On realizing diagrams of Pi-algebras

Given a diagram of Pi-algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized Pi-algebras. This extends a program begun in [J. Pure Appl. Alg. 103 (1995) 167-188] and [Topology 43 (2004) 857-892] to study the realization of a single Pi-algebra. In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations.Comment: This is the version published by Algebraic & Geometric Topology on 21 June 200

Er doped oxide nanoparticles in silica based optical fibres

Erbium doped materials are of great interest in optical telecommunications due to the Er3+ intra-4f emission at 1.54 ?m. Erbium doped fibre amplifiers (EDFA) were developed in silica glass because of the low losses at this wavelength and the reliability of this glass. Developments of new rare earth doped fibre amplifiers aim to control their spectroscopic properties including shape and width of the gain curve and optical quantum efficiency. Standard silica glass modifiers, such as aluminium, result in very good properties in current EDFA. However, for more drastic spectroscopic changes, more important modifications of the rare earth ions local environment are required. To address this aim, we present a fibre fabrication route creating rare earth doped calcia?silica or calcia?phosphosilica nanoparticles embedded in silica glass. By adding alkaline earth elements such as calcium, in low concentration, one can obtain a glass with an immisci- bility gap so that phase separation occurs with an appropriate heat treatment. We investigated the role of two elements: calcium and phosphorus (a standard silica modifier). Scanning electron microscopy shows that nanoparticles are only observed when calcium is incorporated. The size of the particles is determined to be around 50 nm in preform samples. The nature of these particles depends on phosphorus content: without P, electron diffraction shows that the particles are amorphous whilst they are partially crystalline when phosphorus is added. In addition through use of energy dispersive x-ray techniques, we have shown that erbium ions are located in the nanoparticles

Higher homotopy operations and cohomology

We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams.Comment: 28 page

Embeddings of SL(2,Z) into the Cremona group

Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona group are studied. Infinitely many non-conjugate embeddings which preserve the type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many non-conjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing-up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2,Z), preserves an elliptic curve and all its elements of infinite order are hyperbolic.Comment: to appear in Transformation Group

Kolmogorov-Smirnov method for the determination of signal time-shifts

A new method for the determination of electric signal time-shifts is introduced. As the Kolmogorov-Smirnov test, it is based on the comparison of the cumulative distribution functions of the reference signal with the test signal. This method is very fast and thus well suited for on-line applications. It is robust to noise and its performances in terms of precision are excellent for time-shifts ranging from a fraction to several sample durations. PACS. 29.40.Gx (Tracking and position-sensitive detectors), 29.30.Kv (X- and -ray spectroscopy), 07.50.Qx (Signal processing electronics)Comment: 8 pages, 7 figure

Fast analytical methods for the correction of signal random time-shifts and application to segmented HPGe detectors

Detection systems rely more and more on on-line or off-line comparison of detected signals with basis signals in order to determine the characteristics of the impinging particles. Unfortunately, these comparisons are very sensitive to the random time shifts that may alter the signal delivered by the detectors. We present two fast algebraic methods to determine the value of the time shift and to enhance the reliability of the comparison to the basis signals.Comment: 13 pages, 8 figure