Spherical space forms,CR mappings,and proper maps between balls

We determine precisely for which spherical space forms there are nontrivial smooth CR mappings to spheres. Equivalently we determine for which fixed point free finite unitary groups ? there exists a ?-invariant proper holomorphic rational map between balls. The answer is that the group must be cyclic and essentially only two classes of representations can occur. For these there are invariant polynomial examples.     

Finite homogeneous deformations of symmetrically loaded compressible membranes

The equilibrium problem of nonlinear, isotropic and hyperelastic square membranes, stretched by a double symmetric system of dead loads, is investigated. Depending on the form of the stored energy function, the problem considered may admit asymmetric solutions in addition to the expected symmetric solutions. For compressible materials, the mathematical condition allowing the computation of these asymmetric solutions is given. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. Results and basic relations obtained for general isotropic materials are then specialized for a compressible Mooney–Rivlin material and a broad numerical analysis is performed. The qualitatively more interesting branches of asymmetric equilibrium are shown and the influence of the material parameters is discussed. Finally, using the energy criterion, some stability considerations are made.     

The relativistic Riemann invariants and the propagation of initial data surfaces

A method is described by which the relativistic Riemann invariants can be found for a fluid with an arbitrary equation of state, undergoing dissipation and moving in a general metric. Specific formulae are derived for a spherically symmetric system. Limiting cases defined by relativistic and non-relativistic gases, both warm, cold, fast and slow are examined. We prove that the invariants do exist, and a necessary and sufficient condition for their determination is the solution of a differential equation with the structure of an exterior one form of two components. The common parameter of these components is the characteristic space-time direction which is also derived in the process of determining the invariants. The characteristic surfaces, being the surfaces over which initial data is carried, all coalesce to the forward light cone in the extreme relativistic limit. Relativistic fluids emanating from receding sources appear to increase their internal kinetic energy as they decelerate.A non-linear distance-velocity relation for these waves is evident in the differential equations which are found. Their full meaning remains to be explored.     

A System of Differential-Operator Equations of Different Orders in Hilbert Spaces

We consider an abstract Cauchy problem for a system of nonhomogeneous abstract differential equations in Hilbert spaces. The “main” equation is of the second order and “boundary” equations are of the first order. Existence of a solution is proved. Application to mixed (initial boundary-value) problems for one-dimensional second order hyperbolic equations and for fourth order PDEs with the time derivative in boundary conditions has been shown. The first author was partially supported by 60% funds of the University of Bologna and G.N.A.M.P.A. of INdAM; the second author was supported by the Israel Ministry of Absorption.     

Mixed carbonyl coupling induced by aqueous titanium trichloride. Some comments on the mechanism.

Aqueous titanium trichloride promotes reductive dimerization of benzoylcyanide in acetic acid and mixed pinacol reaction in acetone medium. A mechanism is proposed to account for this.     

A tight-binding model for the optical properties of Au55-clusters

We have computed the electronic structure and the imaginary part of the dielectric function of the Au55 cluster using a tight-binding model which takes into account size and boundary effects. Besides the Drude behavior, we obtain anomalous absorption peaks in the infrared region due to the breakdown of the selection rule Δk=0. Taking into account surface coating effects, the onset of the interband absorption above 2.5 eV results to be red shifted, in agreement with the experimental data. As a consequence, we obtain a dramatic increase of the width of the plasmonic absorption peak, which accounts for the experimental optical spectra observed by Kreibig.     

Coerciveness Estimate for Ventcel Boundary Value Problem for a Differential Equation

We give some simple algebraic conditions on the coefficients of a boundary value problem for a differential equations of Ventcel type, depending on a spectral parameter, which guarantee the existence, uniqueness of a solution and coerciveness estimate, for a spectral parameter lying in some sector.     

On the modelling of dissipative solids

Summary The estimate of material parameters, related to models of dissipative solids, is investigated. In particular, upon regarding the solid as viscoelastic, it is shown how the stress functional can be determined by having recourse to experimental curves which account for creep tests.

---

Sommario Si considera il problema della valutazione dei parametri costitutivi per un solido dissipativo. Riguardando il solido come viscoelastico, si mostra che il funzionale per lo stress può essere determinato utilizzando curve sperimentali che descrivono prove di creep.