Foliations invariant under Lie group transverse actions

In this paper we study (smooth and holomorphic) foliations which are invariant under transverse actions of Lie groups. Authors’ address: Alexandre Behague and Bruno Scárdua, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil     

Odd character correspondences in solvable groups

Let G be a finite solvable group, p be some prime, let P be a Sylow p-subgroup of G, and let N be its normalizer in G. Assume that N has odd order. Then, we prove that there exists a bijection from the set of all irreducible characters of G of degree prime to p to the set of all the irreducible characters of degree prime to p of N such that it preserves ± the degree modulo p, the field of values, and the Schur index over every field of characteristic zero. This strengthens a more general recent result [A. Turull, Character correspondences in solvable groups, J. Algebra 295 (2006) 157–178], but only for the case under consideration here. In addition, we prove some other strong character correspondences that have very good rationality properties. As one consequence, we prove that a solvable group G has a non-trivial rational irreducible character with degree prime to p if and only if the order of the normalizer of a Sylow p-subgroup of G has even order.     

Ultraviolet photodissociation of protonated pharmaceuticals in a pressurized linear quadrupole ion trap

Ultraviolet photodissociation (UVPD) was evaluated as a technique for generating ion fragmentation information that is alternative and/or complementary to the information obtained by collision‐induced dissociation (CID). Ions trapped in a pressurized linear ion trap were dissociated using a 355 nm or a 266 nm pulsed laser. Comparisons of UVPD and CID spectra using a set of aromatic chromophore‐containing compounds (desmethyl bosentan, haloperidol, nelfinavir) demonstrated distinct characteristic fragmentation patterns resulting from photodissociation. The wavelength of light and the pressure of the buffer gas in the UVPD cell are important parameters that control fragmentation pathways. The wavelength effect is related to the absorption cross section, location of the chromophore and the energy carried by one photon. Thus, UV irradiation wavelength affects fragmentation pathways as well as the fragmentation rate. The pressure effect can be explained by collisional quenching of ‘slow’ fragmentation pathways. We observed that higher pressure of the buffer gas during UVPD experiments highlights unique fragment ions by suppressing slow fragmentation pathways responsible for CID‐like fragmentation patterns. Copyright © 2010 John Wiley & Sons, Ltd.     

Some aspects of analysis on almost complex manifolds with boundary

We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds, and the elliptic regularity of some diffeomorphisms of almost complex manifolds with boundary. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 47, Complex Analysis, 2007.     

Inner metric geometry of complex algebraic surfaces with isolated singularities

We produce examples of complex algebraic surfaces with isolated singularities such that these singularities are not metrically conical, i.e., the germs of the surfaces near singular points are not bi‐Lipschitz equivalent, with respect to the inner metric, to cones. The technique used to prove the nonexistence of the metric conical structure is related to a development of metric homology. The class of the examples is rather large and includes some Kleinian singularities. © 2008 Wiley Periodicals, Inc.     

Analysis and computation of limit cycles for systems with separable nonlinearities

The variational system obtained by linearizing a dynamical system along a limit cycle is always non-invertible. This follows because the limit cycle is only a unique modulo time translation. It is shown that questions such as uniqueness, robustness, and computation of limit cycles can be addressed using a right inverse of the variational system. Small gain arguments are used in the analysis.     

Topological <Emphasis Type="Italic">K</Emphasis>-equivalence of analytic function-germs

We study the topological K-equivalence of function-germs (ℝ ⁿ , 0) → (ℝ, 0). We present some special classes of piece-wise linear functions and prove that they are normal forms for equivalence classes with respect to topological K-equivalence for definable functions-germs. For the case n = 2 we present polynomial models for analytic function-germs.     

Hydrodynamic Limit for a Boundary Driven Stochastic Lattice Gas Model with Many Conserved Quantities

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics we considered consists of a weakly asymmetric simple exclusion process with collision among particles having different velocities.