offering good prospects for the LHC and the ILC, and in some cases also for the Tevatron.      

A Fast Algorithm for Wave Propagation from a Plane or a Cylindrical Surface

The newly developed Taylor-Interpolation-FFT (TI-FFT) algorithm dramatically increases the computational speeds for millimeter wave propagation from a planar (cylindrical) surface onto a “quasi-planar” (“quasi-cylindrical”) surface. Two different scenarios are considered in this article: the planar TI-FFT is for the computation of the wave propagation from a plane onto a “quasi-planar” surface and the cylindrical TI-FFT is for the computation of wave propagation from a cylindrical surface onto a “quasi-cylindrical” surface. Due to the use of the FFT, the TI-FFT algorithm has a computational complexity of O(N ² log₂  N ²) for an N × N computational grid, instead of N ⁴ for the direct integration method. The TI-FFT algorithm has a low sampling rate according to the Nyquist sampling theorem. The algorithm has accuracy down to −80 dB and it works particularly well for narrow-band fields and “quasi-planar” (“quasi-cylindrical”) surfaces.     

同轴插板式相移器数值模拟与实验研究

 根据同轴插板式相移器的基本工作原理，对该相移器进行了数值模拟与优化设计，并重点研究了其结构工艺和相移控制方式。在此基础上研制了一个中心频率为4.1 GHz的相移器模型，并通过矢量网络分析仪进行了实验测量。测量结果表明：在4.0～4.2 GHz的频带范围内，该相移器可实现90°的相移量，相移量化精度为1°，相移精度为±１０°,相移器插损1.5 dB。     

悬浮液进样-原子吸收光谱法测定核桃粉中的钙、铁和锌

采用悬浮液进样技术应用于原子吸收光谱法,测定了核桃粉中的钙、铁和锌的含量.将核桃粉悬浮于琼脂胶体中制成悬浮液,直接喷入空气-乙炔火焰,用标准加入法测定,将实验结果与灰化法结果进行了比较,经t检验,在显著性水平a=0.05时两种方法无显著性差异,相对标准偏差≤6.1%,结果吻合较好.该方法简便,快速,灵敏度高,准确性好.     

The analysis of process gases: a review

 A general review of key issues involved in the analysis of process gases is presented. The reasons for such measurements – which include safety, quality, environmental and economic factors are considered. The technical issues arising from these measurements are dependent upon a variety of factors, including the overall sampling system, the type of analytical instrumentation, methods of data collection and the specified calibration protocols. The use of gas calibration cylinders as transfer standards is detailed and issues of stability and traceability to reference material discussed. Received: 1 March 2000 / Accepted: 31 March 2000     

Bounded rank-one perturbations in sampling theory

Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from a family of bounded rank-one perturbations of a self-adjoint operator that has only discrete spectrum of multiplicity one.     

Dual-purpose gas chromatographic injection device for pressurized liquid and gas injection

A dual-purpose gas chromatographic injection device, capable of injecting pressurized liquid sample of up to 5000 psig and gas sample with a volume as high as 5000 μL, has been successfully developed and implemented. The injection device is synergized by the effectiveness of a classical flash vaporization of a syringe injection and the reliability of a proven rotary valve. Depending on the matrix involved, this injection device employs either a commercially available four-port internal valve for liquid sampling or a six-port external valve for gas sampling, a modified removable needle used in standard liquid syringe, and an auxiliary flow stream that can be either mechanical or electronic flow controlled for solute transfer. For pressurized liquid, the device was found suitable of up to nC₁₆ hydrocarbon with no observable carry-over despite the injection device was operating at ambient temperature. A relative standard deviation of less than 2% (n = 20) was obtained for hydrocarbon compounds ranging from nC₈ to nC₁₆. For gas injection, the device performed well even under difficult chromatographic conditions such as with a low column inlet pressure of less than 1 psig. A relative standard deviation of less than 0.5% (n = 10) was obtained for reactive sulfur compounds such as alkyl mercaptans. The device can be operated manually or automated with pneumatic or electrical actuator, is platform neutral, and can be moved amongst instruments without hardware modification as well as implemented for on-line or in situ applications. In this paper, the utility of the device was also demonstrated with selected GC applications of industrial significance.     

Randomized approximation of Sobolev embeddings, III

We continue the study of randomized approximation of embeddings between Sobolev spaces on the basis of function values. The source space is a Sobolev space with nonnegative smoothness order; the target space has negative smoothness order. The optimal order of approximation (in some cases only up to logarithmic factors) is determined. Extensions to Besov and Bessel potential spaces are given and a problem recently posed by Novak and Woźniakowski is partially solved. The results are applied to the complexity analysis of weak solution of elliptic PDE.     

Grab vs. composite sampling of particulate materials with significant spatial heterogeneity—A simulation study of “correct sampling errors”

Sampling errors can be divided into two classes, incorrect sampling and correct sampling errors. Incorrect sampling errors arise from incorrectly designed sampling equipment or procedures. Correct sampling errors are due to the heterogeneity of the material in sampling targets. Excluding the incorrect sampling errors, which can all be eliminated in practice although informed and diligent work is often needed, five factors dominate sampling variance: two factors related to material heterogeneity (analyte concentration; distributional heterogeneity) and three factors related to the sampling process itself (sample type, sample size, sampling modus). Due to highly significant interactions, a comprehensive appreciation of their combined effects is far from trivial and has in fact never been illustrated in detail. Heterogeneous materials can be well characterized by the two first factors, while all essential sampling process characteristics can be summarized by combinations of the latter three. We here present simulations based on an experimental design that varies all five factors. Within the framework of the Theory of Sampling, the empirical Total Sampling Error is a function of the fundamental sampling error and the grouping and segregation error interacting with a specific sampling process. We here illustrate absolute and relative sampling variance levels resulting from a wide array of simulated repeated samplings and express the effects by pertinent lot mean estimates and associated Root Mean Squared Errors/sampling variances, covering specific combinations of materials’ heterogeneity and typical sampling procedures as used in current science, technology and industry. Factors, levels and interactions are varied within limits selected to match realistic materials and sampling situations that mimic, e.g., sampling for genetically modified organisms; sampling of geological drill cores; sampling during off-loading 3-dimensional lots (shiploads, railroad cars, truckloads etc.) and scenarios representing a range of industrial manufacturing and production processes. A new simulation facility “SIMSAMP” is presented with selected results designed to show also the wider applicability potential. This contribution furthers a general exposé of all essential effects in the regimen covered by “correct sampling errors”, valid for all types of materials in which non-bias sampling can be achieved.