A generalization of the inertia theorem for quadratic matrix polynomials

We show that the inertia of a quadratic matrix polynomial is determined in terms of the inertia of its coefficient matrices if the leading coefficient is Hermitian and nonsingular, the constant term is Hermitian, and the real part of the coefficient matrix of the first degree term is definite. In particular, we prove that the number of zero eigenvalues of such a matrix polynomial is the same as the number of zero eigenvalues of its constant term. We also give some new results for the case where the real part of the coefficient matrix of the first degree term is semidefinite.     

一种复杂车辆图像中的多车牌定位方法

针对复杂背景中多个车牌的定位问题,提出一种新的定位方法.该方法综合利用边缘检测、连通域分析、倾斜矫正等多种方法,解决了复杂背景中定位难的问题.能够准确定位杂乱背景中的车牌,对天气、光照变化、车牌在图像中的移动和旋转等,具有良好的适应能力.该方法为后续的字符分割和字符识别提供旋转角度、字符区域定位信息.     

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利用分裂的屏蔽氢不透明度模型计算了Ar、Kr、Xe惰性元素混合物随光子能量变化的不透明度以及Rosseland平均不透明度。研究了温度为100～250eV,密度为0.5～2g·cm-3范围内惰性元素混合物的Rosseland平均不透明度与混合物质、混合比例、温度和密度的密切关系。结果显示,Ar-Xe混合以及Xe-Kr混合后的Rosseland平均不透明度比它们为纯元素时有较大的增加;而Ar-Kr混合后的Rosseland平均不透明度则比纯Kr低。通过对比纯惰性元素随光子能量变化的不透明度峰、谷值,分析了造成混合后不透明度增加或降低的原因,同时给出了获得惰性元素混合物平均不透明度为最大时的混合比例。     

Complete synchronization of Kuramoto oscillators with finite inertia

We present an approach based on Gronwall’s inequalities for the asymptotic complete phase-frequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phase-frequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall’s inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations.     

On the Spectra of Striped Sign Patterns

Sign patterns consisting of some positive and some negative columns, with at least one of each kind, are shown to allow any self-conjugate spectrum, and thus to allow any inertia. In the case of the n × n sign pattern with all columns positive, given any self-conjugate multiset consisting of n m 1 complex numbers supplemented by a sufficiently large positive number, it is shown how to construct a positive normal matrix whose spectrum is this multiset. Thus, the positive sign pattern allows any inertia with at least one positive eigenvalue.     

Unsteady rheometry: can we characterize weak gels with a controlled stress rheometer?

This paper is concerned with the influence of apparatus inertia effects in controlled stress rheometry. As evidenced on creep experiments, the coexistence of apparatus inertia and viscoelasticity leads to a coupling frequency. For weak gels, this coupling frequency is typically between 1 and 100 Hz. Therefore, frequency sweeps around and above this coupling frequency also corresponds to an effective shear stress sweep evolution due to a non-trivial resonant effect. In other words, frequency sweep experiments are not made at constant shear stress. The detailed modelling and analysis of this inertia effect on a typical weak gel shows a clear and fundamental limitation for its characterization using a controlled stress rheometer. Also, alternative approaches to standard rheometer software analysis are proposed to take this coupling effect into account. This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27-29, 2006, Crete, Greece.     

使用ANSYS对惯性力作用下的低温绝热气瓶进行应力分析与优化

低温绝热气瓶为移动式压力容器,不仅承受静载荷的作用,还要承受移动工况下的惯性载荷作用。与传统的常规计算方法相比,有限元法更直观准确。文中使用ANSYS软件,对DPL450-175-1.37型低温绝热气瓶的结构建立有限元模型,对受惯性载荷的作用下进行应力分析,并对其应力集中区域进行了应力分类和评定。为低温绝热气瓶的结构设计起到一定的帮助作用。     

The equations of the perturbed motion of a rocket as a thin-walled structure with a liquid

The perturbed motion of a rocket as an elastic thin-walled structure with compartments partially filled with liquid propellant is considered. It is assumed that the normal modes of the hydroelastic oscillations of the rocket are determined under the condition that the velocity potential on the free surface of the liquid is equal to zero and with standard remaining conditions. Certain features of these modes with zero fundamental frequencies are pointed out and the “loss” of mass effect associated with this is explained. Equations are derived for the perturbed motion of a rocket taking account of the hydroelastic oscillations of its structure and the oscillations of the liquid with deviations of the free surface from the equilibrium position under the action of mass forces. The coefficients of these equations, characterizing the relation between the different type of oscillations, are expressed in terms of known hydrodynamic parameters and the values of the oscillation modes at certain points.