Algebraicity of Global Real Analytic Hypersurfaces

Let X be an algebraic manifold without compact component and let V be a compact coherent analytic hypersurface in X, with finite singular set. We prove that V is diffeotopic (in X) to an algebraic hypersurface in X if and only if the homology class represented by V is algebraic and singularities are locally analytically equivalent to Nash singularities. This allows us to construct algebraic hypersurfaces in X with prescribed Nash singularities.     

Additivity for the parametrized topological Euler characteristic and Reidemeister torsion

Dwyer, Weiss, and Williams have recently defined the notions of the parametrized topological Euler characteristic and the parametrized topological Reidemeister torsion which are invariants of bundles of compact topological manifolds. We show that these invariants satisfy additivity formulas paralleling the additive properties of the classical Euler characteristic and the Reidemeister torsion of CW-complexes.     

Arbres de Markov Triplet et fusion de Dempster–Shafer

The hidden Markov chains (HMC) (X,Y) have been recently generalized to triplet Markov chains (TMC), which enjoy the same capabilities of restoring a hidden process X from the observed process Y. The posterior distribution of X can be viewed, in an HMC, as a particular case of the so called “Dempster–Shafer fusion” (DS fusion) of the prior Markov with a probability q defined from the observation Y=y. As such, when we place ourselves in the Dempster–Shafer theory of evidence by replacing the probability distribution of X by a mass function M having an analogous Markov form (which gives again the classical Markov probability distribution in a particular case), the result of DS fusion of M with q generalizes the conventional posterior distribution of X. Although this result is not necessarily a Markov distribution, it has been recently shown that it is a TMC, which renders traditional restoration methods applicable. The aim of this Note is to present some generalizations of the latter result: (i) more general HMCs can be considered; (ii) q, which can possibly be a mass function Q, is itself a result of the DS fusion; and (iii) all these results are finally specified in the hidden Markov trees (HMT) context, which generalizes the HMC one. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Very forward calorimeters readout and machine interface

The paper describes the requirements for the readout electronics and DAQ for the instrumentation of the forward region of the future detector at the international linear collider. The preliminary design is discussed. on behalf of the FCAL Collaboration     

Microwave frequency modulation in CW EPR at W-band using a loop-gap resonator

Loop-gap resonator (LGR) technology has been extended to W-band (94GHz). One output of a multiarm Q-band (35GHz) EPR bridge was translated to W-band for sample irradiation by mixing with 59 GHz; similarly, the EPR signal was translated back to Q-band for detection. A cavity resonant in the cylindrical TE011 mode suitable for use with 100 kHz field modulation has also been developed. Results using microwave frequency modulation (FM) at 50 kHz as an alternative to magnetic field modulation are described. FM was accomplished by modulating a varactor coupled to the 59 GHz oscillator. A spin-label study of sensitivity was performed under conditions of overmodulation and gamma2H1(2)T1T2<1. EPR spectra were obtained, both absorption and dispersion, by lock-in detection at the fundamental modulation frequency (50 kHz), and also at the second and third harmonics (100 and 150 kHz). Source noise was deleterious in first harmonic spectra, but was very low in second and third harmonic spectra. First harmonic microwave FM was transferred to microwave modulation at second and third harmonics by the spins, thus satisfying the "transfer of modulation" principle. The loaded Q-value of the LGR with sample was 90 (i.e., a bandwidth between 3 dB points of about 1 GHz), the resonator efficiency parameter was calculated to be 9.3 G at one W incident power, and the frequency deviation was 11.3 MHz p-p, which is equivalent to a field modulation amplitude of 4 G. W-band EPR using an LGR is a favorable configuration for microwave FM experiments.     

Theory of many-body localization in periodically driven systems

We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.     

Birkhoff’s Polytope and Unistochastic Matrices,N = 3 and N = 4

The set of bistochastic or doubly stochastic N×N matrices is a convex set called Birkhoff’s polytope, which we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff’s polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.     

Properties of doped ceria solid electrolytes in reducing atmospheres

In this work we present investigations of stability of rare earth-doped ceria electrolytes in reducing atmosphere. The effect of dopant type and dopant concentration on reducibility was studied on the basis of thermogravimetric and impedance spectroscopy measurements on materials grouped into two series: Ce_1 − xGd_xO_2 − x/2 (0 ≤ x ≤ 0.4) and Ce_0.85R_0.15O_1.925 (R = Y, Nd, Sm, Gd, and Dy). Relationship between an initial vacancy concentration introduced by the amount of dopant and the characteristic temperature of reduction was found. Much less pronounced dependence was observed for different dopants with the same concentration, which indicates that it is the dopant and vacancy concentration and not the dopant type, which is responsible for reducibility of ceria electrolytes. Impedance spectroscopy measurements allowed for calculation of changes of oxygen ions transport number during the reduction process.