Unbounded critical points for a class of lower semicontinuous functionals

For a general class of lower semicontinuous functionals, we prove existence and multiplicity of critical points, which turn out to be unbounded solutions to the associated Euler equation. We apply a nonsmooth critical point theory developed in [10], [12] and [13] and applied in [8], [9] and [20] to treat the case of continuous functionals.     

Transitive decomposition of symmetry groups for the n-body problem

Periodic and quasi-periodic solutions of the n-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries fulfills certain conditions (such as the rotating circle property). Here we generalize such conditions to more general group types and show how to constructively classify all groups satisfying such hypothesis, by a decomposition into irreducible transitive components. As examples we show approximate trajectories of some of the resulting symmetric minimizers.     

Hard X-rays and soft-matter: processing of sol–gel films from a top down route

A current trend of applied research in the field of nanomaterials is the integration of bottom up and top down fabrication methods. Sol–gel chemistry is widely applied to obtain different functional materials from a bottom up route, especially in the case of thin films. To fabricate devices based on sol–gel films, which include nanocomposites and mesoporous ordered materials, application of lithography technologies is mandatory. Among the different lithographic approaches, photolithography is widely used by companies using micro-fabrication processes. In this context, photolithography is a typical top down method that requires to be integrated as much as possible with deposition of thin films from a liquid phase. Recently we have developed a new integrated fabrication method which uses high energy photons, such as hard X-rays, which typically have energies between 2.5 and 12 keV, for the manipulation and production of a large variety of functional materials and devices. In the present review a short overview of such achievements is presented.     

Comparison of global models of sub-bituminous coal devolatilization by means of thermogravimetric analysis

Coal gasification and combustion are strongly dependent on devolatilization step. Aim of this work is to obtain the parameters of global kinetics of devolatilization of a sub-bituminous coal with high sulfur content. The kinetic parameters are obtained by means of TG experimental data, and applying different approaches to extrapolate the data to industrial relevant conditions. The simpler method is a model-free one which supposes a single step process whose Arrhenius kinetic parameters (A and E _a) have to be determined. Another common approach is the distributed activation energy model (DAEM) which assumes a series of first order parallel reactions occurring and sharing the same pre-exponential factor, A, with a continuous distribution of the activation energy. For the fitting of the experimental data, a numerical solution to DAEM and two approximate methods have been evaluated. Moreover, the results of these kinetic methods based on empirical approaches were compared with simulated data obtained using a more complex model based on percolation theory with cross-linking mechanism and vapor–liquid equilibrium (chemical percolation devolatilization, CPD model), which allows to simulate the coal pyrolysis from volatile yield data.     

Second-order Mø øller–Plesset second derivatives for the polarizable continuum model: theoretical bases and application to solvent effects in electrophilic bromination of ethylene

An analytical theory for the energy second derivatives at second-order Mø øller–Plesset level for solvated molecules described within the polarizable continuum model is presented. The method, which is based on the differentiation of relaxed density equations for the first derivatives, is firstly presented in its formal aspects and is then applied to the study of the rate-determining step of the electrophilic bromination of ethylene in aqueous solution.Contribution to the Jacopo Tomasi Honorary Issue     

Pseudodifferential operators of mellin type on sobolev spaces

Sunto Proposito di questa nota è di introdurre una classe di operatori pseudodifferenziali che agiscono su sottospazi chiusi di W^p,k(R ₊), caratterizzati da opportune condizioni di compatibilità. Per tali operatori vengono studiate proprietà di Fredholm e di indice.

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Research partially supported by C.N.R. Gruppo G.N.A.F.A.     

CIEL*a*b* parameters of white dehydrated grapes as quality markers according to chemical composition,volatile profile and mechanical properties

In the oenological sector, the withering process is of particular importance in the production of dry and sweet dessert wines due to the total or partial use of overripe and/or dehydrated grapes.     

Dispersion and repulsion contributions to the solvation free energy: comparison of quantum mechanical and classical approaches in the polarizable continuum model

We report a systematic comparison of the dispersion and repulsion contributions to the free energy of solvation determined using quantum mechanical self-consistent reaction field (QM-SCRF) and classical methods. In particular, QM-SCRF computations have been performed using the dispersion and repulsion expressions developed in the framework of the integral equation formalism of the polarizable continuum model, whereas classical methods involve both empirical pairwise potential and surface-dependent approaches. Calculations have been performed for a series of aliphatic and aromatic compounds containing prototypical functional groups in four solvents: water, octanol, chloroform, and carbon tetrachloride. The analysis is focused on the dependence of the dispersion and repulsion components on the level of theory used in QM-SCRF computations, the contribution of those terms in different solvents, and the magnitude of the coupling between electrostatic and dispersion-repulsion components. Finally, comparison is made between the dispersion-repulsion contributions obtained from QM-SCRF calculations and the results determined from classical approaches.     

An integrated approach to ultraintense laser sciences: The PLASMON-X project

In the present paper, we aim to show the interest of combining Multiwavelength Anomalous Diffraction (MAD) and Diffraction Anomalous Fine Structure (DAFS) spectroscopy, in grazing incidence, to obtain structural properties (composition, strain and atomic ordering) of semiconductor heterostructures and nanostructures. As an example we report on preliminary results obtained on a series of Ge/Si(001) nano-island samples: pyramides and domes on nominal and prepatterned surfaces. For free standing domes, it is shown that the Ge content strongly depends on the growth condition with a tendency to increase from the bottom to the top of the nano-islands. There is also some indication of atomic ordering in the upper part of the islands. For small, capped pyramids, we show that the Diffraction Anomalous Fine Structure spectroscopy is the unique non destructive method that allows to recover the actual Ge content, the in-plane and out-of-plane strain and to detect atomic ordering.     

Halfordered sets, halfordered chain structures and splittings by chains

Let be a 2-net where the set of chains is not empty and let K _s be a splitting of by a chain . Then there correspond two halforders of the set K which are related, and vice versa, if there are given two related halforders of K then there exists a splitting of by K. The questions "when is ?", "when is convex or an order?" will be studied. Moreover it will be shown that can be embedded in a halfordered chain structure in the sense of [1]. Received 23 March 2001.