Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

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Some inequalities for the polar derivative of a polynomial

LetP(z) be a polynomial of degreen which does not vanish in |z|<1. In this paper, we estimate the maximum and minimum moduli of thekth polar derivative ofP(z) on |z|=1 and thereby obtain compact generalizations of some known results, which among other results, yields interesting refinements of Erdos-Lax theorem and a theorem of Ankeny and Rivlin.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Near-optimal design of Global Positioning System (GPS) networks using the Tabu Search technique

This paper describes an optimization technique based on an heuristic procedure which is applied to analyse and improve the efficiency of the design of Global Positioning System (GPS) surveying networks. GPS is a valuable survey tool because of its ability to increase the accuracy, speed and flexibility of a survey. A GPS network can be defined as a number of stations, which are co-ordinated by a series of sessions, formed by placing receivers on stations. The goal is to select the best order in which these sessions can be organised to give the best possible schedule. Generally, solving large networks to optimality requires impractical computational time. This paper proposes a Tabu Search technique which provides optimal or near-optimal solutions for large networks with an acceptable amount of computational effort. Computational results for several case studies with known and unknown optimal schedules have been presented to assess the performance of the proposed technique.     

A novel capacitive pressure sensor structure with high sensitivity and quasi-linear responseUne nouvelle structure de capteur de pression capacitif avec haute sensibilitée et réponse quasi-linéaire

This paper describes a new capacitive structure of pressure sensor to increase simultaneously the sensitivity and the linearity of the transducer. This structure contains two capacitors which change in response to pressure, but in opposite senses. To increase even more the sensitivity of each capacitor, the pressure sensitive diaphragm carries a central boss. The optimal position and the length of the boss are also calculated. To cite this article: A. Ettouhami et al., C. R. Mecanique 332 (2004).     

The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons

In many metrics of physical interest, the gravitational field can be represented as an optical medium with an effective index of refraction. We show that, in such a metric, the orbits of both massive and massless particles are governed by a variational principle which involves the index of refraction and which assumes the form of Fermat's principle or of Maupertuis's principle. From this variational principle we derive exact equations of motion of Newtonian form which govern both massless and massive particles. These equations of motion are applied to some problems of physical interest.     

Numerical methods for reaction-diffusion problems with non-differentiable kinetics

Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.Dedicated to Ivo Babuka on his sixtieth birthdayResearch partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant Number AFOSR 85-0322     

Studies on the liquid-liquid extraction and ion and precipitate flotation of Co(II) with decanoic acid

The liquid-liquid extraction, ion and precipitate flotation of Co(II) from chloride media of 1·10^–4M initial Co(II) concentration and =0.1 have been investigated using decanoic acid and the results are compared. Organic solvents used were chloroform in the case of liquid-liquid extraction and ethanol (used as a solvent for the collector and a frother) in the case of flotation. From the results it appears that liquid-liquid extraction takes place through the formation of the complex: (CoR₂)₂(HR)₂ but flotation occurs through the formation of a surface active product which has the empirical formula CoR₂. The effects of pH and of decanoic acid concentration on the three separation processes were also investigated and the results discussed. Good agreement was observed between the experimental precipitate flotation curves and the theoretical curve calculated from the data published for Co(II) hydrolysis.