Laguerre geometry of surfaces with plane lines of curvature

We study surfaces with plane lines of curvature in the framework of Laguerre geometry and provide explicit representation formulae for these surfaces in terms of a potential function. As an application, we explicitly integrate allL- minimal surfaces with plane curvature lines. Partially supported by MURST 40.     

A representation formula of sum rules for zeros of polynomials

A representation formula in terms of Lucas polynomials of the second kind in several variables (see formula (4.3)), for the sum rulesJ _s ⁽ⁱ⁾ introduced by K.M. Case [1] and studied by J.S. Dehesa et al. [2]–[3] in order to obtain informations about the zeros’ distribution of eigenfunctions of a class of ordinary polynomial differential operator, is derived. Lavoro eseguito nell’ambito del G.N.I.M. del C.N.R.     

Graded Cluster Expansion for Lattice Systems

In this paper we develop a general theory which provides a unified treatment of two apparently different problems. The weak Gibbs property of measures arising from the application of Renormalization Group maps and the mixing properties of disordered lattice systems in the Griffiths’ phase. We suppose that the system satisfies a mixing condition in a subset of the lattice whose complement is sparse enough namely, large regions are widely separated. We then show how it is possible to construct a convergent multi-scale cluster expansion.The authors acknowledge the support of Cofinanziamento MIUR.     

A generic basis for some simple light-operated mechanical molecular machines

A novel type of mechanical switch is described in which light-induced translation of a macrocycle in a [2]rotaxane quenches anthracene fluorescence. Features of the system include the remarkable 200:1 difference in fluorescence intensity between the two positional states of the molecule ( approximately 85:1 between one isomer and the photostationary state). In principle the same concept could be used for mechanically switching virtually any property that can be influenced by functional group proximity effects.     

Shuttling through reversible covalent chemistry

The first stimuli-responsive molecular shuttle that functions through reversible C-C bond formation is reported.     

A new approach to the statistical treatment of 2D-maps in proteomics using fuzzy logic

A new approach to the statistical treatment of 2D-maps has been developed. This method is based on the use of fuzzy logic and allows to take into consideration the typical low reproducibility of 2D-maps. In this approach the signal corresponding to the presence of proteins on the 2D-maps is substituted with probability functions, centred on the signal itself. The standard deviation of the bidimensional gaussian probability function employed to blur the signal allows to assign different uncertainties to the two electrophoretic dimensions. The effect of changing the standard deviation and the digitalisation resolution are investigated.     

Solving Nonconvex Planar Location Problems by Finite Dominating Sets

It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by finding a finite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location.In this paper it is first established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems.Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal objective value. For the approximation problem two different approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed - to polynomial approximation algorithms with accuracy for solving the general model considered in this paper.     

Identically conserved currents and their charges

We examine, at a classical level, the features that distinguish dynamically conserved currents from identically conserved ones. Then we prove that, in four spacetime dimensions, the quantum charges corresponding to identically conserved currents always annihilate the vacuum state. We illustrate our discussion with several examples.