Algebraic semantics and model completeness for Intuitionistic Public Announcement Logic

In the present paper, we start studying epistemic updates using the standard toolkit of duality theory. We focus on public announcements, which are the simplest epistemic actions, and hence on Public Announcement Logic (PAL) without the common knowledge operator. As is well known, the epistemic action of publicly announcing a given proposition is semantically represented as a transformation of the model encoding the current epistemic setup of the given agents; the given current model being replaced with its submodel relativized to the announced proposition. We dually characterize the associated submodel-injection map as a certain pseudo-quotient map between the complex algebras respectively associated with the given model and with its relativized submodel. As is well known, these complex algebras are complete atomic BAOs (Boolean algebras with operators). The dual characterization we provide naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras (HAOs). Thanks to this construction, the benefits and the wider scope of applications given by a point-free, intuitionistic theory of epistemic updates are made available. As an application of this dual characterization, we axiomatize the intuitionistic analogue of PAL, which we refer to as IPAL, prove soundness and completeness of IPAL w.r.t. both algebraic and relational models, and show that the well known Muddy Children Puzzle can be formalized in IPAL.     

On the Dynamics of Space Debris: 1:1 and 2:1 Resonances

We study the dynamics of the space debris in the 1:1 and 2:1 resonances, where geosynchronous and GPS satellites are located. By using Hamiltonian formalism, we consider a model including the geopotential contribution for which we compute the secular and resonant expansions of the Hamiltonian. Within such model we are able to detect the equilibria and to study the main features of the resonances in a very effective way. In particular, we analyze the regular and chaotic behavior of the 1:1 and 2:1 resonant regions by analytical methods and by computing the Fast Lyapunov Indicators, which provide a cartography of the resonances. This approach allows us to detect easily the location of the equilibria, the amplitudes of the libration islands and the main dynamical stability features of the resonances, thus providing an overview of the 1:1 and 2:1 resonant domains under the effect of Earth’s oblateness. The results are validated by a comparison with a model developed in Cartesian coordinates, including the geopotential, the gravitational attraction of Sun and Moon and the solar radiation pressure.     

Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties

We define Enriques varieties as a higher dimensional generalization of Enriques surfaces and construct examples by using fixed point free automorphisms on generalized Kummer varieties. We also classify all automorphisms of generalized Kummer varieties that come from an automorphism of the underlying abelian surface.     

Addition of Me3SiCN to trifluoromethyl derivates of N‐(pyridylmethylidene) anilines catalyzed by Lewis acids

A series of novel Shiff bases (1a–h) was synthesized by condensation of pyridinecarboxaldehydes (1–4) with 3‐ and 4‐trifluoromethylanilines (5, 6) in the presence of molecular sieves (4 Å). It was found that AlCl₃ and AlBr₃ catalyzed the addition of Me₃SiCN to the C?N bond of the imines obtained, whereas the other Lewis acids studied (YCl₃, LaCl₃, ZnI₂) were not active. The reactivity of the imines in the title reaction, on the whole, correlated with their basicity. Besides the addition giving the expected α‐amino nitriles (2a,b,d–f,h), an unusual reaction leading to unsaturated nitriles (3a–h) was observed. The structures of saturated and unsaturated products 2d and 3c were determined by X‐ray diffraction. Copyright © 2001 John Wiley & Sons, Ltd.     

On certain linear spaces of nilpotent matrices

In this note we describe explicitly those linear spaces of nilpotent matrices, which are stable under conjugation by diagonal matrices. As an application, we deduce a generalized version of a result of Valcher and Fornasini on pairs of nonnegative nilpotent matrices.     

Para‐hydrogen induced polarization of Si‐29 NMR resonances as a potentially useful tool for analytical applications

Para‐hydrogen–induced polarization effects have been observed in the ²⁹Si NMR spectra of trimethylsilyl para‐hydrogenated molecules. The high signal enhancements and the long T₁ values observed for the ²⁹Si hyperpolarized resonances point toward the possibility of using ²⁹Si for hyperpolarization applications. A method for the discrimination of multiple compounds and/or complex mixtures of hydroxylic compounds (such as steroids), consisting of the silylization of alcoholic functionalities with an unsaturated silylalkyl moiety and subsequent reaction with para‐H₂, is proposed. Copyright © 2012 John Wiley & Sons, Ltd.     

Sensitizing effect of bio-based chemicals from urban wastes on the photodegradation of azo-dyes

To promote bio-based products for the industry, six bio-organic substances (cHALi) isolated from yard trimmings (green) and food (humid) urban residues aged under aerobic digestion for 0–60 days were investigated for their potential to perform as sensitizers for azo-dyes photodegradation. Ethylorange (EO) was used as probe molecule at 5 mg L^?1 starting concentration and irradiated in a closed Pyrex^® cell with a Xenon (1500 W) lamp and a cut-off filter for wavelengths below 340 nm or in a cylindrical photochemical reactor equipped with a 125 W medium pressure Hg lamp. The cHALi/EO ratio in the starting EO solution varied in the 0–200 (w/w) range. The % dye abatement was found a function of the irradiation time, of the type of cHALi substance and of the cHALi/EO ratio. The best results were achieved with cHALi isolated after 7 days biomass aerobic digestion. Total dye abatement was achieved within relatively short few hours. A progressive dye mineralization was observed under the same experimental conditions. On the contrary no significant degradation was evident for the cHALi substances within the same irradiation time. Several hydroxylated azo compounds were identified as likely responsible of residual color after total EO abatement. The results, coupled to the previously reported good performance of the same cHALi substances as auxiliaries for textile dyeing, augur well for the development of both efficient and environmentally friendly textile dyeing processes.     

Irradiation of Amelanotic Melanoma Cells with 532 nm High Peak Power Pulsed Laser Radiation in the Presence of the Photothermal Sensitizer Cu(II)-Hematoporphyrin: A New Approach to Cell Photoinactivation

Cu(II)-hematoporphyrin (CuHp) was efficiently accumulated by B78H1 amelanotic melanoma cells upon incubation with porphyrin concentrations up to 52 microM. When the cells incubated for 18 h with 13 microM CuHp were irradiated with 532 nm light from a Q-switched Nd: YAG laser operated in a pulsed mode (10 ns pulses, 10 Hz) a significant decrease in cell survival was observed. The cell photoinactivation was not the consequence of a photodynamic process, as CuHp gave no detectable triplet signal upon laser flash photolysis excitation and no decrease in cell survival was observed upon continuous wave irradiation. Thus, it is likely that CuHp sensitization takes place by photothermal pathways. The efficiency of the photoprocess was modulated by different parameters; thus, while varying the amount of added CuHp in the 3.25-26 microM range had little effect, pulse energies larger than 50 mJ and irradiation times of at least 120 s were necessary to induce a cell inactivation of about 50%. The porphyrin-cell incubation time prior to irradiation had a major influence on cell survival, suggesting that the nature of the CuHp microenvironment can control the efficiency of photothermal sensitization.