Tangent cones and Dini derivatives

We prove a property of the Bouligand tangent cone to the epigraph (or to the graph) of a locally Lipschitz function. It is also shown how this result can be used in determining Dini sequences. Finally, some relationships between such a cone and Dini derivatives are provided.     

Nash Equilibria,Variational Inequalities,and Dynamical Systems

In this paper, we introduce some relationships between Nash equilibria, variational equilibria, and dynamical equilibria for noncooperative games.     

On the Image Regularity Condition

In this paper, we continue the analysis of the image regularity condition (IRC) as introduced in a previous paper where we have proved that IRC implies the existence of generalized Lagrange-John multipliers with first component equal to 1. The term generalized is connected with the fact that the separation (in the image space) is not necessarily linear (when we have classic Lagrange-John multipliers), but it can be also nonlinear. Here, we prove that the IRC guarantees, also in the nondifferentiable case, the fact that 0 is a solution of the first-order homogeneized (linearized) problem obtained by means of the Dini-Hadamard derivatives.     

Study of the Capabilities of the ALICE inner tracking system stand-alone for HBT analysis

Results are shown from a Monte Carlo simulation study of the capabilities of the Inner Tracking System of the ALICE experiment, used in standalone mode, for HBT analysis of Pb?Pb collisions at LHC energies (5.5 ATeV). Different values of the coherence factor and the Gaussian source radius have been studied. For this purpose, a specific ITS stand-alone tracking algorithm, based on the Denby-Peterson neural algorithm, has been developed.     

Shape recognition of alkylammonium ions by 1,3-bridged calix[5]arene crown-6 ethers: endo- vs exo-cavity complexation

A series of tri-O-substituted 1,3-bridged calix[5]arene crown-6 ethers bearing alkyl, arylalkyl, alkoxyalkyl, and alkoxycarbonylmethyl residues at the lower rim and either (t)()Bu or H substituents at the upper rim have been synthesized. (1)H NMR studies have shown that p-tert-butylcalix[5]crowns, irrespective of the size and nature of their lower rim pendant groups, adopt preorganized conelike conformations, whereas p-H-calix[5]crowns with bulky substituents preferentially exist in solution as partial cone conformers (C(1) symmetry). Calix[5]crown derivatives behave as mono- or ditopic receptors for isomeric butylammonium ions, forming endo-cavity (inside the calixarene cup) and/or exo-cavity (at the crown ether moiety) 1:1 complexes according to the shape of the guest. These two binding modes can be clearly distinguished and monitored by (1)H NMR titration experiments.     

Crystal and molecular structure ofN,N′,N″-tritosyl-5,8,14,17,23,26-hexamethyl-2,11,20-triaza[3.3.3]-paracyclophane 1 : 1 dichloromethane clathrate

The crystal and molecular structure of the title compound, C₅₁H₅₇N₃O₆S₃·CH₂Cl₂ has been determined by single crystal X-ray analysis and refined to anR-value of 0.069 for 1032 reflections. The crystal is trigonal, space groupR3, witha = 21.255(7),c = 11.317(4), andZ = 3. One molecule of dichloromethane used as solvent is enclathrated in the crystal lattice.     

Subthreshold pion production from nucleus-nucleus collisions around 100 MeV/nucleon

Several global variables were tested with the aim to determine the impact parameter in nucleus-nucleus collisions producing pions at incident energies around 100 MeV/nucleon. The experimental set-up includes the MEDEA multidetector, part of which is used as a ⁰ spectrometer, and an additional hodoscope of plastic scintillators to cover very forward angles. A statistical model was used to generate bothinclusive and pion-triggered events. Selection ofwell measured events was made through the measured total parallel momentum. Among the different global variables which were tested, the average parallel velocity was seen to give the best correlation with the impact parameter.     

A re-investigation of copper coordination in the octa-repeats region of the prion protein

An aqueous solution spectroscopic (Vis and EPR) study of the copper(II) complexes with the Ac-HGGG-NH2 and Ac-PHGGGWGQ-NH2 polypeptides (generically designated as L) suggests square base pyramids ascribable to [Cu(L)H(-2)] complex species, which contain three nitrogen donor atoms, arising from imidazole and peptide groups, in the equatorial plane and for a pseudo-octahedral geometry in the case of [CuLH-3]- and [Cu(L)H-4]2- which have four nitrogen donor atoms in their equatorial plane. The coordination sphere of the copper complex in the [Cu(L)H(-2)] species, which is present at neutral pH values, is completed by two oxygen donor atoms. ESI-MS spectra ascertained that water molecules are not present in the coordination equatorial plane of this latter species, in comparison with other copper(II) complexes with ligands bearing nitrogen and oxygen donor atoms and surely having equatorial water molecules. This indicates the coordination of a carbonyl oxygen atom in the equatorial plane has to be invoked. However, no direct proof about the involvement of a carbonyl group oxygen donor atom apically linked to copper was obtained, due to the flexibility of these structures at room temperature. Additionally, the low A(ll) value leads one to consider another oxygen atom of a carbonyl group being involved in the apical bond to copper in a fast exchange fashion. This apical interaction, which may also involve a water molecule, is more pronounced in the Cu-Ac-HGGG-NH2 than in the analogous Cu-Ac-PHGGGWGQ-NH2 system, probably because of the presence of tryptophan and proline in the polypeptide sequence.     

Copper(II) interaction with unstructured prion domain outside the octarepeat region: speciation, stability, and binding details of copper(II) complexes with PrP106-126 peptides

Copper(II) complexes of the neurotoxic peptide fragments of human and chicken prion proteins were studied by potentiometric, UV-vis, CD, and EPR spectroscopic and ESI-MS methods. The peptides included the terminally blocked native and scrambled sequences of HuPrP106-126 (HuPrPAc106-126NH2 and ScrHuPrPAc106-126NH2) and also the nona- and tetrapeptide fragments of both the human and chicken prion proteins (HuPrPAc106-114NH2, ChPrPAc119-127NH2, HuPrPAc109-112NH2, and ChPrPAc122-125NH2). The histidyl imidazole-N donor atoms were found to be the major copper(II) binding sites of all peptides; 3N and 4N complexes containing additional 2 and 3 deprotonated amide-N donors, respectively, are the major species in the physiological pH range. The complex formation processes for nona- and tetrapeptides are very similar, supporting the fact that successive deprotonation and metal ion coordination of amide functions go toward the N-termini in the form of joined six- and five-membered chelates. As a consequence, the peptide sequences investigated here, related to the neurotoxic region of the human PrP106-126 sequence, show a higher metal-binding affinity than the octarepeat fragments. In the case of the HuPrP peptide sequences, a weak pH-dependent binding of the Met109 residue was also detected in the 3N-coordinated complexes.     

Synthesis and characterization of oxygen and sulfur bridged aromatic macrocycles

The synthesis of nine 16–18–20–22 membered, oxygen and sulfur bridged aromatic macrocycles is reported, and reaction pathways to macrocycles formation are described. Molecular characterization of the nine compounds has been achieved by their mass spectra. Due to the cyclic nature of the compounds analyzed, the mass spectra are of particular interest. The 16–18-membered macrocycles, containing single oxygen and sulfur bridges, display very strong molecular ion intensities, while the 20–22-membered macrocycles, containing double bridges, show lower stability to electron-impact, and the molecular ion intensities are lower. Some of the salient features of the electron fragmentation processes are briefly discussed in the text.