In memoriam: Boris Dubrovin

Letters in Mathematical Physics -     

Initial interaction of oxygen with aluminium single crystal faces: A LEED,AES and work function study

Auger electron spectroscopy (AES), low energy electron diffraction (LEED) and work function (Kelvin probe) measurements have been used to study the initial interaction of clean Al(111), (100) and (110) surfaces with oxygen at room temperature. The oxidation process was found to be surface orientation dependent, but a common feature has been always observed on the three low-index surfaces: they show two distinct phases, i.e. a chemisorbed phase followed then by an oxidized phase. From analysis of AES, LEED and Kelvin probe results, an adsorption mechanism of O on Al for each surface orientation is proposed.     

Hydrodynamic modes in a gas of magnons

Density waves analogous to second sound are studied in a gas of magnons. Quasiparticle interaction is considered for both equilibrium and non equilibrium thermodynamics. The non equilibrium theory is based on a Boltzmann equation for magnon-magnon scattering. Contrary to the total energy and magnetization, (quasi)-momentum is not strictly conserved. In the hydrodynamic regime, the transport equation is reduced to a set of two coupled equations for the magnetization and the local temperature. For low temperatures these have diffusive and propagating solutions while for high temperatures, where momentum is dissipated by Umklapp processes, the solutions are only diffusive. The magnetization response function and the corresponding spectral function are discussed for various wavenumbers and temperatures.     

Etude de la structure magnetique et de la transition de typr “spin-flop” de Rb2FeF5

The nature of the magnetic interactions in the chain compound Rb₂FeF₅ has been investigated using neutron diffraction and magnetic measurements under high applied fields. Rb₂FeF₅ orders antiferromagnetically at T_N = 8.0 ± 0.5 K; the magnetic structure is of the A_Z + G_X mode and the moment of the Fe³⁺ ion extrapoled to 0K is 3.5 ± 0.2 μ_B, this low value being due to zero-point spin reduction. Within a chain the Fe³⁺ ions are antiferromagnetically coupled with an exchange constant of J/k = ?8.8 K. A spin-flop behavior has been observed and interpreted on the basis of the molecular field theory. The critical field was found to be H_C = 65 kOe at 1.7 K.     

The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II

We prove a general subconvex bound in the level aspect for Rankin–Selberg L-functions associated with two primitive holomorphic or Maass cusp forms over Q. We use this bound to establish the equidistribution of incomplete Galois orbits of Heegner points on Shimura curves associated with indefinite quaternion algebras over Q. Mathematics Subject Classification (2000) 11F66, 11F67, 11M41     

Stability of a Cubically Convergent Method for Generalized Equations

In Geoffroy et al, Acceleration of convergence in Dontchev's iterative method for solving variational inclusions Serdica Math. J. 29 (2003), pp. 45–54] we showed the convergence of a cubic method for solving generalized equations of the form 0 ∈ f(x) +- G(x) where f is a function and G stands for a set-valued map. We investigate here the stability of such a method with respect to some perturbations. More precisely, we consider the perturbed equation y ∈ f(x) +- G(x) and we show that the pseudo-Lipschitzness of the map (f +- G)⁻¹ is closely tied to the uniformity of our method in the sense that the attraction region does not depend on small perturbations of the parameter y. Finally, we provide an enhanced version of the convergence theorem established by Geoffroy, et al.     

On the graph of a function in two variables over a finite field

We show that if the number of directions not determined by a pointset of , of size q² is at least p^e q then every plane intersects in 0 modulo p^e+1 points and apply the result to ovoids of the generalised quadrangles and .     

Simulation of certain multivariate generalized Pareto distributions

The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms are available on the author’s home page .      

Simplicial elimination schemes,extremal lattices and maximal antichain lattices

Fix a partial order P=(X, <). We first show that bipartite orders are sufficient to study structural properties of the lattice of maximal antichains. We show that all orders having the same lattice of maximal antichains can be reduced to one representative order (called the poset of irreducibles by Markowsky [14]). We then define the strong simplicial elimination scheme to characterize orders which have distributive lattice of maximal antichains. The notion of simplicial elimination corresponds to the decomposition process described in [14] for extremal lattices. This notion leads to simple greedy algorithms for distributivity checking, lattice recognition and jump number computation. In the last section, we give several algorithms for lattices and orders.