Infinite dimensional duality and applications

The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example, we find the Lagrange multiplier associated to a general elastic–plastic torsion problem.     

Thin-walled Beams: A Derivation of Vlassov Theory via Γ-Convergence

This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order ε and ε ², as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams.      

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Amphiphilic cyclodextrin carriers embedding porphyrins: charge and size modulation of colloidal stability in heterotopic aggregates

The interaction between the anionic 5,10,15,20-tetrakis(4-sulfonatophenyl)-21H,23H-porphyrin (TPPS) and cationic vesicles formed by heptakis(2-omega-amino-O-oligo(ethylene oxide)-6-hexylthio)-beta-cyclodextrin (SC6CDNH2) has been investigated in detail through a combination of elastic light scattering (ELS), quasi-elastic light scattering (QELS), zeta potential measurements, and time-resolved fluorescence anisotropy. ELS experiments provided the first structural characterization of these cationic vesicles both in the absence and in the presence of TPPS porphyrin, modeling the system as a spherical particle described by a single thin shell form factor. The structure of mixed hetero-aggregates is modulated by charge and size of the two components as function of different porphyrin/cyclodextrin (CD) molar ratios. At the limiting molar ratio studied, the absolute value of zeta potential (/zeta/ = 12.5 mV) seems to be a reference value for the formation of stable colloidal CD vesicular aggregates at thermodynamic equilibrium. New insights on the structure of these heterotopic colloids have been obtained by analysis of rotational correlation times at different molar ratios exploiting time-resolved fluorescence anisotropy experiments. At high porphyrin loads, the anisotropy decays behave as monoexponentials and the rotational correlation times (1-2 ns) together with the r(0) values close to zero suggest the presence of small amounts of TPPS embedded in a hydrophobic environment either in monomeric or in aggregated form. At the lower porphyrin/CD molar ratios, the anisotropy decays exhibit a double-exponential behavior showing a predominant component with a slow rotational correlation time (20-25 ns) and limiting anisotropy values of approximately 0.15. This component has been assigned to molecules that are more stabilized onto the CD vesicles, that is, porphyrins embedded into the oligo-ethylene "wall" of the CD vesicles. Scanning near-field optical microscopy of the samples evaporated on glass surfaces gave further insights on the morphology and optical properties of these systems, confirming the embedding of TPPS on the vesicles and evidencing the role of the solvent.     

Thermal decomposition products of copoly(arylene ether sulfone)s characterized by direct pyrolysis mass spectrometry

Pyrolysis products with mass of up to 850 Da were detected by direct pyrolysis mass spectrometric (DPMS) analysis of a series of copoly(arylene ether sulfone)s (PES-PPO) synthesized by nucleophilic condensation of either 4,4′-dichlorodiphenylsulfone (CDPS) or 4,4′-bis-(4-chlorophenyl sulfonyl) biphenyl (long chain dichloride, LCDC) with different molar ratios of hydroquinone (HQ) or dihydroxydiphenylsulfone (HDPS). Pyrolysis products retaining the repeating units of the initial copolymers were formed at temperatures ranging from 420 °C to 470 °C (near the initial decomposition temperature). At temperatures higher than 450 °C were observed products containing biphenyl units, formed by the elimination process of SO₂ from diphenyl sulfone bridges. Products having biphenyl and dibenzofuran moieties were detected in the mass spectra recorded at temperatures above 550 °C. These units were formed by loss of hydrogen atom from diphenyl ether bridges. Although the EI (18 eV) mass spectra of the pyrolysis products of the samples investigated were very similar, it was found that the relative intensity of some ions reflects the molar composition of the copolymers analysed. Cyclic and linear oligomers with very low molecular mass, present in the crude copolymers, were also detected by DPMS. Thermogravimetric analysis also showed their excellent thermal stability below 400 °C. It indicates that the copolymers yield a char residue of 40-45% at 800 °C, which increases with the PPO mole fraction in the samples.     

Synthesis and characterization of poly(amidoamine)-platinum(II) complexes. Detailed speciation by Matrix-Assisted Laser Desorption Ionization Mass Spectrometry

MALDI and ESI-MS have been applied to the characterization of the reaction products between the labile cis-[Pt(DMSO)₂Cl₂] (1) and trans-[Pt(DMSO)₂Cl(CH₃)] (2) complexes with the simplest poly(amidoamine) ligand (PAMAM, G = 0, 1,2-diaminoethane as core). The comparison of the mass spectra of the starting G₀ and those of the metallo-dendrimers formed upon mixing of the reagents in an equimolecular ratio, and the analysis of the isotopic distribution in the ESI spectra, have revealed the formation of cationic and neutral mononuclear complexes with PAMAM as ligand, e.g., cis-[Pt(DMSO)(PAMAM)Cl]Cl or trans-(C,N)[Pt(DMSO)(PAMAM)Cl(CH₃)], together with various minor components, which have been identified as derivatives from defective structures of PAMAM. The geometry of the main products has been deduced from the values of the protons coupling constants with the isotopically abundant ¹⁹⁵Pt. The metal-to-ligand bond is restricted to the peripheral amino groups of PAMAM which shows sufficient flexibility to involve either one or two branches in the coordination bonding.     

1H-NMR,Ultraviolet and infrared spectra of some (Z)-α-(phenyl)-β-(2-furyl), -(2-pyrrolyl) and -(N-methyl-2-pyrrolyl)acrylonitriles

The ¹H-nmr data of some (Z)-α-(p-substituted-phenyl)-β-(2-furyl), -(2-pyrrolyl), and -(N-methyl-2-pyrrolyl)-acrylonitriles have been investigated to indicate the preferred conformation and to establish the conformational preferences of the β-heterocyclic ring. The ultraviolet spectra have been discussed in order to obtain information about the chromophores responsible for the absorption. The infrared spectra have been analyzed for the identification of the main absorption frequencies of cyano and ethylenic groups and to assign the characteristic absorption bands to specific normal vibrations of the heteroaromatic nuclei.     

Solvent effects in the reaction of 2-thiophenesulfonyl chloride with aniline

The second order rate constants k₂ and the activation parameters for the reaction of 2-thiophenesulfonyl chloride with aniline together with solution enthalpies of the reactants have been measured in methanol, ethanol, 2-propanol, acetonitrile and acetone. The reaction rates are slower in dipolar aprotic solvents than in protic ones due to a remarkable activation negative entropy. The rate constants k₂ are correlated with empirical solvent polarity parameters. The data seem in accord with a S_AN reaction mechanism.     

Review of aminopolycarboxylic acids–based metal complexes application to water and wastewater treatment by (photo-)Fenton process at neutral pH

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