Forcing matchings on square grids

Let G be a graph that admits a perfect matching. The forcing number of a perfect matching M of G is defined as the smallest number of edges in a subset S M, such that S is in no other perfect matching. We show that for the 2n × 2n square grid, the forcing number of any perfect matching is bounded below by n and above by n². Both bounds are sharp. We also establish a connection between the forcing problem and the minimum feedback set problem. Finally, we present some conjectures about forcing numbers in other graphs.     

Sound and weak shock wave propagation in gas-liquid foams

Propagation of sound and weak shock waves in gas-liquid foams is investigated theoretically and experimentally. An original physical model is developed to describe the evolution of small perturbations in a foam of polyhedral structure. The model developed takes into account both peculiarities of interface heat transfer in foam and liquid motion through the system of Plateau-Gibbs borders which results in the appearance of an additional hydrodynamic dissipative force. The Rayleigh equation analog, which takes into account the latter phenomenon, is obtained. Structure and dynamics of weak shock waves are investigated. A vertical shock tube was constructed and used to measure the parameters of weak shock wave propagation in gas-liquid foams of polyhedral structure. Spectral analysis of the data obtained shows that there are weak dispersion and strong dissipation of the initial signal. Comparison of the evolution of experimental and theoretical profiles permits to conclude that the suggested model allows to describe the peculiarities of acoustical perturbations in gas-liquid foam more precisely than it follows from the standard models. Received 15 September 1993 / Accepted 27 December 1993     

Fast deposition of amorphous hydrogenated carbon films using a supersonically expanding arc plasma

Experiments concerning the growth rate and quality of an amorphous hydrogenated carbon film deposited in a reactor based on the supersonic expansion of an arc plasma are reported. In order to be able to calculate the deposition rate, an existing flow model has been completed with chernical reaction rate equations. The methane gas that is injected in the arc appears to be dissociated and ionized completely. The calculated deposition rates agree well with the experimental values obtained within-situ ellipsometry. The growth rates are an order of magnitude larger than those reported in the literature. Still, the film quality, expressed in terms of refractive index, optical bandgap, and hardness, is similar to those obtained by other authors.     

几类特殊测地块的构造(英)

本文给出了一种构造给定直径d和围长g的测地块的方法．它是文［1］中构造法的推广，解决了文［1］中待研究的几个问题．同时，对文［1］中的一个错误进行了修正．     

微分求积方法对于桩基大变形分析的应用

本文基于大变形的理论,采用弧坐标首先建立了具有初始位移的桩基的非线性数学模型,一组强非线性的微分-积分方程,其中,地基的抗力采用了Winkeler模型;其次,引入变数变换将微分-积分方程转化为一组非线性微分方程,并用微分求积方法离散了方程组,得到一组离散化的非线性代数方程;最后用Newton-Raphson迭代方法对离散化方程进行了求解,得到了桩基变形前后的构形、弯矩和剪力.计算中选取了两种不同类型的初始位移,并考察了它们对桩基大变形力学行为的影响.     

Critical Reynolds number in plasma flows on a stabilized plasmatron section

A technique for determining the criterion of transition from the laminar to the turbulent flow regime on a stabilized plasmatron channel section is proposed. The technique uses experimental data and the methods of numerical simulation of plasma flows. A criterial generalization of the experimental data which for the first time makes it possible to establish the boundary of transition from the laminar to the turbulent flow regime on a stabilized plasmatron channel section is proposed. The experimental results are in good agreement with the theoretical dependences derived in the study. A curve (analog of the neutral curve) separating the domains of existence of laminar and turbulent plasma flows in a cylindrical channel is constructed in the space of the plasmatron working parameters.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 49–61. Original Russian Text Copyright © 2004 by Sinkevich and Chikunov.     

Effects of anodic oxidation on corrosion properties of Al coating by arc spraying in seawater

A layer of Al coatings was prepared on the S355 steel by arc spraying, which was conducted by anodic oxidation treatment; the morphologies, chemical element compositions and phases of Al coating, and anodic oxide layer were analyzed with field emission scanning electron microscope (FESEM), energy dispersive spectrometer (EDS) and X‐ray diffraction (XRD), respectively. The corrosion protections of Al coating before and after anodic oxidation were discussed with a seawater immersion test; the corrosion resistance mechanisms of Al coating and anodic oxide layer in the seawater were also investigated. The results show that the thickness of Al coating is about 300 µm by arc spraying, the sample surfaces become loose after seawater immersion corrosion and Cl^? and O^2? penetrate into the substrate from the cracks, destroying the binding properties of coating–substrate, and the coating fails. After anodic oxidation, the oxide layer is formed in the surface of Al coating with the thickness of about 30 µm; the corrosion products are mainly composed of Al(OH)₃, which barraged the holes caused by seawater corrosion. The corrosion cracks are formed during the corrosion, while the number and depth of cracks decrease obviously after anodic oxidation treatment. The corrosion of Al coating becomes the local corrosion after anodic oxidation treatment, and the grains are smaller, which are easily nucleated to form a new corrosion resistance layer. Copyright © 2015 John Wiley & Sons, Ltd.     

Universal arcs in local tournaments

An arc $uv$ of a digraph $D$ is called universal if $uv$ and $w$ are in a common cycle for any vertex $w$ of $D$. In this paper we characterize local tournaments whose every arc is universal.