Reaction of SbPO4 with lithium in non-aqueous electrochemical cells: preliminary study and evaluation of its electrochemical performance in anodes for lithium ion batteries

SbPO₄, a phosphate with a layered structure, was tested as an electrode material for lithium cells spanning the 3.0-0.0 V range. Two main electrochemical processes were detected as extensive plateaus at ca. 1.6 and 0.7 V in galvanostatic measurements. The first process was found to be irreversible, thus excluding a potential intercalation-like mechanism for the reaction and being better interpreted as a decomposition reaction leading to the formation of elemental Sb. This precludes the use of this compound as a cathodic material for lithium cells. By contrast, the process at 0.7 V is reversible and can be ascribed to the formation of lithium-antimony alloys. The best electrochemical response was obtained by cycling the cell at a C/20 discharge rate over the voltage range 1.25-0.25 V. Under these conditions, the cell delivers an average capacity of 165 Ah/kg—a value greater than those reported for other phosphates—upon successive cycling.     

Diffraction of transverse horizontal waves in Fibonacci piezoelectric superlattices

The transfer matrix and global matrix techniques are used in the analysis of diffraction of transverse horizontal waves in piezoelectric superlattices. The system is composed of a set of different piezoelectric layers with quasiperiodic structure according to the Fibonacci sequence. The diffraction spectrum of different configurations of piezoelectric Fibonacci structures is studied. Numerical results for the diffraction spectrum for the piezoelectric Fibonacci superlattice are obtained and a comparison between the results of the transfer and global matrix methods is given, exhibiting the advantage of the latter.     

Young's inequality in trace-class operators

 If a and b are trace-class operators, and if u is a partial isometry, then , where ∥⋅∥₁ denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality. Received: 20 December 2001 / Revised version: 11 July 2002 / Published online: 10 February 2003 Mathematics Subject Classification (2000): 47A63, 15A60     

The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

Quasi-free divisors and duality

We prove a duality theorem for some logarithmic $\text{D}$-modules associated with a class of divisors. We also give some results for the locally quasi-homogeneous case. To cite this article: F.J. Castro-Jiménez, J.M. Ucha-Enr??quez, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Quasioptical Approach for Meniscus Lens Corrected Horn: Application to Cassegrain Systems

The Beam Mode Expansion (BME) approach for corrugated conical feed horn plus meniscus lens is presented. This approach is useful for providing the radiation pattern as it propagates through an optical system. A developed theoretical model has been verified measuring near and far field of a built horn and lens. These results have been used for designing the optical system of a Cassegrain antenna at 100GHz using the fundamental Gaussian beam mode (GBM) of the new approach. Multimode analysis has been performed with the pre-designed system in order to test the fundamental GBM results.