Asymptotic behavior of solutions of variational equations

In questo articolo si considerano equazioni differenziali ordinarie del secondo ordine della forma $$\{ A(u')u'\} ' + \delta (r)A(u')u' + f(r,u) = 0,$$ dove cioè la nonlinearità è presente sia nella variabile soluzioneu che nella sua derivata. Si forniscono proprietà di monotonia, oscillazione e un accurato studio del comportamento asintotico all’ infinito delle soluzioni, quandoA, δ,f hanno crescite asintotiche di tipo algebrico.     

Canonical connections with an algebraic curvature tensor field on naturally reductive spaces

We study Ambrose-Singer connections with an algebraic curvature tensor on simply connected manifolds carrying a homogeneous Riemannian structure of class ₃ in the classification given by F. Tricerri and L. Vanhecke.This work was partially supported by MURST.     

Geometrization of the physics with teleparallelism. I. The classical interactions

A connection viewed from the perspective of integration has the Bianchi identities as constraints. It is shown that the removal of these constraints admits a natural solution on manifolds endowed with a metric and teleparallelism. In the process, the equations of structure and the Bianchi identities take standard forms of field equations and conservation laws.The Levi-Civita (part of the) connection ends up as the potential for the gravity sector, where the source is geometric and tensorial and contains an explicit gravitational contribution.Nonlinear field equations for the torsion result. In a low-energy approximation (linearity andlow energy-momentumtransfer), the postulate that only charge and velocities contribute to the source transforms these equations into the Maxwell system. Moreover, the affine geodesics become the equations of motion of special relativity with Lorentz force in the same approximation [J. G. Vargas,Found. Phys. 21, 379 (1991)]. The field equations for the torsion must then be viewed as applying to an electromagnetic/strong interaction.A classical unified theory thus arises where the underlying geometry confers their contrasting characters to Maxwell-Lorentz electrodynamics and to an Einstein's-like theory of gravity. The highly compact field equations must, however, be developed in phase-spacetime, since the connection is velocity-dependent, i.e., Finsler-like.Further opportunities for similarities with present-day physics are discussed: (a) teleparallelism allows for the formulation of the torsion sector of the theory as a flat space theory with concomitant point-dependent transformations; (b) spinors should replace Lorentz frames in their role as the subjects to which the connection refers; (c) the Dirac equation consistent with the frame bundle for a velocity-dependent metric with Lorentz signature generates a weak-like interaction in the torsion sector.Work done at the Department of Mathematics and Physics of the Interamerican University of Puerto Rico, San German, Puerto Rico 00683.     

Approximations in thermal explosion theory and the nature of the degenerate critical point

Summary In studies of thermal explosion the Frank-Kamenetskii approximation sets exp(–E/RT)=exp(–E/RT ₀)exp (/(1+))exp(–E/RT ₀)exp, where=RT ₀/E i.e. it assumes0. When this approximation is not made, it is known that criticality vanishes for greater than a certain value _*, say. This may occur whether the Arrhenius form is used or some suitable approximation to it; many authors have proposed approximations involving the maximum dimensionless temperature in the reactant. The nature of the degeneracy near the value _* is examined for such approximations in general, some approximations are considered and the results compared.

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Zusammenfassung In Studien von thermischen Explosionen setzt man in der Näherung von Frank-Kamenetskii exp(–E/RT)=exp(–E/RT ₀)exp(/(1+))exp(–E/RT ₀) exp), wobei=RT ₀/E ist, d.h. man nimmt0 an. Wenn diese Näherung nicht benützt wird, so weiß man, daß die Kritikalität verschwindet wenn einen gewissen Wert _* überschreitet. Dies findet man mit Benützung der Formel von Arrhenius oder mit einer Näherung dazu; viele Autoren haben Näherungen vorgeschlagen mit Verwendung der maximalen dimensionslosen Temperatur im Reaktionsgemisch. Es wird für solche Näherungen die Natur der Entartung der Lösung in der Umgebung von _* untersucht; die Resultate für verschiedene Näherungen werden verglichen.

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Résumé Dans les études de la théorie de l'explosion thermale l'approximation de Frank-Kamenetskii pose exp(–E/RT)=exp(–E/RT ₀)exp(/(1+)]exp(–E/RT ₀) exp, avec=RT ₀/E, c'est à dire on admet0.On sait que, en dehors de cette approximation, la limite critique disparaît lorsque dépasse une certaine valeur dénommée _*. Ceci peut se produire soit en utilisant la forme d'Arrhenius ou une approximation adéquate.Plusieurs auteurs ont proposé des approximations utilisant la température maximum non-dimensionelle du réactif. Dans la présente étude on examine d'une façon générale le caractère de la dégénérescence aux alentours de la valeur _* pour ce genre d'approximations. Ensuite on considère quelques approximations particulières et les résultats sont comparés.

     

Structure, 31P and 13C chemical shift anisotrophy of (CH3)3P, (CH3)3PO, (CH3)3PS and (CH3)3PSe as determined by liquid crystal NMR spectroscopy

The ¹³P and ¹³C spectra of the triply ¹³C labelled molecules (CH₃)₃P, (CH₃)₃PO, (CH₃)₃PS and (CH₃)₃PSe oriented in a nematic phase are reported. The CPC bond angles have been measured. The ¹³P chemical shift tensor shows a large anisotropy except in the case of (CH₃)₃P. The abnormal large value observed for the PSe bond length suggests a large anisotropy of the ¹J(PSe) spin coupling.