Free Groups from Fields

In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, ‘The circle cannot be squared’ by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators.     

Generalization of the Gram-Charlier/Edgeworth Series and Application to Time-Frequency Analysis

We derive a general equation relating probability densities and as special cases we the obtain Gram-Charlier and Edgeworth series. This allows us to generalize these methods and clarify a number of issues pertaining to both probability theory and time-frequency analysis. In particular we show how the Gram-Charlier and Edgeworth series are related to the kernel method of time-frequency analysis. The approach allows us to construct densities that satisfy given constraints such as joint moments or conditional moments. Also, we show that the kernel has to be signal dependent and that to obtain a proper distribution it should be the ratio of two characteristic functions.     

Polarisation optical time domain reflectometry for statistical evaluation of polarisation mode dispersion

The authors shows that a commercial optical time domain reflectometer can be modified to measure the statistical nature of polarisation mode dispersion along the length of a communications grade fibre with short-length PMDs<4 ps/km.<>     

A single-chip 12.7 Mchips/s digital IF BPSK direct sequencespread-spectrum transceiver in 1.2 μm CMOS

This paper describes a fully integrated digital-spread spectrum transceiver chip fabricated through MOSIS in 1.2 μm CMOS. It includes a baseband spread spectrum transmitter and a coherent intermediate frequency (IF) receiver consisting of a Costas loop, an acquisition loop for the pseudo-noise (PN) sequence, and a clock recovery loop with a 406.4 MHz onchip numerically controlled oscillator (NCO). The transceiver is capable of operating at a maximum IF sampling rate of 50.8 MS/s and a maximum chip rate of 12.7 R Mchips/s (Mcps) with selectable data rates of 100, 200, 400, and 800 kbps. At the maximum operating speed of 50.8 R MS/s, it dissipates 1.1 W. In an additive white Gaussian noise channel the IF receiver achieves a receiver output SNR within 1 dB of theory and can acquire code with a wide range of input SNR from -17 dB to over 30 dB. The transceiver chip has been interfaced to an RF up/down converter to demonstrate a wireless voice/data/video link operating in the 902-928 MHz band     

Radiochemistry in chemistry and chemistry related undergraduate programmes in Argentina

Summary The evolution of education in Argentina at the university level is described. The detailed search of the educational offer shows that less than half of the universities (35 out of 92) include chemistry and chemistry related undergraduate programmes in their curriculum. The revision of the position of radiochemistry in these programmes reveals that only seven courses on radiochemistry are currently offered. Radiochemistry is included only in few programmes in chemistry and biochemistry. With respect to the programmes in chemical engineering the situation is worse. This offer is strongly concentrated in Buenos Aires and its surroundings.     

Property (<Emphasis Type="Italic">T</Emphasis>) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on L ^p and other Banach spaces. We show that property (T) holds when L ² is replaced by L ^p (and even a subspace/quotient of L ^p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L ^p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L ^p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).     

Local self-similarity and the Hausdorff dimension

Let X be a locally self-similar stochastic process of index 0<H<1 whose sample paths are a.s. C^H?ε for all ε>0. Then the Hausdorff dimension of the graph of X is a.s. 2?H. To cite this article: A. Benassi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Dynamic digital holographic wavelength filtering

This paper describes the theory and results of a new generic technology for use in optical telecommunications and wavelength division multiplexing (WDM): dynamic digital holographic wavelength filtering. The enabling component is a polarization-insensitive ferroelectric liquid crystal (FLC) spatial light modulator (SLM) in conjunction with a highly wavelength-dispersive fixed diffractive element. The technology has been used to perform demultiplexing of single or multiple WDM signals, dynamic erbium doped fiber amplifier (EDFA) gain equalization and channel management, and used to tune an erbium-doped fiber laser (EDFL) functioning as a high power, very narrow linewidth WDM source     

A novel metal-insulator-metal structure for field-programmabledevices

A metal-insulator-metal (MIM) capacitor structure has been developed for use in field-programmable gate arrays (FPGAs) as a voltage-programmable link (VPL). The structure relies on a combination of a refractory metal and aluminum as the lower electrode, and either a similar combination or aluminum alone as the top electrode. The insulator is prepared by means of plasma-enhanced chemical vapor deposition (PECVD). It comprises a sandwich of nearly stoichiometric silicon dioxide interposed between two like layers of silicon-rich silicon nitride. The structure has displayed characteristics desirable for use in emerging FPGA technology, including high density, low on-resistance, reduced capacitance, and low programming voltage     

A shock tube study of the reaction of methyl radicals with hydroxyl radicals

The reaction of CH₃ with OH has been studied near 1200 K and 1 atmosphere pressure in shock tube experiments in which UV absorption was used to monitor [OH]. A rate coefficient of (1.1 ± 0.3) × 10¹³ cm³/mol-s was measured for removal of OH by CH₃. This measured value is compared with previous experimental data and calculations. Several possible reaction channels are discussed, and although products were not monitored, it seems probable, on the basis of other work and theoretical estimates, that the primary mechanism (?75%) for the removal of OH by CH₃ at these conditions is their combination to form CH₃OH. Rate coefficients of (5.3 ± 0.8) × 10¹² and (9.0 ± 1.4) × 10¹² cm³/mol-s were measured for the reactions of OH with acetone and ethane, respectively, at the same temperature and pressure.