Exponential convergence to equilibrium for subcritical solutions of the Becker-D\"oring equations

We prove that any subcritical solution to the Becker-D\"{o}ring equations converges exponentially fast to the unique steady state with same mass. Our convergence result is quantitative and we show that the rate of exponential decay is governed by the spectral gap for the linearized equation, for which several bounds are provided. This improves the known convergence result by Jabin & Niethammer (see ref. [14]). Our approach is based on a careful spectral analysis of the linearized Becker-D\"oring equation (which is new to our knowledge) in both a Hilbert setting and in certain weighted $\ell^1$ spaces. This spectral analysis is then combined with uniform exponential moment bounds of solutions in order to obtain a convergence result for the nonlinear equation

Symbolic calculus on the time-frequency half-plane

The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.Comment: 25 pages, Latex, minor changes and more references; to be published in the "Journal of Mathematical Physics" (special issue on "Wavelet and Time-Frequency Analysis"

Computer program performs rectangular fitting stress analysis

Computer program simulates specific bulkhead fittings by subjecting the desired geometry configuration to a membrane force, an external force, an external moment, an external tank pressure, or any combination of the above. This program generates a general model of bulkhead fittings for the Saturn booster

Flat rank of automorphism groups of buildings

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a topological Kac-Moody group G with Weyl group W, we derive the inequalities: alg-rk(W)\le flat-rk(G)\le rk(|W|\_0). Here, alg-rk(W) is the maximal $\mathbb{Z}$-rank of abelian subgroups of W, and rk(|W|\_0) is the maximal dimension of isometrically embedded flats in the CAT0-realization |W|\_0. We can prove these inequalities under weaker assumptions. We also show that for any integer n \geq 1 there is a topologically simple, compactly generated, locally compact, totally disconnected group G, with flat-rk(G)=n and which is not linear

Proposed experiments to probe the non-abelian \nu=5/2 quantum Hall state

We propose several experiments to test the non-abelian nature of quasi-particles in the fractional quantum Hall state of \nu=5/2. One set of experiments studies interference contribution to back-scattering of current, and is a simplified version of an experiment suggested recently. Another set looks at thermodynamic properties of a closed system. Both experiments are only weakly sensitive to disorder-induced distribution of localized quasi-particles.Comment: Additional references and an improved figure, 5 page

Seasonal and Long Run Fractional Integration in the Industrial Production Index of Some Latin Americ

In this article we propose a new approach that permits us to simultaneously test unit and fractional roots at the long run and the seasonal frequencies. We examine the industrial production indexes in four Latin American countries (Brazil, Argentina, Colombia and Mexico), using new statistical tools based on seasonal and non-seasonal long memory processes. Results show that the root at the long run or zero frequency plays a much more important role than the seasonal one. Nevertheless, in the cases of Brazil and Argentina a component of long memory behaviour is also present at the seasonal structure, indicating that shocks modify the seasonal structure for a long period. Policy makers should thus pay attention to this result in choosing the optimal economic policy.