Rotating discs of unconventional profile

Summary On the basis of a general relation — capable of expressing analytically the thickness law for a wide range of rotating discs of different shapes — the Author proposes formulas, having the same general validity, whereby the quasi-plane stress system in such discs may be described in terms of absolutely convergent hypergeometric series.After highlighting the extreme suitableness of the mentioned formulas for calculating discs having an arbitrary profile, he adapts the results to the particular case of the conic-shaped disc and emphasizes the consequent remarkable simplification in regard to the conventional solutions.Dealing with the same procedure the Author puts forward some accurate tables pertaining to the interesting case of the discoid in the form of an ellipsoid of revolution.Finally he relates about the possibility of obtaining closed solutions for a group of discoid-frustums characterized by a particular relation which binds their geometry.

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Sommario Sulla scorta d'una relazione generale atta ad esprimere analiticamente la legge di variazione dello spessore d'una vasta categoria di dischi rotanti diversamente configurati, si prospettano delle formule altrettanto generali attraverso le quali lo stato quasi piano di tensione a questi ultimi relativo risulta praticamente definibile in termini di serie ipergeometriche assolutamente convergenti. Dopo aver fatto rilevare l'estrema convenienza di utilizzare le stesse formule per il calcolo dei dischi di profilo arbitrario si specializzano i risultati per il caso del disco conico, evidenziandone la notevole semplificazione rispetto alle soluzioni convenzionali, nonchè per l'interessante caso del discoide a forma di elissoide di rotazione per il quale si prospettano accurate tabelle. Si riferisce infine sulla possibilità di ottenere soluzioni chiuse per tutta una schiera di tronchi discoidali caratterizzati da un particolare legame che ne vincola la geometria.

     

Existence and nonexistence results for critical growth biharmonic elliptic equations

We prove existence of nontrivial solutions to semilinear fourth order problems at critical growth in some contractible domains which are perturbations of small capacity of domains having nontrivial topology. Compared with the second order case, some difficulties arise which are overcome by a decomposition method with respect to pairs of dual cones. In the case of Navier boundary conditions, further technical problems have to be solved by means of a careful application of concentration compactness lemmas. The required generalization of a Struwe type compactness lemma needs a somehow involved discussion of certain limit procedures. Also nonexistence results for positive solutions in the ball are obtained, extending a result of Pucci and Serrin on so-called critical dimensions to Navier boundary conditions. A Sobolev inequality with optimal constant and remainder term is proved, which is closely related to the critical dimension phenomenon. Here, this inequality serves as a tool in the proof of the existence results and in particular in the discussion of certain relevant energy levels.Received: 18 April 2002, Accepted: 3 September 2002, Published online: 17 December 2002Mathematics Subject Classification (2000): 35J65; 35J40, 58E05The first author was supported by MURST project "Metodi Variazionali ed Equazioni Differenziali non Lineari".     

Possibility to deduce the emission time sequence of neutrons and protons from the neutron-proton correlation function

Experimental information has been derived from the neutron-proton correlation function in order to deduce the time sequence of neutrons and protons emitted at 45 degrees in the E/A = 45 MeV 58Ni + 27Al reaction.     

Application of VUV laser harmonic radiation to the measurement of porous silicon dielectric function

Vacuum ultra-violet (VUV) laser harmonics have been generated in a noble gas jet, which, combined with a standard spectrophotometer, have allowed measurements of the reflectance of porous silicon over a wide energy spectral range from 1 to 16 eV. Porous silicon dielectric function was, then, deduced from reflectance measurements by Kramers–Kronig analysis. Data are found to be in good agreement with those reported in literature, thus showing that laser harmonics represent a new, alternative, and suitable VUV source for optical characterisation of materials such as semiconductors and thin films.     

The deconfining phase transition in the finite temperature twisted Eguchi-Kawai model

We present the results obtained from a Monte Carlo study of a finite temperature twisted Eguchi-Kawai model as previously introduced by the authors. The deconfining temperature of the model is determined to be (206 ± 20) Λ_L.     

Su un modello di geometria non euclidea

In this paper, by using the method of [4], a new model of non-euclidean geometry that is non-comparable with the Loba?evskij geometry is given.