Sulla rilassazione di alcuni funzionali integrali in dimensione infinita

Summary In this work we consider the problem ()of the minimum for integral functionals I _f of the Calculus of Variations, where we don't suppose any hypothesis of convexity on the integrand and in which the state takes values in a Suslin metric space, while the last variable of the integrand is in a separable reflexive Banach space. We study two different types of relaxed problems, associated to (),and we prove that the infima of the three functionals considered are the same, that (),one of the relaxed problems, has solution and that the accumulation points of the minimizing sequences for ()are the only solutions of ().

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Lavoro eseguito nell'ambito dell'Istituto per la Matematica Applicata del C.N.R., Genova.     

The Dinitramide Anion, N(NO(2))(2)(-)

The infrared and Raman spectra of the NH(4)(+), K(+), and Cs(+) salts of N(NO(2))(2)(-) in the solid state and in solution have been measured and are assigned with the help of ab initio calculations at the HF/6-31G and MP2/6-31+G levels of theory. In agreement with the variations observed in the crystal structures, the vibrational spectra of the N(NO(2))(2)(-) anion are also strongly influenced by the counterions and the physical state. Whereas the ab initio calculations for the free N(NO(2))(2)(-) ion indicate a minimum energy structure of C(2) symmetry, Raman polarization measurements on solutions of the N(NO(2))(2)(-) anion suggest point group C(1) (i.e., no symmetry). This is attributed to the very small (<3 kcal/mol) N-NO(2) rotational barrier in N(NO(2))(2)(-) which allows for easy deformation.