Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.     

CCD摄像机交汇测量目标脱靶量布站分析

分析线列CCD摄像机交汇测量的原理,以空间虚拟的光电靶代替实特靶来实现对弹丸目标脱靶量的实时获取。在分析了CCD摄像机测你精度与布站方式等影响交汇测量精度的因素后,对光电靶面上不同位置点的CCD摄像机交汇坐标测量精度进行了计算,给出测量精度与布站的关系。     

Used digital speckle correlation method to realize orientation function of optical mouse

Used digital speckle correlation method (DSCM) to realize orientation function of optical mouse is researched. The experiment is designed to obtain the dynamic speckle patterns which are shot by CCD, then the DSCM is used to process the sequential images and also the experiment is simulated. The experimental results show the DSCM can confirm orientation function of the optical mouse, and have a good agreement with the simulation results, and the resolution we obtained is higher than the resolution of mouse on the market.     

Vignetting in electro-optical distance meters

Vignetting in the optical system of an electro-optical distance meter is described, and the impact of the measuring conditions is dealt with. The method of analysis, involving numerical calculations, is given and the results for three typical cases are shown.     

Resource allocation model and double-sphere crowding distance for evolutionary multi-objective optimization

Convergence speed and diversity of nondominated solutions are two important performance indicators for Multi-Objective Evolutionary Algorithms (MOEAs). In this paper, we propose a Resource Allocation (RA) model based on Game Theory to accelerate the convergence speed of MOEAs, and a novel Double-Sphere Crowding Distance (DSCD) measure to improve the diversity of nondominated solutions. The mechanism of RA model is that the individuals in each group cooperate with each other to get maximum benefits for their group, and then individuals in the same group compete for private interests. The DSCD measure uses hyper-spheres consisting of nearest neighbors to estimate the crowding degree. Experimental results on convergence speed and diversity of nondominated solutions for benchmark problems and a real-world problem show the efficiency of these two proposed techniques.     

Métriques de révolution d'un disque et invariance par rotation de la longueur des géodésiques

We give a geometrical proof of a Muhometov type inequality, for a single Riemannian metric defined on a closed disc in the plane. We mainly study the case of equality which is achieved if and only if the distance between points on the boundary is invariant under rotation along the boundary. We show that this implies that the metric itself must be invariant under rotation, at least when the metric is analytic or of nonpositive curvature.     

An Edgeworth expansion for functionals of Gaussian fields and its applications

This paper is concerned with the rate of convergence in the normal approximation of the sequence $\left\{F_n\right\}$, where each $F_n$ is a functional of an infinite-dimensional Gaussian field. We develop new and powerful techniques for computing the exact rate of convergence in distribution with respect to the Kolmogorov distance. As a tool for our works, the Edgeworth expansion of general orders, with an explicitly expressed remainder, will be obtained, and this remainder term will be controlled to find upper and lower bounds of the Kolmogorov distance in the case of an arbitrary sequence $\left\{F_n\right\}$. As applications, we provide the optimal fourth moment theorem of the sequence $\left\{F_n\right\}$ in the case when $\left\{F_n\right\}$ is a sequence of random variables living in a fixed Wiener chaos or a finite sum of Wiener chaoses. In the former case, our results show that the conditions given in this paper seem more natural and minimal than ones appeared in the previous works.     

The Fréchet distance between multivariate normal distributions

The Fréchet distance between two multivariate normal distributions having means μ_X, μ_Y and covariance matrices Σ_X, Σ_Y is shown to be given by $\text{d}{}^2\text{= |μ}{}_{\mathrm{X}}\text{? μ}{}_{\mathrm{Y}}\text{|}{}^2\text{+}\text{tr}\text{(Σ}{}_{\mathrm{X}}\text{+ Σ}{}_{\mathrm{Y}}\text{? 2(Σ}{}_{\mathrm{X}}\text{Σ}{}_{\mathrm{Y}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$. The quantity d₀ given by $\text{d}{}_0{}^2\text{=}\text{tr}\text{(Σ}{}_{\mathrm{X}}\text{+ Σ}{}_{\mathrm{Y}}\text{? 2(Σ}{}_{\mathrm{X}}\text{Σ}{}_{\mathrm{Y}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ is a natural metric on the space of real covariance matrices of given order.     

Heavy alkali metal-arsenic alloy-based graphite intercalation compounds: Investigation of their synthesis and of their physical properties

Heavy alkali metal-arsenic alloys intercalate easily into graphite, leading to the formation of a new family of ternary graphite intercalation compounds (GICs). Pure phases formulated as MAsxC4s (M = K, Rb or Cs; s = stage; x ≤ 1) have been synthesized at the laboratory. This article aims to expose all physical measurements performed on these intercalation compounds to get an idea about their electronic properties.Electrical conductivity measurements have been performed both parallel and perpendicular to the basal planes, between 4.2 and 295 K. Room temperature resistivity values lie between 16 and 35 μΩ cm and the anisotropic resistivity takes a value of an order of magnitude of 10⁴. Dynamic magnetic susceptibility measurements, carried out at low temperature on some phases, showed that they do not exhibit superconducting transition up to 1.3 K. Raman spectroscopy investigation, which is a useful tool to study the electronic and the chemical stability of GICs, highlighted a significant up-shift of the G-band of the carbon intra-layer vibration frequency, compared to the pure graphite vibration mode. Undoubtedly, this is related to the electronic charge transfer established between graphite layers and intercalated species.