Growth Series and Random Walks on Some Hyperbolic Graphs

 Consider the tessellation of the hyperbolic plane by m-gons, ℓ per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate holly trees, a family of proper loops in these graphs. We then apply Grigorchuk’s result relating cogrowth and random walks to obtain lower estimates on the spectral radius of the Markov operator associated with a symmetric random walk on these graphs. Received 19 September 2001; in revised form 23 December 2001     

Correlation of 2-, 3-, 4- and disubstituted pyridine gas-phase proton affinities with ab initio calculated energies at the sto-3g basis set level

Total energies of 2-, 3-, 4- and disubstituted pyridines were calculated for the salt and the free base using ab initio molecular orbital calculations at the STO-3G basis set level [2]. In each set, the difference in energy, ΔE_H, between the salt and the free base was calculated and plotted against experimentally derived gas-phase proton affinities. The correlation was very good for each of the substituent categories listed. All of the energies and proton affinities were then plotted together on the same graph. The result was an excellent correlation with r = 0.97. The linear equation for gas phase proton affinity, PA_B = 28.51 + 435.45ΔE_H kcal/mole, was derived from this plot and was used to calculate proton affinities for all of the thirty-one compounds used in this study as well as for a series of dicyanopyridines for which values of proton affinity are not available at this time.     

A Combined Experimental and Theoretical Study on the Stereodynamics of Monoaza[5]helicenes: Solvent‐Induced Increase of the Enantiomerization Barrier in 1‐Aza‐[5]helicene

Helicenes and heterohelicenes are attractive compounds with great potential in materials sciences to be used in optoelectronics as ligand backbones in enantioselective catalysis and as chiral sensors. The properties of these materials are related to the stereodynamics of these helical chiral compounds. However, little is known about features controlling stereodynamics in helicenes; in particular, for heterohelicenes the position of the heteroatom could be relevant in this respect. Herein the complete stereodynamic characterization of monoaza[5]helicenes is shown by enantioselective dynamic HPLC and DFT calculations. At variance with previous theoretical calculations, 1‐aza[5]helicene shows a surprisingly high enantiomerization barrier, which is triggered by specific solvent interactions.     

Tensorial formulation of neutron diffusion theory

Summary In this paper a tensorial formulation of monoenergetic neutron diffusion theory is presented as can be derived starting from the integral form of the Boltzmann equation. A result of this tensorial approach is that, as a consequence of a spatial variation of the macroscopic cross sections or of the finite dimensions of the body under examination, the diffusion coefficient is no longer a constant scalar quantity, but a second order symmetric tensor, whose components are functions of both the position and the properties of the material the body is made of. The components of the diffusion coefficient tensor are explicitly evaluated in the case of some homogeneous convex bodies.

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Sommario In questa nota viene presentata una formulazione tensoriale della teoria della diffusione di neutroni monoenergetici, quale può essere dedotta a partire dalla forma integrale dell'equazione di Boltzmann. Nell'ambito di questa formulazione si precisa che il coefficiente di diffusione, in conseguenza di una variazione regolare delle sezioni d'urto macroscopiche con la posizione o delle dimensioni finite del mezzo in esame, non è più una quantità scalare costante, ma un tensore simmetrico del secondo ordine, le cui componenti sono funzioni della posizione e delle proprietà del materiale. Queste componenti vengono calcolate esplicitamente per alcuni mezzi omogenei convessi.

     

Sul postulato della completezza lineare dell'Hilbert

Sunto Si disente criticamente il detto postulato, con particolare riguardo al problema della sua compatibilità entro il sistema ipotetico — deduttivo dell'Hilbert. A Giovanni Sansone nel suo 70^mo compleanno.     

Sulle successioni di funzioni quasi continue negli spazi astratti

Sunto Si studia una definizione del tutto generale di funzione quasi continua; si enuncia e dimostra poi un teorema, concettualmente nuovo, per le successioni di funzioni che sono quasi continue nel senso generale studiato. A Mauro Picone nel suo 70^mo compleanno. Lavoro eseguito presso l'Istituto Nazionale per le Applicazioni del Calcolo.