Spectral norms on valued fields

Let be a perfect valued field, be an algebraic closure of be an extension of to and be the G-spectral norm on Let be an algebraic extension of K and be the completion of L relative to We associate to any element a real number and prove that if for all x in , then and is a zero-dimensional regular ring. We show that and prove that is algebraic over (with some additional conditions on K and L). We give a Galois type correspondence between the set of all closed K-subalgebras of and the subfields of L. We prove that is an algebraic closed and zero-dimensional regular ring. Received: 3 March 1999; in final form: 21 February 2000 / Published online: 4 May 2001     

Multivariable Alexander invariants of hypersurface complements

We start with a discussion on Alexander invariants, and then prove some general results concerning the divisibility of the Alexander polynomials and the supports of the Alexander modules, via Artin's vanishing theorem for perverse sheaves. We conclude with explicit computations of twisted cohomology following an idea already exploited in the hyperplane arrangement case, which combines the degeneration of the Hodge to de Rham spectral sequence with the purity of some cohomology groups.

     

Gravitational motion of a two-particle cluster between two parallel plane solid wallsSédimentation de deux particules solides entre deux plans parallèles

The slow viscous settling migration of a 2-particule cluster between two solid and parallel plane walls is investigated by resorting to a Boundary Element Method. The procedure, valid for arbitrarily-shaped bodies, is presented and preliminary numerical results for both identical spheres and a spheroid-sphere cluster are discussed. To cite this article: L. Pasol, A. Sellier, C. R. Mecanique 334 (2006).     

Hodge genera of algebraic varieties, II

We study the behavior of Hodge-genera under algebraic maps. We prove that the motivic ${\chi^c_y}$ -genus satisfies the “stratified multiplicative property”, which shows how to compute the invariant of the source of a morphism from its values on varieties arising from the singularities of the map. By considering morphisms to a curve, we obtain a Hodge-theoretic version of the Riemann–Hurwitz formula. We also study the monodromy contributions to the ${\chi_y}$ -genus of a family of compact complex manifolds, and prove an Atiyah–Meyer type formula in the algebraic and analytic contexts. This formula measures the deviation from multiplicativity of the ${\chi_y}$ -genus, and expresses the correction terms as higher-genera associated to the period map; these higher-genera are Hodge-theoretic extensions of Novikov higher-signatures to analytic and algebraic settings. Characteristic class formulae of Atiyah–Meyer type are also obtained by making use of Saito’s theory of mixed Hodge modules.     

Effective Use of Empirical Data for Virtual Screening against APJR GPCR Receptor

Alzheimer’s disease is a neurodegenerative disorder incompatible with normal daily activity, affecting one in nine people. One of its potential targets is the apelin receptor (APJR), a G-protein coupled receptor, which presents considerably high expression levels in the central nervous system. In silico studies of APJR drug-like molecule binding are in small numbers while high throughput screenings (HTS) are already sufficiently many to devise efficient drug design strategies. This presents itself as an opportunity to optimize different steps in future large scale virtual screening endeavours. Here, we ran a first stage docking simulation against a library of 95 known binders and 3829 generated decoys in an effort to improve the rescoring stage. We then analyzed receptor binding site structure and ligands binding poses to describe their interactions. As a result, we devised a simple and straightforward virtual screening Stage II filtering score based on search space extension followed by a geometric estimation of the ligand—binding site fitness. Having this score, we used an ensemble of receptors generated by Hamiltonian Monte Carlo simulation and reported the results. The improvements shown herein prove that our ensemble docking protocol is suited for APJR and can be easily extrapolated to other GPCRs.     

Arc-analytic roots of analytic functions are Lipschitz

Let be an arc-analytic function (i.e., analytic on every analytic arc) and assume that for some integer the function is real analytic. We prove that is locally Lipschitz; even if is less than the multiplicity of . We show that the result fails if is only a , arc-analytic function (even blow-analytic), . We also give an example of a non-Lipschitz arc-analytic solution of a polynomial equation , where are real analytic functions.

     

Study of a new semi-continuous model of the Boltzmann equation

For a semi-continuous model of the Boltzmann equation (1) peculiar solutions are obtained and generally the global existence of solutions of the initial value problem is discussed. The global existence is possible even in some cases for partially negative initial number densities, which are not physical problems, but mathematical ones. It can be shown that in some cases the entropy begins to increase, reaches a maximum and decreases again.     

Assessment of calibration parameters for gamma-ray spectrometry systems

The Gamma-ray spectrometers are complex instruments and the quality of the data they provide depends strongly on their proper calibration. This paper describes the energy and efficacy calibration of two gamma-ray spectrometers in order to validate the method for measuring the activity of gamma-ray emitting radionuclides. The punctiform standard sources ⁶⁰Co, ¹³³Ba, ¹³⁷Cs and ²⁴¹Am were used in this study. Minimum Detectable Activity, Peak to Compton Ratio and the peak shape parameters were determinate. An inter-comparison of the results obtained with both systems was done. The results demonstrated that the activity values are comparable with low errors respecting with those for conventionally true activities.     

Migration of a solid particle in the vicinity of a plane fluid–fluid interface

The slow migration of a small and solid particle in the vicinity of a gas–liquid, fluid–fluid or solid–fluid plane boundary when subject to a gravity or an external flow field is addressed. By contrast with previous works, the advocated approach holds for arbitrarily shaped particles and arbitrary external Stokes flow fields complying with the conditions on the boundary. It appeals to a few theoretically established and numerically solved boundary-integral equations on the particle’s surface. This integral formulation of the problem allows us to provide asymptotic approximations for a distant boundary and also, implementing a boundary element technique, accurate numerical results for arbitrary locations of the boundary. The results obtained for spheroids, both settling or immersed in external pure shear and straining flows, reveal that the rigid-body motion experienced by a particle deeply depends upon its shape and also upon the boundary location and properties.