On Lusin's condition for the inverse function

Sia ? una funzione invertibile, continua e quasi ovunque differenziabile, da un aperto di IR ⁿ in IR ⁿ . Allora ?^?1soddisfa alla condizione di Lusin (N) se e solo se lo Jacobiano di ? è quasi ovunque diverso da zero.     

Regiospecific synthesis of 1-arylpyrazoles

A new regiospecific synthesis of 1-aryl-substituted pyrazoles by reaction of aryl-hydrazines with β-aminoenones is reported.     

Spectral smoothed boundary methods: The role of external boundary conditions

The spectral smoothed boundary method (SSBM) is a recently proposed numerical method to approximate the solution of partial differential equations in irregular domains with no‐flux boundary conditions by means of Fourier spectral methods. In this article we explore the robustness and accuracy of the scheme under variations of the artificial boundary conditions that must be imposed on the boundary of the enlarged domain in which the problem is solved. As a test model, we present quantitative numerical results based on a problem of propagation of waves of electrical activity in cardiac tissue for which the method is relevant. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Radial Solutions to a Dirichlet Problem Involving Critical Exponents when

In this paper we show that, for each , the set of radially symmetric solutions to the boundary value problem

is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

     

Torsion,string tension,and topological origin of charge and mass

We consider the analogy between torsion line defects and vortex lines in a superconductor to suggest that the electric charge and masses of elementary particles may have a geometrical origin. Just as the field vanishes everywhere in a superconductor except along the vortex line, where the flux is confined, we have the torsion being concentrated only along the topological defects, giving rise to charge as well as mass. The mass is related to the string tension (c ²/G) and charge is connected with the gravitational permeability (G/c ²), both induced by torsion.     

A mass spectral study of 1-(aryldimethylsilyl)-2-propanones and their isomeric 2-(aryldimethylsiloxy)-1-propenes

The mass spectra of a series of β-ketosilanes, p-Y? C₆H₄Me₂SiCH₂C(O)Me and their isomeric silyl enol ethers, p-Y? C₆H₄Me₂SiOC(CH₃)?CH₂, where Y = H, Me, MeO, Cl, F and CF₃, have been recorded. The fragmentation patterns for the β-ketosilanes are very similar to those of their silyl enol ether counterparts. The seven major primary fragment ions are [M? Me·]⁺, [M? C₆H₄Y·]⁺, [M? Me₂SiO]⁺˙, [M? C₃H₄]⁺˙, [M? HC?CCF₃]⁺˙, [Me₂SiOH]⁺˙ and [C₃H₆O]⁺˙ Apparently, upon electron bombardment the β-ketosilanes must undergo rearrangement to an ion structure very similar to that of the ionized silyl enol ethers followed by unimolecular ion decompositions. Substitutions on the benzene ring show a significant effect on the formation of the ions [M? Me₂SiO]⁺˙ and [Me₂SiOH]⁺˙, electron donating groups favoring the former and electron withdrawing groups favoring the latter. The mass spectral fragmentation pathways were identified by observing metastable peaks, metastable ion mass spectra and ion kinetic energy spectra.     

Structure and dynamics of catalytically competent but labile paramagnetic metal-hydrides: the Ti(iii)-H in homogeneous olefin polymerization

Metal hydride complexes find widespread application in catalysis and their properties are often understood on the basis of the available crystal structures. However, some catalytically relevant metal hydrides are only spontaneously formed in situ, cannot be isolated in large quantities or crystallised and their structure is therefore ill defined. One such example is the paramagnetic Ti(iii)-hydride involved in homogeneous Ziegler–Natta catalysis, formed upon activation of CpTi(iv)Cl₃ with modified methylalumoxane (MMAO). In this contribution, through a combined use of electron paramagnetic resonance (EPR), electron-nuclear double resonance (ENDOR) and hyperfine sublevel correlation (HYSCORE) spectroscopies we identify the nature of the ligands, their bonding interaction and the extent of the spin distribution. From the data, an atomistic and electronic model is proposed, which supports the presence of a self-assembled ion pair between a cationic terminal Ti-hydride and an aluminate anion, with a hydrodynamic radius of ca. 16 Å.

Catalytically competent titanium-hydrides are reactive and difficult to isolate. We use EPR spectroscopy to define the electronic and geometrical structures as well as dynamics of an open-shell Ti-H active in syndiospecific olefin polymerization.     

Vanchrobactin: absolute configuration and total synthesis

The stereochemistry of vanchrobactin, a siderophore produced by the bacterial fish pathogenVibrio anguillarum serotype O2, was elucidated by chiral capillary electrophoresis analysis and total synthesis as N-[N′-(2,3-dihydroxybenzoyl)-d-arginyl]-l-serine.