On the singular PDE's geometry and boundary value problems

A geometric formulation of singular partial differential equations (PDEs) is considered. Surgery techniques and integral bordism groups are utilized, following previous works by Prástaro on PDEs, in order to build global solutions crossing also singular points and to study their stability properties.     

Electronic properties of (3/2 × 3/2)-Na/Cu(1 1 1)

High-resolution electron energy loss spectroscopy was used to study the electronic properties of (3/2 × 3/2)-Na/Cu(1 1 1) at room temperature. Loss spectra showed two-well distinct losses at 114 and 180 meV assigned to not dispersive charge density waves. Mechanisms to explain their existence are proposed. Moreover, the expected 2D plasmon of the Na quantum well state was not observed. The strong influence of the underlying Cu substrate may be responsible for the absence of such mode.     

Twisted Spectral Triple for the Standard Model and Spontaneous Breaking of the Grand Symmetry

Grand symmetry models in noncommutative geometry, characterized by a non-trivial action of functions on spinors, have been introduced to generate minimally (i.e. without adding new fermions) and in agreement with the first order condition an extra scalar field beyond the standard model, which both stabilizes the electroweak vacuum and makes the computation of the mass of the Higgs compatible with its experimental value. In this paper, we use a twist in the sense of Connes-Moscovici to cure a technical problem due to the non-trivial action on spinors, that is the appearance together with the extra scalar field of unbounded vectorial terms. The twist makes these terms bounded and - thanks to a twisted version of the first-order condition that we introduce here - also permits to understand the breaking to the standard model as a dynamical process induced by the spectral action, as conjectured in [24]. This is a spontaneous breaking from a pre-geometric Pati-Salam model to the almost-commutativegeometryofthestandardmodel,withtwoHiggs-likefields: scalar and vector.     

Coriacenins: A New Class of Long Alkyl Chain Amino Alcohols from the Mediterranean Sponge Clathrina coriacea

The Mediterranean sponge Clathrina coriacea contains a series of long chain amino alcohols, named coriacenins (2-6), belonging to a new class of alkaloids. The structures of the novel compounds were elucidated by studying, with a combination of spectral and chemical methods, their peracetyl derivatives (2a-6a). Coriacenins are characterized by a bis(1,3-diamino-2-propanol) moiety and a linear alkyl chain varying both by length and by degree of unsaturation. The biosynthetic pathway leading to coriacenins seems to be unprecedented. It should, however, occur through condensation of an acetogenin with an uncommon amino acid.     

Intramolecular cyclisation of isosorbide by dimethylcarbonate chemistry

In this work the synthesis of a tricyclic isosorbide derivative in moderate yield directly from the dicarboxymethyl isosorbide in a continuous-flow apparatus is reported. The tricyclic structure has been isolated as pure and fully characterized. This product confirms the potentiality of dimethylcarbonate (DMC) as dehydrating agent also for complicated structure and opens up further investigation and application of DMC chemistry on renewable starting materials.     

On plastic dynamics of discrete structural models

Summary This paper discusses the dynamic loading of rigid-perfectly plastic structures by adopting a structural model discretized with constant stress finite elements. This assumption together with the hypothesis of small displacements and of a piecewise linear yield surface leads to the formulation of a problem in linear inequalities, which is, implicitly, time discretized. It is shown how the non linearity of the associated plastic flow laws leads to an equivalent extremal formulation. A numerical algorithm for solving the problem is directly derived from the mechanical statements. Numerical examples illustrate this approach. In the appendix an approximate technique is developed, which takes into account the influence of the strain-hardening and the strain rate sensitivity of material.

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Sommario Il problema del caricamento dinamico delle strutture rigido-plastiche viene affrontato attraverso un modello discretizzato per elementi finiti a stato di sollecitazione costante. Tale assunzione insieme alle ipotesi di superficie di plasticizzazione lineare a tratti e di piccoli spostamenti, conduce alla formulazione di un problema retto da diseguaglianze lineari che si presenta discretizzato, implicitamente, nel tempo. Si mostra che la non linearità delle leggi del flusso plastico associato conduce ad una equivalente formulazione di estremo.È esposto un algoritmo risolvente affatto aderente alla formulazione meccanica. Alcuni esempi illustrano il procedimento. Una proposta di adattamento al caso di materiali incrudenti e sensibili alle velocità di deformazione è presentata in appendice.

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Research supported by the National Research Council (C.N.R. - P.A.d.I.S.) of Italy.     

A composite Bayesian hierarchical model of compositional data with zeros

We present an effective approach for modelling compositional data with large concentrations of zeros and several levels of variation, applied to a database of elemental compositions of forensic glass of various use types. The procedure consists of the following: (i) partitioning the data set in subsets characterised by the same pattern of presence/absence of chemical elements and (ii) fitting a Bayesian hierarchical model to the transformed compositions in each data subset. We derive expressions for the posterior predictive probability that newly observed fragments of glass are of a certain use type and for computing the evidential value of glass fragments relating to two competing propositions about their source. The model is assessed using cross‐validation, and it performs well in both the classification and evidence evaluation tasks. Copyright © 2014 John Wiley & Sons, Ltd.