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.     

Nickel-Ruthenium Mixed-Metal Carbonyl Clusters Syntheses and Solid State Structures of the Two Tetrahedral Clusters [PPh4][NiRu3(μ3 H)(CO)9(μ-CO)3] and [NEt4]2[NiRu3(CO)8(μ-CO)4]

Redox condensation of [Ru₃H(CO)₁₁]- with Ni(CO)₄, in tetrahydrofuran solution, under a nitrogen atmosphere, yields the tetranuclear anion [NiRu_H(CO)₁₁)-. Subsequent deprotonation with Bu'OK in acetonitrile solution leads to the formation of the related dianion. Both anions have been characterized by spectroscopic techniques, elemental analysis and single crystal X-ray diffraction. [PPh₄][NiRu₃H(CO)₁₂] crystallizes in the triclinic space group PI with unit cell dimensionsof a = 11.842(2) Å,b = 12.335(3) Å, c = 13.3080) Å,a = 91.89(2)°, = 93.35(1)°,y = 96.41(2)°, Z = 2, V= 1926.9(7) Å'. The NiRu₃, metal core of the molecule defines a distorted tetrahedron with nine terminal and three edge bridging carbonyl groups. The hydrido ligand was located by difference Fourier techniques and was found to bridge the NiRu₂ basal triangle at a distance of 0.88(6) A from this plane. Selected average distances and angles are: Ru-Ru = 2.839 Å, Ru-Ni = 2.640 Å, Ru-C, = 1.910 A,Ru-C _b = 2.084 Å, Ni-C _b = 2.022 Å, Ru-H = 1.77 Å, C-0, = 1.135 Å, C-O _b = 1.159 Å, M-C-O, = 176.3°,M-C--O _b = 139.3°;other distances are: Ni-C₁ = l.758(7) Å, Ni-H= 1.85(7) Å. [NEt₄]₂[NiRu₃(CO)₁₂] crystallizes in the orthorhombic space group Pnma (no. 62) with unit cell dimensions ofa=20.247(5) Å,b = 15.038(4)Å,c = 12.079(3) Å, Z=4, V=3678(2) A'. The molecule contains a tetrahedral NiRu₃ core with eight terminal and four edge bridging carbon monoxide groups which bridge the three Ni-Ru and one Ru-Ru bond. Average distances and angles are: Ru -Ru =2.3050A Ru-Ni 2.648 Å, Ru-C _t = 1.878 Å, Ru-C _b 2.045 Å, Ni-C _b = 2.055 Å, C-O _t = 1.145 Å, C-01,=1.157 Å, M-C-O,= 176.9°, M-C-O _b = 138.6°; other distance is: Ni-C _t = 1.754(10) Å,t = terminal,b = bridging.     

Toward efficient Zn(II)-based artificial nucleases

A series of cis-cis-triaminocyclohexane Zn(II) complex-anthraquinone intercalator conjugates, designed in such a way to allow their easy synthesis and modification, have been investigated as hydrolytic cleaving agents for plasmid DNA. The ligand structure comprises a triaminocyclohexane platform linked by means of alkyl spacers of different length (from C(4) to C(8)) to the anthraquinone group which may intercalate the DNA. At a concentration of 5 microM, the complex of the derivative with a C(8) alkyl spacer induces the hydrolytic stand scission of supercoiled DNA with a rate of 4.6 x 10(-6) s(-1) at pH 7 and 37 degrees C. The conjugation of the metal complex with the anthraquinone group leads to a 15-fold increase of the cleavage efficiency when compared with the anthraquinone lacking Zn-triaminocyclohexane complex. The straightforward synthetic procedure employed, allowing a systematic change of the spacer length, made possible to gain more insight on the role of the intercalating group in determining the reactivity of the systems. Comparison of the reactivity of the different complexes shows a remarkable increase of the DNA cleaving efficiency with the length of the spacer. In the case of too-short spacers, the advantages due to the increased DNA affinity are canceled due to the incorrect positioning of the reactive group, thus leading to cleavage inhibition.     

Adsorption-penetration studies of glucose oxidase into phospholipid monolayers at the 1,2-dichloroethane/water interface.

The interaction between glucose oxidase (GOx) and phospholipid monolayers is studied at the 1,2-dichloroethane/water interface by electrochemical impedance spectroscopy. Electrochemical experiments show that the presence of GOx induces changes in the capacitance curves at both negative and positive potentials, which are successfully explained by a theoretical model based on the solution of the Poisson-Boltzmann equation. These changes are ascribed to a reduced partition coefficient of GOx and an increase of the permittivity of the lipid hydrocarbon domain. Our results show that the presence of lipid molecules enhances the adsorption of GOx molecules at the liquid/liquid interface. At low lipid concentrations, the adsorption of GOx is probably the first step preceding its penetration into the lipid monolayer. The experimental results indicate that GOx penetrates better and forms more stable monolayers for lipids with longer hydrophobic tails. At high GOx concentrations, the formation of multilayers is observed. The phenomenon described here is strongly dependent on 1) the GOx and lipid concentrations, 2) the nature of the lipid, and 3) the potential drop across the interface.