Computation of Spatial Covariance Matrices

In an earlier article, Ghosh derived the density for the distance between two points uniformly and independently distributed in a rectangle. This article extends that work to include the case where the two points lie in two different rectangles in a lattice. This density allows one to find the expected value of certain functions of this distance between rectangles analytically or by one-dimensional numerical integration.

In the case of isotropic spatial models or spatial models with geometric anisotropy terms for agricultural experiments one can use these theoretical results to compute the covariance between the yields in different rectangular plots. As the numerical integration is one-dimensional these results are computed quickly and accurately. The types of covariance functions used come from the Matérn and power families of processes. Analytic results are derived for the de Wijs process, a member of both families and for the power models also.

Software in R is available. Examples of the code are given for fitting spatial models to the Fairfield Smith data. Other methods for the estimation of the covariance matrices are discussed and their pros and cons are outlined.     

最小二乘配点法解壳体弯曲问题

本文用最小二乘配点法分析弹性壳体弯曲问题。采用了加权残数法中的混合法—事先既不满足壳体弯曲定解微分方程式亦不满足边界条件,所选试函数为文献[1]中提到的双重幂级数。对于4边简支圆柱壳,其数值计算解与经典解析解误差不超过1.5％;对于悬臂圆柱壳,取其特例一悬臂效分析时,其结果与解析解误差亦不大。用本法可以编制出壳体弯曲问题的通用计算程序。     

Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions

In the paper, we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions. We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity. And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept. Our mathematical tool is the logarithmic trial equation method.     

基于Excel VBA 的年调节电站水能计算程序编译及应用

水电站电能指标计算在工程规划设计中对电站发电能力评估,其中等出力法的计算涉及大量的假设试算插值工作。结合实际需要,在利用Excel强大数据处理功能的同时,引入VBA编程方法,用编译的计算程序实现试算和插值过程,使计算更加快捷准确。程序应用结果表明,程序计算速度快,计算过程灵活,取得了良好的应用效果。     

Pulsed arterial spin labeling perfusion imaging at 3 T: estimating the number of subjects required in common designs of clinical trials

Pulsed arterial spin labeling (PASL) is an increasingly common technique for noninvasively measuring cerebral blood flow (CBF) and has previously been shown to have good repeatability. It is likely to find a place in clinical trials and in particular the investigation of pharmaceutical agents active in the central nervous system. We aimed to estimate the sample sizes necessary to detect regional changes in CBF in common types of clinical trial design including (a) between groups, (b) a two-period crossover and (3) within-session single dosing. Whole brain CBF data were acquired at 3 T in two independent groups of healthy volunteers at rest; one of the groups underwent a repeat scan. Using these data, we were able to estimate between-groups, between-session and within-session variability along with regional mean estimates of CBF. We assessed the number of PASL tag-control image pairs that was needed to provide stable regional estimates of CBF and variability of regional CBF across groups. Forty tag-control image pairs, which take approximately 3 min to acquire using a single inversion label delay time, were adequate for providing stable CBF estimates at the group level. Power calculations based on the variance estimates of regional CBF measurements suggest that comparatively small cohorts are adequate. For example, detecting a 15% change in CBF, depending on the region of interest, requires from 7-15 subjects per group in a crossover design, 6-10 subjects in a within-session design and 20-41 subjects in a between-groups design. Such sample sizes make feasible the use of such CBF measurements in clinical trials of drugs.     

Optimized t-expansion method for the Rabi Hamiltonian

A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E₀ of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E₀ is assumed to be stationary with respect to the free parameters. A high accuracy of E₀ estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than ¹⁰−4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E₁, with the relative error smaller than ¹⁰−2 (1%).     

Trace elements in bovine muscle: an ongoing project for a new certified reference material

In the framework of the activities of the Community Reference Laboratory (CRL) for residues at the Istituto Superiore di Sanità (ISS) of Rome, a number of proficiency tests were performed in order to assess and improve, wherever necessary, the quality of regulatory residue analysis within the EU. In this context, a pilot study was undertaken with the purpose of ascertaining the feasibility of a project for the certification of a new reference material for trace elements in bovine muscle. On behalf of the ISS, approximately 70 kg of bovine muscle, collected at a slaughterhouse in Geel (Belgium), were freeze-dried, homogenized, stabilized and bottled under argon atmosphere by the Institute for Reference Materials and Measurements, Joint Research Centre, European Commission (IRMM-JRC-EC). Preliminary analyses were carried out with Quadrupole (Q) and High Resolution (HR) Inductively Coupled Plasma Mass Spectrometry (ICP-MS) to evaluate the content of As, Cd, Cu and Pb, whereas the Flow Injection Mercury System (FIMS) was used to quantify Hg. Digestion of the matrix was achieved by acid-assisted microwave irradiation. The mean values of experimentally obtained data were the following (in nanograms per gram): As, 24.2±1.2; Cd, 5.48±0.29; Cu, 4765±95; Hg, 3.37±0.73; and Pb, 184±7. Subsequently, 16 National Reference Laboratories (NRLs) for residues in the Member States plus the Norwegian one and eight Italian public laboratories were accepted to participate in the project and received one bottle of the freeze-dried bovine muscle. The laboratories were requested to perform three different analytical runs (in three different days), each consisting of three individual measurements. Preliminary results showed good agreement and fair evidence for homogeneity of the entire mass, thus setting the stage for the future certification of this candidate CRM.     

我国社区矫正制度探析——以福州市为例

社区矫正制度在我国还是个新生事物,司法实践中观念陈旧、立法滞后等各方面的原因严重制约了我国社区矫正工作的开展。推动社区矫正制度在我国的深入开展,亟需构建完善的社区矫正法律体系,建立司法行政机关与相关部门的工作协调机制,加强司法所及社区矫正工作人员队伍的建设。     

"同辉"号建造完工船舶的船型改进

一艘已经建造完工的船舶——“同辉”号油轮，因设计不当，导致试航速度仅为设计航速的55％，后经过采取最小限度的船型改进措施：18站至20站的船首部分加装球鼻首，以改善进流角和首舭涡；尾部0站至3站的底部进行线型修改，使水流流动变成尾纵流，以改善螺旋桨供水；其他部位均保持不变，以减小损失．模型试验和实船试航结果均表明，船型改进措施少而有效，实船试航速度竞达到了原设计航速，“同辉”号油轮最终顺利交船．     

Analysis of patient self-assessment visual analogue scales

The present paper describes an example of practical analysis of data from an application of visual analogue scales. Potentially useful and simple methods for analysing visual analogue scales are described for effective handling of complex data when the desire is to compare two or more groups of patients. Visual analogue scales were used to assess subjective tolerability in the International Prospective Primary Prevention Study in Hypertension, a large scale clinical trial. The methods are illustrated on the IPPPSH data.