Polyanalytic Hardy decomposition of higher order Lipschitz functions

This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve Γ into a sum of two polyanalytic functions in each open domain defined by Γ. Our basic tools are the Hardy projections related to a singular integral operator arising in polyanalytic function theory, which, as it is proved here, represents an involution operator on the higher order Lipschitz classes. Our result generalizes the classical Hardy decomposition of Hölder continuous functions on the boundary of a domain.     

Rhodium/tris-binaphthyl chiral monophosphite complexes: Efficient catalysts for the hydroformylation of disubstituted aryl olefins

A family of threefold symmetry phosphite ligands, P(O–BIN–OR)₃ (BIN = 2,2′-binaphthyl; R = Me, Bn, CHPh₂, 1-adamantyl), derived from enantiomerically pure (R)-BINOL, was developed. Cone angles within the range 240–270° were calculated for the phosphite ligands, using the computational PM6 Hamiltonian. Their rhodium complexes formed in situ showed remarkable catalytic activity in the hydroformylation of hindered phenylpropenes, under relatively mild reaction conditions, with full chemoselectivity for aldehydes, high regioselectivity, however with low enantioselectivity. The ether substituents at the ligand affected considerably the catalytic activity on the hydroformylation of 1,1- and 1,2-disubstituted aryl olefins. The kinetics of the hydroformylation of trans-1-phenyl-1-propene, using tris[(R)-2′-benzyloxy-1,1′-binaphthyl-2-yl]phosphite as model ligand, was investigated. A first order dependence in the hydroformylation initial rate with respect to substrate and catalyst concentrations was found, as well as a positive order with respect to the partial pressure of H₂, and a slightly negative order with respect to phosphite concentration and CO partial pressure.     

Landauʼs necessary density conditions for the Hankel transform

We will prove an analogue of Landau?s necessary conditions [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52] for spaces of functions whose Hankel transform is supported in a measurable subset S of the positive semi-axis. As a special case, necessary density conditions for the existence of Fourier–Bessel frames are obtained.     

A comparison of a gas chromatographic with electron-capture detection and a gas chromatographic with mass spectrometric detection screening methods for the analysis of famoxadone in grapes and wines

Famoxadone is a recent oxazolidinedione fungicide widely used in viticulture and in Integrated Pest Management strategies. In this work, after a simple and fast liquid-liquid extraction (LLE), two new gas chromatographic methods were developed to analyze famoxadone residues in grapes and wines, one with electron-capture detection (GC-ECD) and the other with mass spectrometry (GC-MS). Global uncertainties for validation parameters of both methods were compared. Limits of detection (LODs) were 0.06 and 0.02 mg/L, precision was not above 11.7 and 6.8% and recoveries were, on average, 103%+/-12 and 96%+/-12, respectively, for the GC-ECD and GC-MS methods. Similar expanded uncertainties in the range from 0.25 to 1.00 mg/L were below 35%, with increasing values for lower levels of famoxadone. GC-MS method had a lower LOD and a lower uncertainty if compared with the GC-ECD method.     

Obtaining gauge invariant actions via symplectic embedding formalism

The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non‐invariant ones. Both are named also as first‐ and second‐class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non‐invariant theories. Once established, this kind of mapping between first‐class (gauge invariant) and second‐class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non‐invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non‐Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non‐Abelian systems.