Sulle soluzioni non analitiche dell'equazione funzionalef(x 2)-[f(x)]2=kx e su quelle analitiche dell'equazionef(x α)=λ[f(x)]b

Annali di Matematica Pura ed Applicata (1923 -) -     

Sopra alcune limitazioni per la sollecitazione elastica e sopra la dimostrazione del principio del De Saint Venant

Sunto L'A, studia in questa Memoria la distribuzione delle tensioni interne in un solido elastico convesso quando gli spostamenti, dati in superficie, sono diversi da zero solo in una piccola zona. Nei campi a due dimensioni il risultato è esteso al caso in cui sul contorno siano date le forze; si giunge così ad una dimostrazione del principio del De Saint Venant.     

Effective mechanism for social recommendation of news

Recommender systems represent an important tool for news distribution on the Internet. In this work we modify a recently proposed social recommendation model in order to deal with no explicit ratings of users on news. The model consists of a network of users which continually adapts in order to achieve an efficient news traffic. To optimize the network’s topology we propose different stochastic algorithms that are scalable with respect to the network’s size. Agent-based simulations reveal the features and the performance of these algorithms. To overcome the resultant drawbacks of each method we introduce two improved algorithms and show that they can optimize the network’s topology almost as fast and effectively as other not-scalable methods that make use of much more information.     

A class of piecewise interpolating functions based on barycentric coordinates

Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolant function by means of polynomial pieces and ensure that some regularity conditions are guaranteed at the break-points. In this work, we propose a novel class of piecewise interpolating functions whose expression depends on the barycentric coordinates and a suitable weight function. The underlying idea is to specialize to the 1D settings some aspects of techniques widely used in multi-dimensional interpolation, namely Shepard’s, barycentric and triangle-based blending methods. We show the properties of convergence for the interpolating functions and discuss how, in some cases, the properties of regularity that characterize the weight function are reflected on the interpolant function. Numerical experiments, applied to some case studies and real scenarios, show the benefit of our method compared to other interpolant models.     

A general framework for the construction of piecewise-polynomial local interpolants of minimum degree

In this paper we consider the problem of designing piecewise polynomial local interpolants of non-uniformly spaced data. We provide a constructive approach that, for any assigned degree of polynomial reproduction, continuity order, and support width, allows for generating the fundamental spline functions of minimum degree having the desired properties. Finally, the proposed construction is extended to handle open sets of data and to the case of multiple knots.     

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.