New approach to the synthesis of 6-ketosteroids via organoiron complexes.

New Methodology is described for the synthesis 6-ketosteroids, of potential value for the synthesis of β-ecdysone, $\text{via}$ tricarbonyl (4-methoxy-1-methylcyclohexadienyl) iron hexafluorophosphate $\text{1}$.     

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

A Mauro Picone nel suo 70^mo compleanno.     

An identity for T-ordered exponentials with applications to quantum mechanics

The solution of the Cauchy problem for Liouville's equation φ_xy = e^φ is shown to be equivalent to the calculation of a T-ordered exponential of a two-dimensional variable matrix. This gives rise to an identity for the T-ordered exponential involving two arbitrary functions. The formalism is applied to the time evolution of a magnetic dipole in a time dependent magnetic field and to the one-dimensional Dirac equation with external potential $\text{V(x) = (n +}\text{1}\text{2}\text{)λ}$ tanh λx which is relevant for field theoretic applications. A generalization to n-dimensional matrices is also given.     

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.     

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.