Über endliche Gruppen linearer Transformationen einer Veränderlichen

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Ueber lineare homogene Differentialgleichungen mit algebraischen Relationen zwischen den Fundamentallösungen

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Bulky monodentate phosphoramidites in palladium-catalyzed allylic alkylation reactions: aspects of regioselectivity and enantioselectivity

A series of bulky monodentate phosphoramidite ligands, based on biphenol, BINOL and TADDOL backbones, have been employed in the Pd-catalysed allylic alkylation reaction. Reaction of disodium diethyl 2-methyl malonate with monosubstituted allylic substrates in the presence of palladium complexes of the phosphoramidite ligands proceeds smoothly at room temperature. The regioselectivities observed depend strongly on the leaving group and the geometry of the allylic starting compounds. Mono-coordination occurs when these ligands are ligated in [Pd(allyl)(X)] complexes (allyl=C3H5, 1-CH3C3H4, 1-C6H5C3H4, 1,3-(C6H5)2C3H3; X=Cl, OAc). The solid-state structure determined by X-ray diffraction of [Pd(C3H5)(1)(Cl)] reveals a non-symmetric coordination of the allyl moiety, caused by the stronger trans influence of the phosphoramidite ligand relative to X-. In all of these complexes, the syn,trans isomer is the major species present in solution. Because of fast isomerisation and high reactivity of the syn,cis complex, the major product formed upon alkylation is the linear product, especially for monosubstituted phenylallyl substrates in the presence of halide counterions. In the case of biphenol- and BINOL-based phosphoramidites, however, a strong memory effect is observed when 1-phenyl-2-propenyl acetate is employed as the substrate. In this case, nucleophilic attack competes effectively with the isomerisation of the transient cinnamylpalladium complexes. The asymmetric allylic alkylation of 1,3-diphenyl-2-propenyl acetate afforded the chiral product in up to 93 % ee. Substrates with smaller substituents gave lower enantioselectivities. The observed stereoselectivity is explained in terms of a preferential rotation mechanism, in which the product is formed by attack on one of the isomers of the intermediate [Pd[1,3-(C6H5)2C3H3](L)(OAc)] complex.     

Synthesis and characterization of Zr(IV) and Y(III) complexes with monocyclopentadienyl ligands containing an additional site tethered by a coordinating 2,6-pyridine bridge. X-ray crystal structures of the zirconium complexes

A new monocyclopentadienyl ligand containing an additional site tethered by a coordinating 2,6-pyridine unit has been prepared, rac-2-(1′-hydroxy-2′,2′-dimethylpropyl)-6-(1″,1″-dimethyl-cyclopentadienylmethyl) pyridine dilithium salt, LLi₂ (rac-4) that is analogous to the ligands present in CGC. After reacting the dilithium salt of the ligand with ZrCl₄ in a molar ratio of 1:1 in THF the complex LZrCl₂·THF (rac-5) was obtained which forms an insoluble oligomeric species after the loss of THF upon purification. From the mater liquor two crystalline species of the formula LHZrCl₃ (rac-6) and LH₂ZrCl₄·THF (rac-7) were isolated, whose X-ray crystal structures are reported. The reaction of LLi₂ with Y(OTf)₃ afforded the probably dimeric species [LYOTf]₂ (rac-8) from which the complex [LY(CH₂Si(CH₃)₃)]₂ (rac-9) was obtained after reaction with LiCH₂Si(CH₃)₃.     

Chemical Profile,In Vitro Biological Activity and Comparison of Essential Oils from Fresh and Dried Flowers of Lavandula angustifolia L.

The chemical composition of essential oils (EOs) from dried and fresh flowers of Lavandula angustifolia L. (lavender), named LA 2019 and LA 2020, respectively, grown in central Italy was analyzed and compared by GC and GC-MS. For both samples, 61 compounds were identified, corresponding to 97.9% and 98.1% of the total essential oils. Explorative data analysis, performed to compare the statistical composition of the samples, resulted in a high level of global similarity (around 93%). The compositions of both samples were characterized by 10 major compounds, with a predominance of Linalool (35.3–36.0%), Borneol (15.6–19.4%) and 1,8-Cineole (11.0–9.0%). The in vitro antibacterial activity assay by disk diffusion tests against Bacillus subtilis PY79 and Escherichia coli DH5α showed inhibition of growth in both indicator strains. In addition, plate counts revealed a bactericidal effect on E. coli, which was particularly noticeable when using oil from the fresh lavender flowers at the highest concentrations. An in vitro antifungal assay showed that the EOs inhibited the growth of Sclerotium rolfsii, a phytopathogenic fungus that causes post-harvest diseases in many fruits and vegetables. The antioxidant activity was also assessed using the ABTS free radical scavenging assay, which showed a different antioxidant activity in both EOs. In addition, the potential application of EOs as a green method to control biodeterioration phenomena on an artistic wood painting (XIX century) was evaluated.     

On the Spectrum of the Dirac Operator and the Existence of Discrete Eigenvalues for the Defocusing Nonlinear Schrödinger Equation

We revisit the scattering problem for the defocusing nonlinear Schrödinger equation with constant, nonzero boundary conditions at infinity, i.e., the eigenvalue problem for the Dirac operator with nonzero rest mass. By considering a specific kind of piecewise constant potentials we address and clarify two issues, concerning: (i) the (non)existence of an area theorem relating the presence/absence of discrete eigenvalues to an appropriate measure of the initial condition; and (ii) the existence of a contribution to the asymptotic phase difference of the potential from the continuous spectrum.     

Pseudoradial Spaces: Results and Problems

In this paper it is given a survey of principal results (old and new) concerning the class of pseudoradial spaces. In this class cardinal invariants and their inequalities are considered. The behaviour of pseudoradial spaces under the operations of taking topological products and subspaces are examined and a typical proof is given. A particular attention is dedicated to the so called “small cardinals” in connection with pseudoradiality. Pseudoradiality of 2^{ω 2} is also examined. It is proved that pseudoradiality can be ω¹ productive for spaces of weight at most ω². Finally, several open problems are presented. This work was supported by the National Group “Real Analysis, Measure Theory with Applications to Economy” of the Italian Ministery of Education, University and Research.     

A two-phase method for selecting IMRT treatment beam angles: Branch-and-Prune and local neighborhood search

This paper presents a new two-phase solution approach to the beam angle and fluence map optimization problem in Intensity Modulated Radiation Therapy (IMRT) planning. We introduce Branch-and-Prune (B&P) to generate a robust feasible solution in the first phase. A local neighborhood search algorithm is developed to find a local optimal solution from the Phase I starting point in the second phase. The goal of the first phase is to generate a clinically acceptable feasible solution in a fast manner based on a Branch-and-Bound tree. In this approach, a substantially reduced search tree is iteratively constructed. In each iteration, a merit score based branching rule is used to select a pool of promising child nodes. Then pruning rules are applied to select one child node as the branching node for the next iteration. The algorithm terminates when we obtain a desired number of angles in the current node. Although Phase I generates quality feasible solutions, it does not guarantee optimality. Therefore, the second phase is designed to converge Phase I starting solutions to local optimality. Our methods are tested on two sets of real patient data. Results show that not only can B&P alone generate clinically acceptable solutions, but the two-phase method consistently generates local optimal solutions, some of which are shown to be globally optimal.