Abnormal ring closure and oxidation in situ of 2-hydroxy-5-nitrobenzaldehyde in the hantzsch synthesis

The Hantzsch condensation of 2-hydroxy-5-nitrobenzaldehyde, ethyl acetoacetate and ammonia gave the hitherto unknown 2-methyl-3-ethoxycarbonyl-4-ethoxycarbonylmethyl-6-(2-hydroxy-5-nitrophenyl)-pyridine via an unusual condensation and oxidation in situ.     

OnL 1-vorticity for 2-D incompressible flow

We prove the existence of a classical weak solution for the 2-D incompressible Euler equations with initial vorticity ω₀=ω ₀ ^′ + ω ₀ ^″ , where ω ₀ ^′ is inL ¹(R ²)⌢H ⁻¹(R ²), compactly supported, and ω ₀ ^″ is a compactly supported positive Radon measure inH ⁻¹(R ²).     

Teoremi di Liouville e stime a priori per equazioni ellittiche semilineari

Conferenza tenuta il giorno 30 Marzo 1998     

Optimal graphs for chromatic polynomials

Let F(n,e) be the collection of all simple graphs with n vertices and e edges, and for G∈F(n,e) let P(G;λ) be the chromatic polynomial of G. A graph G∈F(n,e) is said to be optimal if another graph H∈F(n,e) does not exist with P(H;λ)?P(G;λ) for all λ, with strict inequality holding for some λ. In this paper we derive necessary conditions for bipartite graphs to be optimal, and show that, contrarily to the case of lower bounds, one can find values of n and e for which optimal graphs are not unique. We also derive necessary conditions for bipartite graphs to have the greatest number of cycles of length 4.     

On the toughening mechanisms of MoSi<Subscript>2</Subscript> reinforced Si<Subscript>3</Subscript>N<Subscript>4</Subscript> ceramics

The toughness increment occurring in Si₃N₄-based composites due to the addition of MoSi₂ particles was compared to the predictions of theoretical models based on the combination of residual stresses and crack deflection toughening mechanisms. A direct application of theoretical models led to a substantial discrepancy between predicted and observed values. For this reason, the basic parameters of the theoretical models were experimentally evaluated. The residual stresses were assessed by measuring the strain in the reinforcing particles by X-ray diffraction. Moreover, the MoSi₂ interparticle distance was calculated by image analysis and the crack paths were analyzed in order to check the actual extent of crack deflection. The overall toughness increase recalculated as the sum of the newly estimated values of residual stresses and crack deflection contributions, was shown to be in good agreement with the experimental results. PACS 81.05.Je; 81.40.Np     

Penalty methods for minimal surfaces with obstacles

Summary In this paper, we discuss an approach to the obstacle problem for minimal boundaries via penalty techniques. After investigating some classes of penalized problems, a general method is introduced, based on the minimization of a suitable functional containing an extra term related to the mean curvature of the given obstacle.     

A quantum transition from localized to extended states in a classically chaotic system

We study the quantum dynamics of a particle in a one dimensional triangular well under a monochromatic perturbation. Though the classical dynamics is described by the Standard Map, the quantum motion is not always localized. At a certain threshold field intensity, a transition takes place, from a, regime of power-localized quasi-energy eigenstates to one of extended states.     

Helicity and Kirillov forms in incompressible Euler flow

The Hamiltonian structure induced by the Kirillov symplectic form on coadjoint orbits of incompressible inviscid flow is studied. Helicity is shown to be associated to a degeneracy of the corresponding Kirillov-Poisson bracket.