Long Term Stability of Proper Rotations of the Perturbed Euler Rigid Body

We study the long term stability of the proper rotations of the perturbed Euler rigid body, in the framework of Nekhoroshev theory. For simplicity we treat here in detail only the kinetically symmetric case (the potential needs not to be symmetric), but we indicate how to extend the results to the triaxial case. We show that the proper rotations around the symmetry axis are Nekhoroshev stable: more precisely, if the initial datum is sufficiently close to a proper rotation, then for a very long time it remains such, and the tip of the unit vector parallel to the angular momentum precesses, up to a small noise, along the level curves of a regular function on the unit sphere. If the proper rotations are resonant, chaotic motions with positive Lyapunov exponents are possible, but chaos (unlike the case of ordinary motions, that is motions not close to proper rotations) is always localized, and does not affect in an essential way the motion of the angular momentum in space. Preliminary numerical results indicate that the theory is, in many aspects, optimal, although in some points it can still be improved.     

One‐Pot,High‐Yielding Synthesis of Novel Dihydrothiazolo[3,2‐a]pyrimidinones

Reaction between 6‐(un)substituted‐2‐thiouracils and E‐ethyl 4‐bromocrotonate under basic conditions at room temperature is an easy, mild, high‐yielding, and regioselective method for the preparation of 7‐(un)substituted dihydrothiazolo[3,2‐a]pyrimidinone derivatives.     

Oxidative Addition of 4-Hydroxycoumarin to Alkenes. An Expeditious Entry to 2,3-Dihydro-4H-furo-[3,2-c][1]benzopyran-4-ones1

In the presence of one-electron metal oxidants (CAN, MAH), 4-hydroxycoumarin (1) adds to alkenes to give 2,3-dihydro-4H-furo[3,2-c][1]benzopyran-4-ones.     

Comparison of Spaces of Hardy Type for the Ornstein–Uhlenbeck Operator

Denote by γ the Gauss measure on ℝ ⁿ and by ${\mathcal{L}}${\mathcal{L}} the Ornstein–Uhlenbeck operator. In this paper we introduce a Hardy space \mathfrakh¹g{{\mathfrak{h}}^1}{{\rm \gamma}} of Goldberg type and show that for each u in ℝ ∖ {0} and r > 0 the operator (rI+L)^iu(r{\mathcal{I}}+{\mathcal{L}})^{iu} is unbounded from \mathfrakh¹g{{\mathfrak{h}}^1}{{\rm \gamma}} to L ¹γ. This result is in sharp contrast both with the fact that (rI+L)^iu(r{\mathcal{I}}+{\mathcal{L}})^{iu} is bounded from H ¹γ to L ¹γ, where H ¹γ denotes the Hardy type space introduced in Mauceri and Meda (J Funct Anal 252:278–313, 2007), and with the fact that in the Euclidean case (rI-D)^iu(r{\mathcal{I}}-\Delta)^{iu} is bounded from the Goldberg space \mathfrakh¹\mathbbRⁿ{{\mathfrak{h}}^1}{{\mathbb{R}}^n} to L ¹ℝ ⁿ . We consider also the case of Riemannian manifolds M with Riemannian measure μ. We prove that, under certain geometric assumptions on M, an operator T{\mathcal{T}}, bounded on L ² μ, and with a kernel satisfying certain analytic assumptions, is bounded from H ¹ μ to L ¹ μ if and only if it is bounded from \mathfrakh¹m{{\mathfrak{h}}^1}{\mu} to L ¹ μ. Here H ¹ μ denotes the Hardy space introduced in Carbonaro et al. (Ann Sc Norm Super Pisa, 2009), and \mathfrakh¹m{{\mathfrak{h}}^1}{\mu} is defined in Section 4, and is equivalent to a space recently introduced by M. Taylor (J Geom Anal 19(1):137–190, 2009). The case of translation invariant operators on homogeneous trees is also considered.     

Template effects in the formation of [2]pseudo-rotaxanes containing diazapyrenium units

The template effects exerted by guests 14 and 15 in the ring closure reaction of 3 have been quantitatively evaluated. The rate largely increases in the presence of the two templates. The results are compared with those relative to the ring closure reaction of 1 yielding cyclobis(paraquat-p-phenylene), 2. The comparison indicates that the formation of tetracationic aromatic cycles templated by aromatic donors benefits from the use of extended pi surfaces both in the acceptor and in the donor components.     

Sequential gold-catalyzed reactions of 1-phenylprop-2-yn-1-ol with 1,3-dicarbonyl compounds

A variety of sequential gold-catalyzed reactions of 1-phenylprop-2-yn-1-ol with 1,3-dicarbonyl compounds are directed towards different outcomes by a suitable choice of the catalytic system, feature of 1,3-dicarbonyl and reaction conditions.     

Electronic structure of uracil-like nucleobases adsorbed on Si(001): uracil,thymine and 5-fluorouracil

We study the electronic properties of the Si(001):Uracil, Si(001):Thymine, andSi(001):5-Fluorouracil systems, focusing on the Si dimer-bridging configuration withadsorption governed by carbonyl groups. While the overall structural and electronicproperties are similar, with small differences due to chemical substitutions, much largereffects on the surface band dispersion and bandgap show up as a function of the molecularorientation with respect to the surface. An off-normal orientation of the molecular planesis favored, showing larger bandgap and lower total energy than the upright position. Wealso analyze the localization of gap-edge occupied and unoccupied surface states.