Asymptotic description of Dirac mass formation in kinetic equations for quantum particles

In this paper, the detailed asymptotic behaviour of the solutions of a kinetic equation for quantum particles is studied. It is shown that this behaviour is sensitive not only to the total mass of the initial data but also to its precise behaviour near the origin. In some cases, solutions develop a Dirac mass at the origin for long times in a self-similar manner that is analysed in detail.     

Controlling rough paths

We formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints. This allows us to define a good notion of integral with respect to irregular paths with Hölder exponent greater than 1/3 (e.g. samples of Brownian motion) and study the problem of the existence, uniqueness and continuity of solution of differential equations driven by such paths. We recover Young's theory of integration and the main results of Lyons’ theory of rough paths in Hölder topology.     

Stability results for Mountain Pass and Linking type solutions of semilinear problems involving Dirichlet forms

Some stability results for Mountain Pass and Linking type solutions of semilinear problems involving a very general class of Dirichlet forms are stated. The non linear terms are supposed to have a suitable superlinear growth and the family of Dirichlet forms is required to be dominated from below and from above by a fixed diffusion type form. Some concrete examples are also given.     

Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds

This paper studies several aspects of asymptotically hyperbolic (AH) Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed conformal infinity. We then describe natural conditions which are sufficient to ensure finiteness.     

An algebra of meromorphic corner symbols

Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.     

Minimal Bar Tableaux

Motivated by recent results of Stanley, we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of S_n vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur’s Q_λ symmetric functions in terms of the power sum symmetric functions. Received November 20, 2003     

1H and 13C NMR spectroscopic study of oxidation of D,L‐cystine and 3,3′‐dithiobis(propionic acid) with hydrogen peroxide in aqueous solution

The oxidation of symmetrical disulfides [D ,L ‐cystine ( 1 ) and 3,3′‐dithiobis(propionic acid) ( 2 )] with hydrogen peroxide in D₂O–NaOH solution (pH 10–11) was studied by NMR spectroscopy. Assignments of the proton and carbon NMR signals of starting materials ( 1 and 2 ) and products of oxidation are based on conventional 1D NMR methods (DEPT, selective spin decoupling). Formation of C—S bond cleavage products or, in case of 2 , partially oxidized intermediates was not detected. The accelerating effect of Cu²⁺ cations, but not Fe³⁺ cations, on the oxidation rate of 1 in basic medium was demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Well-dispersed gold nanowire suspension for assembly application

A method for fabricating well-dispersed nanowire suspension has been demonstrated in the paper. Thin gold nanowires were prepared by template synthesis, and then functionalized with sulphonate group-terminated thiols before suspended in different solvents. The degree of aggregation of the obtained suspension was evaluated with transmission electron microscopy (TEM) and UV-vis spectroscopy. It was found that the degree of aggregation was predominated by the solvents, and the best degree of dispersion was obtained when isopropyl alcohol (IPA) was used as the solvent. The gold nanowires from the suspension can be selectively assembled onto chemically patterned substrates. This well-dispersed nanowire suspension is potentially useful for fabricating novel nanodevices.