Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Avalanche multiplication in a compact bipolar transistor model forcircuit simulation

A simple weak avalanche model valid in a wide range of voltages and currents, is presented. The proposed model is derived by using the base-collector depletion capacitance for predicting the avalanche current. The model needs only one additional transistor parameter; the extraction method and temperature dependence of this parameter are discussed. The decrease in avalanche current for high collector current densities may originate from internal device heating, a voltage drop in the epilayer, or mobile carriers in the depleted part. From experimental results it is concluded that, below a critical hot-carrier current, the decrease in avalanche current due to mobile carriers is negligible     

Analysis of queueing policies in QoS switches

It is widely accepted that next-generation networks will provide guaranteed services, in contrast to the “best effort” approach today. We study and analyze queueing policies for network switches that support the QoS (Quality of Service) feature. One realization of the QoS feature is that packets are not necessarily all equal, with some having higher priorities than the others. We model this situation by assigning an intrinsic value to each packet. In this paper we are concerned with three different queueing policies: the nonpreemptive model, the FIFO preemptive model, and the bounded delay model. We concentrate on the situation where the incoming traffic overloads the queue, resulting in packet loss. The objective is to maximize the total value of packets transmitted by the queueing policy. The difficulty lies in the unpredictable nature of the future packet arrivals. We analyze the performance of the online queueing policies via competitive analysis, providing upper and lower bounds for the competitive ratios. We develop practical yet sophisticated online algorithms (queueing policies) for the three queueing models. The algorithms in many cases have provably optimal worst-case bounds. For the nonpreemptive model, we devise an optimal online algorithm for the common 2-value model. We provide a tight logarithmic bound for the general nonpreemptive model. For the FIFO preemptive model, we improve the general lower bound to 1.414, while showing a tight bound of 1.434 for the special case of queue size 2. We prove that the bounded delay model with uniform delay 2 is equivalent to a modified FIFO preemptive model with queue size 2. We then give improved upper and lower bounds on the 2-uniform bounded delay model. We also show an improved lower bound of 1.618 for the 2-variable bounded delay model, matching the previously known upper bound.     

The structure of invertible substitutions on a three-letter alphabet

We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a finite set of invertible substitutions such that any invertible substitution can be written as I_wσ₁σ₂σ_k, where I_w is the inner automorphism associated with w, and for 1jk. As a consequence, M is the matrix of an invertible substitution if and only if it is a finite product of non-negative elementary matrices.     

固态继电器为电动汽车电池监测提供便利

电动汽车常被喻作“归来的孩子”，因为这项技术在多年前进入市场后便一直沉寂，直至最近才再次活跃起来。其实，电动汽车早于1835年首次于美国出现，到1899年，纽约市接近90％的出租车都是由电力驱动。然而，当电力启动器和内燃机变得完善时，电动汽车的使用就迅速衰退。随着如今对环境保护的关注，由燃烧碳氢化合物造成的污染，加之汽油成本高升的影响，再次     

凹整数规划的分枝定界解法

凹整数规划是一类重要的非线性整数规划问题，也是在经济和管理中有着广泛应用的最优化问题．本文主要研究用分枝定界方法求解凹整数规划问题，这一方法的基本思想是对目标函数进行线性下逼近，然后用乘子搜索法求解连续松弛问题．数值结果表明，用这种分枝定界方法求解凹整数规划是有效的．     

基于μCLinux的NAT设备的设计与开发

NAT(网络地址翻译)技术有效地解决了IP地址紧缺的问题,为实现IPv4到IPv6的平滑过渡发挥了巨大的作用.在一个体积小、重量轻、价格低廉的嵌入式平台上实现NAT设备具有很好的实际意义.文中介绍了NAT技术的原理和实现过程,在自行设计的ARM7嵌入式硬件平台上基于μCLinux操作系统实现了NAT的功能,并通过实现其他相关功能,构建了完整的NAT设备,完成了小型网络接入Internet的方案.     

Nanoscale structural characteristics and electron field emission properties of transition metal–fullerene compound TiC60 films

Transition-metal compound TiC₆₀ thin films were grown by co-deposition from two separated sources of fullerene C₆₀ powder and titanium. Study of structural properties of the films, by Raman spectroscopy, atomic force microscopy, and scanning tunneling spectroscopy reveals that the films have a deformed C₆₀ structure with certain amount of sp³ bonds and a rough surface with a large number of nanoclusters. z–V tunnelling spectroscopic measurements suggest that several charge transport mechanisms are involved in as the tip penetrates into the thin film. Conventional field electron emission (FEE) measurements show a high emission current density of 10 mA/cm² and a low turn-on field less than 8 V/μm, with the field enhancement factors being 659 and 1947 for low-field region and high-field region, respectively. By exploiting STM tunneling spectroscopy, local FEE on nanometer scale has also been characterized in comparison with the conventional FEE. The respective field enhancement factors are estimated to be 99–355 for a gap varying from 36 to 6 nm. The enhanced FEE of TiC₆₀ thin films can be ascribed to structural variation of C₆₀ in the films and the electrical conducting paths formed by titanium nanocrystallites embedded in C₆₀ matrix.     

Séries trigonométriques à coefficients arithmétiques

Journal d'Analyse Mathématique -     

The preparation of 2-iodoamides from glucals and their further transformations into oxazolines

2-Deoxy-2-iodo-glycosylamides have been prepared from a variety of protected d-glucals by their reaction with N-iodosuccinimide and amides. Benzyl protected 2-iodoamides, when treated with sodium hydride and 15-crown-5, gave stable C1 N-linked 2-glycooxazolines as the major products. Silyl protected 2-iodoamides afforded the C1 O-linked 2-glycooxazolines; presumably by the rearrangement of unstable N-acylaziridine intermediates.