Covariance estimation under spatial dependence

Correlated multivariate processes have a dependence structure which must be taken into account when estimating the covariance matrix. The natural estimator of the covariance matrix is introduced and is shown that to be biased under the dependence structure. This bias is studied under two different asymptotic models, namely increasing the domain by increasing the number of observations, and increasing the number of observations in the fixed domain. Using the first asymptotic model, we quantify the convergence rate of the bias and of the covariance between the components of the estimated covariance matrix. The second asymptotic model serves to derive a fast and accurate bias correction. As shown, under mild hypotheses, the asymptotic normality of the estimated covariance matrix holds and can be used to test whether the bias is significant, for example, in the sense that the eigenvectors of the estimated and true covariance matrices are significantly different.     

Electrode “edge effects” analyzed by the Green function method

An exact method based on Green's equation is used to find the diffusion-controlled faradaic current for certain electrode geometries that incorporate edges and vertices. Thereby the magnitudes of the time-independent current density associated with angled electrode/electrode and electrode/insulator junctions are calculated. As well, the square-root-of-time-dependent currents associated with vertices, receive attention. These terms extend to longer times, the Cottrell formulation appropriate for short times. Though most of the problems solved here have been tackled previously, the novel Green function approach is shown to be straightforward and intuitive.     

Studies on recoil proton tracks in NTA films with the T(d,n)He reaction

Recoil proton tracks in nuclear emulsion are counted by scanning them using strip, square or circular field of view of optical microscope. In this paper, the overestimate due to the edge effects in counting recoil proton tracks at different neutron energies produced from the T(d,n)⁴He reaction has been determined by measuring the true track density in NTA film. The overestimate has also been calculated using the measured value of the mean projected track length (L) in the film. The percentage of measured overestimates has been compared with those obtained by calculation and the results agree reasonably well. Fading effect in NTA film has been studied and found to be 22% more in the summer than in the winter season. A great reduction in fading rate could be achieved if the films are desiccated and sealed in highly pure dry nitrogen maintained at an over-pressure of 1000 Pa to reduce water vapour ingress. After the edge effect correction, the sensitivity of NTA film has been calculated from (1.72±0.08)×10⁻³ tracksn⁻¹ to (1.97±0.16)×10⁻³ tracksn⁻¹ in the neutron energy ranges from 15.91 to 18.88 MeV. The response was found to be from 0.24±0.02 trackscm⁻² permSv to 0.26±0.01 trackscm⁻² permSv in the same energy range.     

Logarithmic asymptotics of solutions of the large deviation problem for the boltzmann equation with small transfer of momentum

For the Boltzmann equation with small transfer of momentum, we derive a system of nonlinear integral-differential equations describing the logarithmic asymptotics of the solution to the Cauchy problem in the domain at the distanceO(1) from the support of the initial condition.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 73–94, July, 1998.This research was partially supported by INTAS-RFBR under grant No. 95-91 in the case of the first author, and by INTAS under grant No. 96-0698 in the case of the second author.     

Covering projective planar graphs with three forests

It is known that all planar graphs and all projective planar graphs have an edge partition into three forests. Gonçalves proved that every planar graph has an edge partition into three forests, one having maximum degree at most four [5]. In this paper, we prove that every projective planar graph has an edge partition into three forests, one having maximum degree at most four.     

The asymptotic behavior of queueing systems: Large deviations theory and dominant pole approximation

This paper presents the exact asymptotics of the steady state behavior of a broad class of single-node queueing systems. First we show that the asymptotic probability functions derived using large deviations theory are consistent (in a certain sense) with the result using dominant pole approximations. Then we present an exact asymptotic formula for the cumulative probability function of the queue occupancy and relate it to the cell loss ratio, an important performance measure for service systems such as ATM networks. The analysis relies on a new generalization of the Taylor coefficients of a complex function which we call characteristic coefficients. Finally we apply our framework to obtain new results for the M/D/1 system and for a more intricate multiclass M/D/n system.     

Cyclic Voltammograms of Ferrocene on Multi‐Walled Carbon Nanotubes (MWCNTs)‐Modified Edge Plane Pyrolytic Graphite (EPPG) Electrode in Room Temperature Ionic Liquids (RTILs) of 1‐Ethyl‐3‐Methylimidazolium Tetrafluoroborate (EMIBF4)

In this work, the electrochemical behavior of ferrocene (Fc) was investigated by cyclic voltammetry (CV) in room temperature ionic liquids (RTILs) of 1‐ethyl‐3‐methylimidazolium tetrafluoroborate (EMIBF₄) on glass carbon (GC), edge plane pyrolytic graphite (EPPG) and multi‐walled carbon nanotube (MWCNTs)‐modified EPPG electrodes, respectively. The results demonstrated that on GC electrode, pairs of well‐defined reversible peaks were observed, while for the electrode of EPPG, the peak potential separation (ΔE_p) is obviously larger than the theoretical value of 59 mV, hinting that the electrode of EPPG is distinguished from the commonly used electrode, consistent with the previous proposition that EPPG has many “defects”. To obtain an improved electrochemical response, multi‐walled carbon nanotubes (MWCNTs) were modified on the electrode of EPPG; the increased peak current and promoted peak potential separation not only proved the existence of “defects” in MWCNTs, but also supported that “creating active points” on an electrode is the main contribution of MWCNTs. Initiating the electrochemical research of Fc on the MWCNTs‐modified EPPG electrode in RTILs and verifying the presence of “defects” on both EPPG and MWCNTs using cyclic voltammograms (CVs) of Fc obtained in RTILs of EMIBF₄, is the main contribution of this preliminary work.     

基于方向信息测度的最小模糊度准则边缘检测

将像素点的方向信息测度作为判别边缘点的特性指标,借用Huang等构造的自适应确定分割阈值的思想,本文提出了一种基于方向信息测度的最小模糊度准则边缘检测方法。文中提出的方法,一方面由于采用了方向信息测度,可以很好地将边缘点和非边缘点区分开来;另一方面通过最小化模糊度,自适应地将给定图像的所有像素点按照方向信息测度分成两类,从而达到提取边缘的目的。实验结果证明,我们提出的方法能够很好地判别边缘点,有效地提取图像的边缘。     

自适应设计广义线性模型极大拟似然估计的渐近性

在对Fisher信息矩阵的最小特征根最一般的假定,响应变量的矩条件尽可能弱和其它正则条件下,证明了自适应设计广义线性模型中极大拟似然估计的强相合性与渐近正态性,同时给出了强收敛速度.     

蒸发器支撑板板孔精密测量系统

建立了蒸发器支撑板板孔精密测量系统,并提出了基于边缘约束条件的轮廓参量测量方法.首先采用图像处理技术将待测目标转化为二维离散坐标点,计算其最小外接矩形并对轮廓进行预定位;然后将轮廓分割成相互重合的"扩展邻域轮廓",建立以曲率角为原则的边缘约束算法对各轮廓段精确定界,实现对轮廓参量的精密测量.实验和误差分析表明,该系统测量准确度优于0.02mm,对具有复杂轮廓的零件参量测量有参考价值.