Combinatorial invariants for nets of conics in $$\mathrm {PG}(2,q)$$ PG ( 2 , q )

Designs, Codes and Cryptography - The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics...     

Instability of the paramagnetic state towards incommensurate magnetic order in the 2-d Hubbard model

We determine the instability line separating the paramagnetic phase in the phase diagram of the 2-d Hubbard Model from a phase with incommensurate magnetic order. A mean-field approximation of the Kotliar-Ruckenstein slave boson representation is used to calculate the wave-vector dependent magnetic susceptibility. For largeU/t the instability occurs at a densityn0.37, and a wave-vector close toq=(0,). The dependence ofq onU andn is also given.     

Two unexpected effects concerning perturbations of the B3Π0u+ state of molecular iodine

We present in this paper two new effects observed in the state of molecular iodine: a very high diamagnetic correction in the vibrational level υ′ = 62 and an important orientation of the optically excited molecules due to predissociation. Both effects can be interpreted by taking into consideration the perturbation of the B state by other electronic states.     

On the Correlation between Ionization Potentials and Excitation Energies,part III: Pyrazine

A recently suggested scheme for relating ionisation potentials (IP) to excitation energies (E) has been applied to pyrazine and 2,6-dimethylpyrazine. The results indicate that in these systems the energy gap (ΔE) between the two lowest lying ¹n,π*-states is significantly smaller than that (ΔIP) between the corresponding ²n-states of the parent radical cations. The values estimated for ΔE on the basis of ΔIP, measurable by photoelectron spectroscopy, disagree with those calculated theoretically but seem to be supported by the experimental evidence available. Since ΔE = ΔIP would normally be expected, the relationship ΔE < ΔIP actually present in these systems is discussed and related to the different shape of the n-MO's involved in the ionization and excitation processes.     

Reductive cleavage of axially disymmetric tertiary amines and quaternary ammonium salts by lithium aluminium hydride. Synthesis of new 1,1′-binaphthyl substituted amines

Axially disymmetric tertiary amines or quaternary ammonium salts $\text{A}$ are synthesized by double alkylation of primary or secondary amines with racemic or optically pure 2,2′-bis (bromomethyl)-1,1′-binaphthyl. Their reductive cleavage by lithium aluminium hydride in refluxing THF leads to chiral secondary or tertiary amines $\text{B}$, substituted by a binaphthyl unit, with high yields and absence of racemization.