Sui problemi di derivata obliqua regolare per le equazioni lineari del secondo ordine di tipo ellittico

A Mauro Picone nel suo 70^mo compleanno.     

Zinc(II)cysteine and zinc(II)cystine systems: Selection of species from potentiometric data

Summary The formation constants of species formed in the systems H⁺-Zn²⁺-cysteine and H⁺-Zn²⁺-cystine have been determined in aqueous solution at 37° and I = 0.15 mot dm^–3 (NaClO₄), using the pH-metric method. The existence of the following species [ZnL], [ZnL₂], [ZnL₂H] and [Zn₂L₃] (2.3 pH 7.7) was proved for the Zn²⁺-cysteine system, whereas for the Zn²⁺-cystine [Zn₂L] (5.3 pH 6.4) was the only species found. In the Zn²⁺-cystine system the pH range was severely restricted because of precipitation occurring at pH > 6.4. A new experimental and numerical approach was employed in order to implement the possibility of rigorously selecting the species present in each system. The results have been compared with data previously reported on the same systems, considering in particular the different sets of species found in the various works.     

Equazioni quasi ellittiche e spaziL p, θ (ω, δ) (I)

Summary Regularity theorems inL ^{2, θ} (ω, δ) spaces are proved for weak solutions of quasielliptic differential equations. In particular, regularization results are obtained in the class of holder continuous functions (with respect to a suitable metric related to the operator). As a consequence, we obtain results and estimates in L^p andL ^{p, θ} spaces for the solution of the Dirichlet problem.

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Lavoro eseguito nell’ambito del Gruppo di Ricerca n^o 46 del Comitato per la Matematica del C N.R.     

Space tensors in general relativity II: Physical applications

The general theory of space tensors is applied to the study of a space-time manifoldsV ₄ carrying a distinguished time-like congruence Γ. The problem is to determine a physically relevant spatial tensor analysis over (V ₄, Γ), in order to proceed to a correct formulation of Relative Kinematics and Dynamics. This is achieved by showing that each choice of gives rise to a corresponding notion of ‘frame of reference’ associated with the congruence Γ. In particular, the frame of reference (Γ, ∇*) determined by the standard spatial tensor analysis is shown to provide the most natural generalization of the concept of frame of reference in Classical Physics. The previous arguments are finally applied to the study of geodesic motion inV ₄. As a result, the general structure of the gravitational fields in the frame of reference (Γ, ∇*) is established. This work was assisted by funds from the C.N.R. under the aegis of the activity of the National Group for Mathematical Physics.     

Space tensors in general relativity III: The structural equations

A self-consistent theory of spatial differential forms over a pair (M,Γ)is proposed. The operators d(spatial exterior differentiation), d_T (temporal Lie derivative) andL (spatial Lie derivative) are defined, and their properties are discussed. These results are then applied to the study of the torsion and curvature tensor fields determined by an arbitrary spatial tensor analysis \((\tilde \nabla ,\tilde \nabla T)\) (M,Γ). The structural equations of \((\tilde \nabla ,\tilde \nabla T)\) and the corresponding spatial Bianchi identities are discussed. The special case \((\tilde \nabla ,\tilde \nabla T) = (\tilde \nabla *,\tilde \nabla T*)\) is examined in detail. The spatial resolution of the Riemann tensor of the manifold M is finally analysed; the resultingstructure of Eintein's equations over a pair (ν₄,Γ)is established. An application to the study of the problem of motion in terms of co-moving atlases is proposed.