A convenient preparation of 3-isopropyl-1-methylcyclopentylmethanol and 1-isopropyl-3-methylcyclopentylmethanol via Favorskii rearrangement

The Favorskii rearrangement of suitable α-chloro derivatives of commercially available (+)- and (−)-carvone, and (−)-menthone served efficiently to prepare the title compounds featuring delicious fruity, floral olfactory notes.     

Wave features of a hodograph-like transformation for quasilinear hyperbolic systems

We study the properties of a variables transformation for a 2×2 quasilinear hyperbolic nonhomogeneous system of first order, related to wave propagation. The considered variables transformation transforms characteristic curves of the original system, into characteristic curves of the transformed system. We make use of this property to study the propagation of weak discontinuities (acceleration waves) compatible with the quasilinear system (1.1). Finally a special class of rate-type media is considered and asymptotic solutions are investigated.

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Sommario Si studiano le proprietà di una trasformazione di variabili per un sistema quasilineare iperbolico del primo ordine non omogeneo. La trasformazione considerata trasforma curve caratteristiche del sistema originale in curve caratteristiche del sistema trasformato. Utilizzando queste proprietà si studia la propagazione delle onde di discontinuità (onde di accelerazione) compatibile con il sistema quasilineare iperbolico considerato e si cercano soluzioni asintotiche.

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This work was supported by the C.N.R. through the G.N.F.M. and partially under contract No. 88. 01855.01.     

The Dirichlet problem for second order elliptic equations with coefficients in the Stummel class in unbounded domains

In this note we prowe existence and unicity of solution of a Dirichlet problem for second order elliptic operator in the divergence form, with the coefficients of the lower order terms belonging to a variant of the Stummel-Kato class, in an unbounded domain, extending the works [6] and [2].

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Sunto In questa nota proviamo un Teorema di esistenza e unicità per la soluzione di un problema di Dirichlet relativo ad un operatore ellittico del secondo ordine in forma di divergenza, con i coefficienti dei termini di ordine inferiore appartenenti ad una variante dello spazio di Stummel-Kato, in un dominio non limitato, estendendo i lavori [6] e [2].

     

Similarity analysis and exact solutions for a general discrete two-velocity model of Boltzmann equation

Summary This paper concerns with the similarity analysis for a general discrete two-velocity model of the Boltzmann equation introduced by Illner [12]. We find the general groups of invariance and we get some exact solutions, recovering general results which contain either solutions extensively described in the literature or undiscovered ones.

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Sommario In questa nota si applica l'analisi dei gruppi infinitesimi di trasformazione ad un modello generale discreto a due velocità dell'equazione di Boltzmann introdotto da Illner [12]. Si trovano i più generali gruppi di invarianza e si ottengono alcune soluzioni esatte, ritrovando risultati generali che contengono sia soluzioni ampiamente descritte in letteratura che nuove soluzioni.

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Work supported by the C.N.R. through the G.N.F.M.     

Application of 2d-nmr spectroscopy in the structural determination of gracilin b,a bis-nor-diterpene from the sponge spongionella gracilis1.

The structure of gracilin B, an unusual metabolite based on a bis-nor-diterpene skeleton isolated from the sponge $\text{Spongionella gracilis}$, has been determined mainly by using two dimensional heteronuclear ¹³C -¹H shift correlation spectroscopies.     

Copolymerisation of Pt-carbonyl clusters with Lewis acids: synthesis and crystal structure of the molecular [Cd2Cl4[Pt9(CO)18]2-]infinity 1-D polymer

Reaction of [NBu4]2[Pt9(CO)18] with the soft Lewis acid CdCl2 gives the [Pt9(CO)18(micro3-CdCl2)2]2- adduct, which self-assembles upon crystallization into a 1-D [[Pt9(CO)18(micro3-CdCl2)2]2-]infinity polymer via the formation of chloride bridges.     

Turing vegetation patterns in a generalized hyperbolic Klausmeier model

The formation of Turing vegetation patterns in flat arid environments is investigated in the framework of a generalized version of the hyperbolic Klausmeier model. The extensions here considered involve, on the one hand, the strength of the rate at which rainfall water enters into the soil and, on the other hand, the functional dependence of the inertial times on vegetation biomass and soil water. The study aims at elucidating how the inclusion of these generalized quantities affects the onset of bifurcation of supercritical Turing patterns as well as the transient dynamics observed from an uniformly vegetated state towards a patterned state. To achieve these goals, linear and multiple-scales weakly nonlinear stability analysis are addressed, this latter being inspected in both large and small spatial domains. Analytical results are then corroborated by numerical simulations, which also serve to describe more deeply the spatio-temporal evolution of the emerging patterns as well as to characterize the different timescales involved in vegetation dynamics.     

Wave features of a hyperbolic prey–predator model

A hyperbolic predator–prey model is proposed within the context of extended thermodynamics. The nature of the steady state solutions for the uniform and non‐uniform perturbations are analyzed. The existence of smooth traveling wave‐like solutions, related to the invasion of the predator population into a prey‐only state is discussed. Validation of the model in point is also accomplished by searching for numerical solutions of the system, which also points out limit cycles in the populations. Copyright © 2010 John Wiley & Sons, Ltd.     

Clustering of financial time series

This paper addresses the topic of classifying financial time series in a fuzzy framework proposing two fuzzy clustering models both based on GARCH models. In general clustering of financial time series, due to their peculiar features, needs the definition of suitable distance measures. At this aim, the first fuzzy clustering model exploits the autoregressive representation of GARCH models and employs, in the framework of a partitioning around medoids algorithm, the classical autoregressive metric. The second fuzzy clustering model, also based on partitioning around medoids algorithm, uses the Caiado distance, a Mahalanobis-like distance, based on estimated GARCH parameters and covariances that takes into account the information about the volatility structure of time series. In order to illustrate the merits of the proposed fuzzy approaches an application to the problem of classifying 29 time series of Euro exchange rates against international currencies is presented and discussed, also comparing the fuzzy models with their crisp version.