On the order of global branches

We give both a topological and an algebraic definition of the order of a global branch of a variety along a subvariety. Then we show that these two definitions agree. Finally we compare this order with the orders of the related local branches.

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Sunto Diamo due definizioni, una topologica e una algebrica, di ordine di un ramo globale di una varietà lungo una sottovarietà. Poi mostriamo che queste due definizioni coincidono. Infine confrontiamo questo ordine con gli ordini dei relativi rami locali.

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Partially supported by CNR funds.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Enclosing a Set of Objects by Two Minimum Area Rectangles

In this paper, we face the problem of computing an enclosing pair of axis-parallel rectangles of a set of polygonal objects in the plane, serving as a simple container. We propose anO(nα(n)log n) worst-case time algorithm, where α( ) is the inverse Ackermann's function, for finding, given a setMof points, segments and polygons defined bynvertices, a pair of axis-parallel rectangles (s, t) such thats∪tencloses all objects inMand area(s)+area(t) is minimum. The algorithm works inO(nα(n) log log n) worst-case space. Moreover, we prove an Ω(n log n) lower bound for the one-dimensional version of the problem. We also show that for the special case of enclosing a set of polygons with axis-parallel sides, our algorithm runs in optimal worst-case timeO(n log n), using worst-case spaceO(n log log n).     

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.     

Quadratic programming and theory of elastic-perfectly plastic structures

Summary For elastic perfectly plastic discretized structures acted upon by given loads and dislocations, it is shown, under holonomic constitutive laws or no local unloading hypothesis, that the formulation of the analysis problem in terms of finite (not incremental) stresses, is amenable to the Kuhn-Tucker conditions of a quadratic program. Then it is readily derived a generalized form of the principle of Haar and Kármán, together with an extremum theorem for displacements and plastic strains, which is the dual of the preceding one. As special cases of this theorems known variational principles follow, which thus turn out to be related in pairs by the duality notion as understood in programming theory. Also the statical and kinematical theorems of limit analysis are proved by means of the unitary conceptual framework supplied by quadratic programming.

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Sommario Con riferimento a strutture discretizzate idealmente elastoplastiche, soggette a dati carichi e distorsioni, si mostra che nell'ipotesi di olonomia dei legami costitutivi o di assenza di ritorni elastici, la formulazione del problema strutturale negli sforzi finiti (non incrementali) è riducibile alle condizioni di Kuhn e Tucker di un programma quadratico. Se ne deducono direttamente una forma generalizzata del principio di Haar e Kármán ed un teorema di estremo negli spostamenti e nelle deformazioni plastiche, duale al precedente. Dai due teoremi discendono come casi speciali noti principi variazionali, che cosi risultano collegati in coppie dalla nozione di dualitá propria della teoria delle ottimizzazioni.Si mostra come anche i teoremi statico e cinematico del calcolo a rottura trovano una nuova dimostrazione nell'inquadramento teorico unitario fondato sulla programmazione quadratica.

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The results presented here form part of a series of studies supported by the C.N.R. (National Research Council).     

Elastic-plastic dynamic behavior of a beam-column model

Summary An elastoplastic beam-column model with one degree of freedom subjected statically to an on-center or off-center axial compressive force is considered. Its dynamic behavior in the elastoplastic range, resulting from a transverse periodic acting force in resonance with the structure in the elastic range, is examined. The principal features are highlighted by a phase plane study.

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Sommario Si considera il modello a un grado di libertà di un'asta elastoplastica sollecitata staticamente da una forza assiale di compressione centrata o eccentrica. Si esamina il suo comportamento dinamico in campo elastoplastico per effetto di una forza trasversale periodica e in risonanza con la struttura in campo elastico, evidenziandone le principali caratteristiche attraverso lo studio nel piano delle fasi.

     

Dynamic pressure and response factors for progressive gravity waves to third order approximation

Summary This paper proposes expressions of the dynamic pressure and of the transfer functions (response factors) between the dynamic pressure amplitude and the wave amplitude and between the dynamic pressure and the vertical displacement of the wave profile, for irrotational progressive gravity waves to third order approximation (non-linear theory).Some characteristic behaviours of the dynamic pressure and of the response factors are examined and compared with those of waves to first order approximation (linear theory).

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Sommario Si ricavano le espressioni della pressione dinamica per onde irrotazionali progressive di gravità al terzo ordine di approssimazione (modello non lineare).Si individuano le funzioni di trasferimento (fattori di risposta) sia tra l'ampiezza della pressione dinamica e l'ampiezza d'onda, sia tra la pressione dinamica e lo spostamento verticale della superficie di ondulazione.Si esaminano comportamenti caratteristici della pressione dinamica e dei fattori di risposta e si confrontano tali comportamenti con quelli relativi alle onde al primo ordine di approssimazione (modello lineare).

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Changes in the morphology of interstellar ice analogues after hydrogen atom exposure

The morphology of water ice in the interstellar medium is still an open question. Although accretion of gaseous water could not be the only possible origin of the observed icy mantles covering dust grains in cold molecular clouds, it is well known that water accreted from the gas phase on surfaces kept at 10 K forms ice films that exhibit a very high porosity. It is also known that in the dark clouds H(2) formation occurs on the icy surface of dust grains and that part of the energy (4.48 eV) released when adsorbed atoms react to form H(2) is deposited in the ice. The experimental study described in the present work focuses on how relevant changes of the ice morphology result from atomic hydrogen exposure and subsequent recombination. Using the temperature-programmed desorption (TPD) technique and a method of inversion analysis of TPD spectra, we show that there is an exponential decrease in the porosity of the amorphous water ice sample following D-atom irradiation. This decrease is inversely proportional to the thickness of the ice and has a value of ?(0) = 2 × 10(16) D-atoms cm(-2) per layer of H(2)O. We also use a model which confirms that the binding sites on the porous ice are destroyed regardless of their energy depth, and that the reduction of the porosity corresponds in fact to a reduction of the effective area. This reduction appears to be compatible with the fraction of D(2) formation energy transferred to the porous ice network. Under interstellar conditions, this effect is likely to be efficient and, together with other compaction processes, provides a good argument to believe that interstellar ice is amorphous and non-porous.     

Resveratrol Analogues as Dual Inhibitors of Monoamine Oxidase B and Carbonic Anhydrase VII: A New Multi-Target Combination for Neurodegenerative Diseases?

Neurodegenerative diseases (NDs) are described as multifactorial and progressive syndromes with compromised cognitive and behavioral functions. The multi-target-directed ligand (MTDL) strategy is a promising paradigm in drug discovery, potentially leading to new opportunities to manage such complex diseases. Here, we studied the dual ability of a set of resveratrol (RSV) analogs to inhibit two important targets involved in neurodegeneration. The stilbenols 1–9 were tested as inhibitors of the human monoamine oxidases (MAOs) and carbonic anhydrases (CAs). The studied compounds displayed moderate to excellent in vitro enzyme inhibitory activity against both enzymes at micromolar/nanomolar concentrations. Among them, the best compound 4 displayed potent and selective inhibition against the MAO-B isoform (IC₅₀ MAO-A 0.43 µM vs. IC₅₀ MAO-B 0.01 µM) with respect to the parent compound resveratrol (IC₅₀ MAO-A 13.5 µM vs. IC₅₀ MAO-B > 100 µM). It also demonstrated a selective inhibition activity against hCA VII (K_I 0.7 µM vs. K_I 4.3 µM for RSV). To evaluate the plausible binding mode of 1–9 within the two enzymes, molecular docking and dynamics studies were performed, revealing specific and significant interactions in the active sites of both targets. The new compounds are of pharmacological interest in view of their considerably reduced toxicity previously observed, their physicochemical and pharmacokinetic profiles, and their dual inhibitory ability. Compound 4 is noteworthy as a promising lead in the development of MAO and CA inhibitors with therapeutic potential in neuroprotection.