Hyperbolic unitals in the Hall planes

A new transformation method for incidence structures was introduced in [8],an open problem is to characterize classical incidence structures obtained by transformation of others. In this work we give some, sufficient conditions to transform, with the procedure of [8],a unital embedded in a projective plane into another one. As application of this result we construct unitals in the Hall planes by transformation of the hermitian curves and we give necessary and sufficient conditions for the constructed unitals to be projectively equivalent. This allows to find different classes of not projectively equivalent Buekenhout's unitals, [2],and to find the class of unitals descovered by Grüning, [4],easily proving its embeddability in the dual of a Hall plane. Finally we prove that the affine unital associated to the unital of [4]is isomorphic to the affine hyperbolic hermitian curve.Work performed under the auspicies of G.N.S.A.G.A. and supported by 40% grants of M.U.R.S.T.     

Influence of the cation distribution on the magnetization of Y-type hexagonal ferrites

Mössbauer absorption and magnetization measurements have been made in Mg₂?Y and Co₂?Y ferrites. The magnetizations of the various iron sublattices did not show any marked difference in Mg₂?Y, whilst in the case of Co₂?Y three different behaviours of the sublattice magnetizations have been detected. Low-temperature magnetization measurements in Mg₂Y gave evidence of a noncollinear magnetic order. The different magnetic properties of these compounds have been explained on the ground of a preferential occupation by Mg²⁺ and Co²⁺ ions of the inner octahedral sites of the T crystallographic block. The presence in these sites of a non-magnetic ion such as Mg²⁺ is responsible for the peculiar magnetic order observed in Mg₂?Y.     

Water dimer in liquid water

Summary A Self-Consistent Reaction Field Model is used to study the effect of the molecular environment on the electronic distribution and on the equilibrium geometry of the water dimer in liquid water. Computations are performed at the 6-311G++(2d,2p) MP2 level. Comparison of the results for the monomer and the dimer, in a vacuum and in the liquid, is made in order to gain a deeper insight on the cooperative phenomenon. The discussion emphasizes the trends which should be considered for deriving more sophisticated water-water potentials.     

Stereodivergent <Emphasis Type="Italic">Baylis-Hillman</Emphasis> Reaction of a Chiral Acryloyl Imide Exploiting Ion-Chelation Effect: Mechanistic Insight on the Rearrangement of Trichloroacetimidates of the <Emphasis Type="Italic">Baylis-Hillman</Emphasis> Adducts to Trichloroacetamides

Summary. In the presence of DABCO, ethyl glyoxalate and (4S,5R)-1,5-dimethyl-3-acryloyl-4-phenylimidazolidin-2-one gave mixtures of the corresponding Baylis-Hillman adducts enriched in either isomer, depending on the absence or the presence of LiClO₄ in the reaction mixture. A diastereomeric mixture in 10:90 dr allowed to definitively establish the mechanism of the reaction leading to trichloroacetamides starting from trichloroacetimidates of the Baylis-Hillman adducts.     

Synthesis of double core chromophore-functionalized nanothreads by compressing azobenzene in a diamond anvil cell

Carbon nanothreads are likely the most attracting new materials produced under high pressure conditions. Their synthesis is achieved by compressing crystals of different small aromatic molecules, while also exploiting the applied anisotropic stress to favor nontopochemical paths. The threads are nanometric hollow structures of saturated carbon atoms, reminiscent of the starting aromatic molecule, gathered in micron sized bundles. The examples collected so far suggest that their formation can be a general phenomenon, thus enabling the design of functionalities and properties by suitably choosing the starting monomer on the basis of its chemical properties and crystal arrangement. The presence of heteroatoms or unsaturation within the thread is appealing for improving the processability and tuning the electronic properties. Suitable simple chromophores can fulfill these requirements and their controlled insertion along the thread would represent a considerable step forward in tailoring the optical and electronic properties of these mechanically extraordinary materials. Here, we report the synthesis and extensive characterization of double core nanothreads linked by azo groups. This is achieved by compressing azobenzene in a diamond anvil cell, the archetype of a wide class of dyes, and represents a fundamental step in the realization of nanothreads with tailored photochemical and photophysical properties.

One-step high-pressure synthesis of 2D crystalline double nanothreads linked by azo groups.     

A Self-consistent Reaction Field Model of Solvation Using Distributed Multipoles. II: Second Energy Derivatives and Application to Vibrational Spectra

The use of distributed multipoles in the formalism of the reaction field factors allowed us to develop a computational scheme adapted to quantum chemical computations on a molecule solvated by a dielectric continuum. The algorithm used to compute the second energy derivatives is developed and, after its implementation in a quantum chemical computational code, permits the computation of the vibrational frequencies of the solute. This approach has been tested successfully on two test molecules and applied to the study of the solvent effect on the structure and the vibrational spectrum of a series of parasubstituted benzonitriles.     

Calculation of coulomb integrals in molecules over an spd basis of STO

A spherical tensor expansion of 1/r ₁₂ (where r ₁₂ is the separation considered) is used to represent Coulomb integrals in a molecular context for an MNDO method over an spd basis of STO. This is rendered invariant of the space fixed axes chosen using Wigner rotation matrices which transform the integrals from the molecular frame (as distinct from Dewar [1])-This procedure is found to be rigorous only in the long range limit but is satisfactory at separations of the order of most single bond lengths (as Dewar [1]). The pole at R _ab=0 is avoided by adding a constant to the separation, which takes the value that reproduces the Slater-Condon monocentric integrals there. Extension over the whole range is carried out using a unique multiplicative polynomial from the Legendre function expansion of 1/(R _ab ² +A ²) for small R _ab and an exponential decay in R _ab is dictated by symmetry in the overlap region expression, which retains rotational invariance.This calculation results in an easy evaluation of these functions and their first derivatives leading to a very rapid molecular geometry optimisation taking the d-orbitals into account in an MNDO hypothesis.Unité Associée au CNRS no 510 Interactions Moléculaires     

The evaluation map in field theory,sigma-models and strings—II

In this paper, we examine specifically the rôle of the evaluation map in sigma-models and strings. We discuss the difference between sigma-models and field theory, as far as anomaly cancellation is concerned. The introduction of the Wess—Zumino terms in different sigma-models is considered. Anomalies in string theory are discussed, with special attention to the conformal anomalies and to the sigma-model anomalies for the imbedded (or immersed) world-sheet of the string. Conformal anomalies in two dimensions are connected to holomorphic and gravitational anomalies. In order to have the cancellation of the sigma-model anomalies of the string, certain topological conditions must be satisfied by the ambient manifold. The rôle of the evaluation map in the calculations of global anomalies is also discussed, both for field theories and for sigma-models. In particular global anomalies are connected with the differential characters of Cheeger and Simons. We show that the absence of global anomalies in sigma-models is guaranteed by the absence of torsion in suitable homology groups of the target space.On leave of absence from Dipartimento di Fisica dell'Università di Padova and Instituto Nazionale di Fisica Nucleare, Sezione di PadovaWork supported in part by: Ministero Pubblica Istruzione (research project on Geometry and Physics)On leave of absence from Department of Mathematics, University of North Carolina, Chapel Hill, N.C. 27514. From August 1 until December 20 at the School of Mathematics, Institute for Advanced Study Princeton NJ 08540, USA. Work supported in part by N.S.F.