Links in a thickened surface

For a given two-dimensional surface μ, we studi invariants for oriented links in μ×[0,1] which generalize the two-variable HOMFLY polynomials when μ is the 2-disk. These invariants are connected to multiparameter quantum groups whose special properties are discussed. Si studiano gli invarianti dei nodi in spazi del tipo μ×[0,1], dove μ è una superficie. Questi invarianti generalizzano gli invarianti di HOMFLY.

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(Conferenza tenuta dal Prof. P. Cotta-Ramusino il 16 maggio 1991)     

The hydrogen molecule in an arbitrarily oriented magnetic field

Summary The modifications induced by a magnetic field of arbitrary direction and intermediate strength (i.e not larger than 2.35·10⁵ tesla, the ?atomic tesla?) on the lowest singlet and triplet energy states of the hydrogen molecule are studied. Using a linear combination of products of field-modified atomic orbitals, it is found that increasing the field strength the depth of the singlet energy well increases and the equilibrium internuclear distance decreases, yielding more rigid and localized nuclear vibrations. For sufficiently strong fields perpendicular to the internuclear axis, the triplet state exhibits a bonding behaviour. An explanation of the above results is given in terms of the field-modified electronic-charge distributions in the internuclear region. Based on the thesis submitted by S. Basile to the University of Palermo for graduation in Physics.     

2D Ising Model with Layers of Quenched Spins

The model considered is a d=2 disordered Ising system on a square lattice with nearest neighbor interaction. The disorder is induced by layers (rows) of spins, randomly located, which are frozen in an antiferromagnetic order. It is assumed that all the vertical couplings take the same positive value J _v, while all the horizontal couplings take the same positive value J _h. The model can be exactly solved and the free energy is given as a simple explicit expression. The zero-temperature entropy can be positive because of the frustration due to the competition between antiferromagnetic alignment induced by the quenched layers and ferromagnetic alignment due to the positive couplings. No phase transition is found at finite temperature if the layers of frozen spins are independently distributed, while for correlated disorder one finds a low-temperature phase with some glassy properties.     

The preparation theorem on banach spaces

We give a generalization, for smooth Fredholm maps between Banach spaces, of the Preparation Theorem known in finite dimension. As an application we obtain the Prepared Form Theorem which is a basic tool in singularity theory.     

FLUORESCENCE OF Euglena gracilis PHOTORECEPTOR PIGMENT: AN in vivo MICROSPECTROFLUOROMETRIC STUDY

Abstract— The spectroscopic characterization of the photoreceptor pigment is one of the main questions in the study of the photosensory transduction chains in photomotile microorganisms. One of the possible techniques that can be used is in vivo microspectrofluorometry. By means of a tunable dye-laser microspectrofiuorometer developed by us, we have investigated some of the spectroscopic properties of the photoreceptor pigment of the green flagellate Euglena gracilis. The in vivo fluorescence excitation spectrum has been determined and the fluorescence quantum yield has been measured. The results show that flavins are indeed present in the paraflagellar body of E. gracilis and that their fluorescence quantum yield is much lower than that of a free flavin. An estimate of the order of magnitude of the rate constants for primary molecular reactions is tentatively given.