Sizes of Critical Graphs with Small Maximum Degrees

In this paper, we give new lower bounds for the size of Δ-critical graphs with Δ=8,9 which improve the partial results of Luo [6] and Y. Zhao [12].     

极紫外望远镜各通道夹角的测量

极紫外望远镜是由四个单通道的望远镜捆绑在一起,以便同时对太阳的相同部分观测,由于受地面装调以及发射过程中的影响,无法保证四个通道光轴严格平行,必然带来观测位置上的误差。只要测出各通道之间的光轴夹角,便可在像面上采取适当的处理方法,以便减小这种误差,但这一夹角的测量精度必须控制在0.1″内。为达到如此高的精度,采用了太阳局部边缘探测的方法,很好地解决了这一问题。     

Growth of Lévy trees

We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure. T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries, EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779.     

The analysis of thermal stresses in thermopiezoelastic semi-infinite body with an edge crack

Summary  Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved. The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated. Received 20 March 2001; accepted for publication 18 October 2001     

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.     

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.     

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.     

NUMERICAL LOCALIZATION OF ELECTROMAGNETIC IMPERFECTIONS FROM A PERTURBATION FORMULA IN THREE DIMENSIONS

This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms： the Current Projection method, the MUltiple Signal Classification （MUSIC） algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.     

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.