Cantor families of periodic solutions for wave equations via a variational principle

We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation—variational in nature—defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to “small divisors” phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical “Arnold non-degeneracy condition” of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities.     

Pedestrian flows and non‐classical shocks

We present a model for the flow of pedestrians that describes features typical of this flow, such as the fall due to panic in the outflow of people through a door. The mathematical techniques essentially depend on the use of non‐classical shocks in scalar conservation laws. Copyright © 2005 John Wiley & Sons, Ltd.     

Reaction diastereoselectivity of chiral aminoalcohols/[Co(II)NO3]+ complexes in evaporating ESI nanodroplets: new insights from a joint experimental and computational investigation

The nature of the ionic species, formed by electrospray ionization (ESI) of Co(NO₃)₂/CH₃OH solutions with a pair of aminoalcohols W and Y, has been investigated by mass spectrometric and computational methods. Collision induced dissociation (CID) of ions, formally corresponding to the [WYCoNO₃]⁺ structures, yields fragmentation patterns which reflect not only the expected [WYCoNO₃]⁺ connectivity but also that of other isomeric structures. Formation of these latter species is observed only in the presence of a tertiary aminoalcohol, like N‐methylpseudoephedrine. The CID patterns are found to be strongly dependent on the chemical form (whether the free aminoalcohol or its hydrochloride), the configuration, and the relative concentration of the W and Y aminoalcohols. This variability parallels the results of classical MD (molecular dynamics) simulations of the [WYCoNO₃]⁺ adducts which show a drastic alteration of the mechanical–dynamical features of the adducts by simply changing the charge state of W and/or Y, their absolute configuration, or by removing the solvent. The present experimental and computational study confirms the observation of fast stereoselective reactions in ESI nanodroplets before their evaporation and warns against any automatic correlation between the ESI spectrum of an analyte and its structure in solution. Copyright © 2009 John Wiley & Sons, Ltd.     

Reactivity of lithium 2,3-dihydro-1-benzothiophene-1-oxide toward aldehydes and imines and DFT calculations

The sulfinyl carbanion derived from 2,3-dihydro-1-benzothiophene-1-oxide and its lithium salt has been investigated by DFT calculations. The lithium carbanion was treated with aldehydes and imines to give chiral hydroxy and amino derivatives, with high stereoselectivity at the carbon α to the sulfoxide group (trans diastereoisomers), but with low diastereoselectivity at the hydroxyl or amine group. DFT calculations were used to rationalize the different stereochemical behavior of cyclic and acyclic lithiated sulfoxides in the reaction with aldehydes and azomethines.     

N-Substituted and N-unsubstituted 1,3-Oxazolium-5-olates cycloaddition reactions with 3-substituted coumarins

The 1,3-dipolar cycloaddition reaction of unsymmetrically N-substituted and N-unsubstituted 1,3-oxazolium-5-olates with selected 3-substituted coumarins has been examined. Various types of pyrrole derivatives are isolated and their formation seems to be a function of the regio- and diastereochemistry of the initial cycloaddition step.     

Equivalent dissipation postulates in classical plasticity

Summary In classical plasticity dissipation postulates on cycles, such as those proposed by Drucker, Martin e Il'yushin, rule the evolution of elastic-plastic deformation processes. In this paper, within the framework of the infinitesimal theory of isotropic materials with elastic range of [7], each one of those three postulates is given an equivalent local formulation; moreover, they are shown to be all equivalent.

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Sommario In plasticitá classica l'evoluzione dei processi elasto-plastici é regolata da postulati di dissipazione su cicli quali quelli proposti da Drucker, Martin e Il'yushin. In questo lavoro, nell'ambito della teoria infinitesima dei materiali isotropi con dominio elastico proposta in [7], si fornisce una formulazione locale equivalent per ciascuno di quei tre postulati e si mostra che essi sono tutti tra loro equivalenti.

     

Real-time algorithm,based on two extra sensors,for monitoring platform’s orientation of underactuated parallel wrists

The direct position analysis of parallel manipulators (PMs) brings to determine a finite number of platform poses compatible with an assigned set of actuated-joint variables’ values. Therefore, when, during functioning, the need to check the actual platform pose arises, the sensors usually located on the actuators are not sufficient and the additional pieces of information coming from ad-hoc-devised extra sensors are necessary. Here, for the first time, the actual implementation of extra sensors in underactuated parallel wrists (PWs) which contain a nonholonomic constraint is addressed. Differently from “ordinary” (i.e., non-underactuated) PWs, these PWs requires a continuous monitoring of the actual platform orientation to compensate the possible sliding in the nonholonomic constraint. Thus, in this case, the algorithms that interpret the pieces of information coming from the sensors must work in real time and must be integrated in the control software that manages the motion of the machine. All these special requirements are satisfied by the proposed algorithm. Moreover, the proposed hardware can also be implemented in some ordinary PWs with a cheap add-on kit.     

KAM for Reversible Derivative Wave Equations

We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.