Su un problema unidimensionale di diffusione in un mezzo a contorno mobile con condizioni ai limiti non lineari

Summary It is considered a one dimensional heat diffusion probelm in a medium bounded by two parallel planes, x=0 and x=s(t), with a temperature specification on the moving face and a nonlinear relationship between the heat flux and the temperature on the other one. Existence, uniquenesses and computability of the solution are investigated. Continuous and monotone dependence on the data and related properties are also studied. The case s(0)=0 is then widely discussed. The class of boundary problems for which these results hold seems to be very wide.

---

---

Entrata in Redazione il 9 ottobre 1971.

---

Lavoro eseguito nell'ambito dell'attività del Gruppo Nazionale per la Fisica Matematica del C.N.R.     

Sulla esistenza e sulla costruzione effettiva con la «piccola variazione» delle curve algebriche piane con assi di simmetria obliqua e in particolare ortogonale

Riassunto In primo luogo viene giustificata la possibilità per un diametro autoconiugato di una quartica piana di essere asse di simmetria obliqua (in particolare ortogonale) e dopo aver illustrato alcune proprietà sulla simmetria, vengono dati appropriati accorgimenti onde procedere, con la ?piccola variazione?, alla costruzione effettiva delle quartiche piane (dei vari generi) dotate di tutti i possibili assi di simmetria obliqua (in particolare ortogonale), dandone anche, caso per caso, la corrispondente equazione.

---

Résumé D'abord on justifie la possibilité, pour les diamètres auto-conjugués, d'être aussi des axes de symmetrie oblique (en particulier orthogonale) pour les quartiques planes et après avoir illustré plusieurs propriétés sur la symmetrie, on donne quelques avisements opportuns pour procéder après à la construction effective, avec la ?petite variation? des quartiques planes (de tous les genres) douées de tous les possibles axes de symmetrie oblique (en particulier, orthogonale), en donnant aussi, chaque cas à part, l'équation correspondante.

---

---

Nota II     

A Callan-Symanzik study of the λϕ34+gϕ36 theory

We investigate a $\text{L}{}_{\mathrm{<mtext>I</mtext>}}\text{=λ?}{}_3{}^4\text{+g?}{}_3{}^6$ theory using Callan-Symanzik equations. Logarithmic corrections to trivial fixed-point behaviour are obtained. The theory is shown to correspond to a model for tri-critical phenomena in ³He⁴He mixtures.     

A theoretical investigation of the electric field dependence of core ionization phenomena in carbon monoxide

The influence of an applied electric field on core binding and relaxation energies accompanying core ionization has been theoretically investigated by means of non-empirical LCAO MO SCF calculations within the ASCF formalism, on a simple prototype molecule (carbon monoxide). Single orbital contributions to the total relaxation energies, together with Mulliken population analyses and density difference contours, are presented. Investigations of the effect of an electric field on shake-up transitions, and potential energy surfaces, as evidenced by band profile analysis, are also considered.     

Studies on the synthesis of heterocyclic compounds. III. Synthesis of 1,3,2-benzodioxa- and 1,3,2-benzoxathiarsole derivatives

The preparation and reaction of 1,3,2-benzodioxa- and 1,3,2-benzoxathiarsoles (IIa-b) are described. Spiran derivatives Va-c are obtained by treating IIa-b with Ia-b and triethylamine, while the reaction of IIa-b with sodium hydroxide, ethoxide and p-cresolate gives the compounds VIa-b, VIIa-b and VIIIa-b, that can evolve to Xa-b. Reaction of IIa-b with sodium p-toluenethio-late and n-butyllithium gave the compounds IXa-b and XIa-b respectively. The structure of the prepared compounds has been determined by elemental analysis and spectroscopic data.