Eigenanalysis on a bivariate covariance kernel

Certain constructions of copulas can be interpreted as an eigendecomposition of a kernel. We study some properties of the eigenfunctions and their integrals of a covariance kernel related to a bivariate distribution. The covariance between functions of random variables in terms of the cumulative distribution function is used. Some bounds for the trace of the kernel and some inequalities for a continuous random variable concerning a function and its derivative are obtained. We also obtain relations to diagonal expansions and canonical correlation analysis and, as a by-product, series of constants for some particular distributions.     

Tranversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near L2 in the restricted three-body problem

The restricted three-body problem is considered for values of the Jacobi constant C near the value C₂ associated to the Euler critical point L₂. A Lyapunov family of periodic orbits near L₂, the so-called family (c), is born for C = C₂ and exists for values of C less than C₂. These periodic orbits are hyperbolic. The corresponding invariant manifolds meet transversally along homoclinic orbits. In this paper the variation of the transversality is analyzed as a function of the Jacobi constant C and of the mass parameter μ. Asymptotical expressions of the invariant manifolds for C ? C₂ and μ ? 0 are found. Several numerical experiments provide accurate information for the manifolds and a good agreement is found with the asymptotical expressions. Symbolic dynamic techniques are used to show the existence of a large class of motions. In particular the existence of orbits passing in a random way (in a given sense) from the region near one primary to the region near the other is proved.     

General properties of the electronic structure of alkali metal clusters and Ia-IIa mixed clusters

The results of the systematic ab-initio CI investigation of neutral and charged Li _n , Na _n , BeLi _k and MgNa _k clusters are summarized and analyzed. The general characteristic features of the electronic structure are pointed out:a) The participation of the atomic orbitals, which are empty in Ia and IIa metal atoms, allows for a higher valency of these atoms in clusters.b) Jahn-Teller and pseudo-Jahn-Teller effects strongly influence the electronic and geometric structure of clusters.c) Deformations of cluster geometry can lead to biradicaloid structures with higher spin multiplicity in their ground states.d) The peculiarities of the electronic structures of clusters can be deduced from the presence of many “surface” atoms. The theoretical results agree with experimental data presently available and they are useful for interpretation of the experimental findings.     

On n ‐contractive fuzzy logics

It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w. r. t. the class of all finite MTL‐chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since each finite MTL‐chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced in [9] and the axiom of weak cancellation defined in [31]. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple, and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embeddability property, finite model property, decidability, and standard completeness. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zur Bestimmung der Gesamt-Weins?ure in weins?urehaltigen Rohmaterialien

Ohne ZusammenfassungAus dem Französischen übersetzt von der Redaktion     

Semiclassical Asymptotics for Weakly Nonlinear Bloch Waves

We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB–analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.     

Characterization of acylated flavonoid-O-glycosides and methoxylated flavonoids from Tagetes maxima by liquid chromatography coupled to electrospray ionization tandem mass spectrometry

Liquid chromatography coupled to negative electrospray ionization (ESI) tandem mass spectrometry (MS/MS) employing a triple quadrupole mass spectrometer was used in the structural determination of acylated flavonoid-O-glycosides and methoxylated flavonoids occurring in Tagetes maxima. The compounds were identified by experiments in full scan mode (MS), and tandem mass experiments (MS/MS) of precursor ion scan, product ion scan, and neutral loss scan modes. In order to characterize the aglycones of the flavonoid glycosides, in-source fragmentation of the deprotonated molecule [M-H]- followed by product ion scan of the resulting aglycone [A-H]- were performed. This combined approach allowed the identification of 51 phenolic compounds, including flavonoid-O-glycosides acylated with galloyl, protocatechuoyl, coumaroyl or caffeoyl groups, methoxylated flavonoids, and hydroxycinnamic acid and phenolic acid derivatives, none of them previously reported in Tagetes maxima.     

Ab initio and DFT modelling of complex materials: towards the understanding of electronic and magnetic properties of polyoxometalates

In this review we summarise the quantum chemistry studies carried out by several groups over the last ten years on polyoxometalates, or polyoxoanions. This is an immense family of compounds made up of transition metal ions in their highest oxidation state and oxo ligands. The continuous progress of computers in general, and quantum chemistry software in particular, has enabled a number of topics in polyoxometalate chemistry to be studied from the electronic structure of the most representative polyoxometalate, the so-called Keggin anion, to the factors governing the inclusion complexes and the magnetism in reduced complexes.     

Computational insight into the reaction intermediates in the glycosylation reaction assisted by donor heteroatoms

We studied the geometric and electronic structure of several cations (9 and 18-23) that are usually proposed as intermediates for glycosylation reactions using DFT methods. For ions 9 and 18-23 the geometries obtained corresponded to an open ion (6b type) irrespective of the exocyclic heteroatom (S, Se, I) and the size of the cycle (furanoses as well as pyranoses). We studied how substituents bonded to the exocyclic heteroatom (R in SR and SeR) affect the structure of ions and found that the geometry approached that of episulfonium and episelenonium ions (6a type) when the substituents were electron donors. The tert-butyl group and the 2,4,6-trimethyl- and 2,4,6-trimethoxyphenyl and trimethylsilyl groups produced the strongest of these effects. The presence of an electron-withdrawing group (CO-CF(3)) bonded to the hydroxymethyl group produced a similar but weaker effect. We analyzed this behavior in terms of molecular orbital interactions.