The Gauss-Green theorem and removable sets for PDEs in divergence form

Applying a very general Gauss-Green theorem established for the generalized Riemann integral, we obtain simple proofs of new results about removable sets of singularities for the Laplace and minimal surface equations. We treat simultaneously singularities with respect to differentiability and continuity.     

On fluid limit for the semiconductors Boltzmann equation

This paper is devoted to the derivation of (non-linear) drift-diffusion equations from the semiconductor Boltzmann equation. Collisions are taken into account through the non-linear Pauli operator, but we do not assume relation on the cross section such as the so-called detailed balance principle. In turn, equilibrium states are implicitly defined. This article follows and completes the contribution of Mellet (Monatsh. Math. 134 (4) (2002) 305-329) where the electric field is given and does not depend on time. Here, we treat the self-consistent problem, the electric potential satisfying the Poisson equation. By means of a Hilbert expansion, we shall formally derive the asymptotic model in the general case. We shall then rigorously prove the convergence in the one-dimensional case by using a modified Hilbert expansion.     

A constructive proof of the Peter‐Weyl theorem

We present a new and constructive proof of the Peter‐Weyl theorem on the representations of compact groups. We use the Gelfand representation theorem for commutative C*‐algebras to give a proof which may be seen as a direct generalization of Burnside's algorithm [3]. This algorithm computes the characters of a finite group. We use this proof as a basis for a constructive proof in the style of Bishop. In fact, the present theory of compact groups may be seen as a natural continuation in the line of Bishop's work on locally compact, but Abelian, groups [2]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microbeam analysis of irradiated materials: practical aspects.

Among the microanalytical techniques, electron probe microanalysis (EPMA) is one of the most powerful. Its performances can be used to provide an accurate characterization. In the present article the differences between the EPMA of highly irradiated materials and standard EPMA are highlighted. It focuses on the shielded EPMA specificities. Then, the article presents the difficulties encountered during the sample preparation and the analysis (mainly due to the radioactive background). In spite of these difficulties, some valuable results can be provided by a shielded EPMA on the in-pile behavior of nuclear irradiated fuel. Some results of specific examples analyzed by EPMA in nuclear fuel research are presented.     

Two applications of Boolean models

Semantical arguments, based on the completeness theorem for first-order logic, give elegant proofs of purely syntactical results. For instance, for proving a conservativity theorem between two theories, one shows instead that any model of one theory can be extended to a model of the other theory. This method of proof, because of its use of the completeness theorem, is a priori not valid constructively. We show here how to give similar arguments, valid constructively, by using Boolean models. These models are a slight variation of ordinary first-order models, where truth values are now regular ideals of a given Boolean algebra. Two examples are presented: a simple conservativity result and Herbrand's theorem. Received December 5, 1995     

Bismuth triflate-catalyzed mild and efficient epoxide opening by aromatic amines under aqueous conditions

Bismuth triflate catalyzes the ring opening of epoxides with aromatic amines under aqueous conditions. The reaction proceeds rapidly and affords the corresponding β-amino alcohols in excellent yields.     

On topological set theory

This paper is concerned with topological set theory, and particularly with Skala's and Manakos' systems for which we give a topological characterization of the models. This enables us to answer natural questions about those theories, reviewing previous results and proving new ones. One of these shows that Skala's set theory is in a sense compatible with any ‘normal’ set theory, and another appears on the semantic side as a ‘Cantor theorem’ for the category of Alexandroff spaces. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel diazinyl 3-pyridyl ketones: Efficient synthesis and complete assignment of 1H and 13C NMR spectra

The preparation of six diazinyl 3-pyridyl ketones 3–8 is described. Detailed ¹H and ¹³C nmr data of these novel building blocks are given.     

Clustering and ensembles inequivalence in the φ and φ mean-field Hamiltonian models

We investigate a model of globally coupled conservative oscillators. Two different algebraic potentials are considered that display in the canonical ensemble either a second (φ⁴) or both a second and a first-order phase transition separated by tricritical points (φ⁶). The stability of highly clustered states appearing in the low temperature/energy region is studied both analytically and numerically for the φ⁴-model. Moreover, long-lived out-of-equilibrium states appear close to the second-order phase transition when starting with “water-bag” initial conditions, in analogy with what has been found for the Hamiltonian mean-field model. The microcanonical simulations of the φ⁶-model show strong hysteretic effects and metastability near the first-order phase transition and a narrow region of negative specific heat.