Vibrational Stark effect: Theoretical determination through the semiempirical AM1 method

The vibrational Stark effect of a series of small molecules has been calculated by means of the semiempirical AM1 method through addition of the electron–field interaction term in the one-electron Hamiltonian. Optimized geometrical parameters along with harmonic frequencies and line intensities are determined for different strengths of the applied uniform electric field. The perturbed spectra are compared with theoretical studies carried out at the ab initio level and with experimental results. The vibrational Stark effect of the retinal molecule is also computed, showing that this kind of study is feasible in systems of biochemical interest. © 1992 by John Wiley & Sons, Inc.     

Stereoselective |2+2| photocycloaddition of chiral 2(5H)-furanones to alkenes

The steric and stereoelectronic dependence of the diastereoselectivity in the photochemical |2+2| cycloaddition of chiral 2(5H)-furanones to alkenes is investigated to prepare eventually cyclobutanic natural products. It is shown that the alkenes approach to different chiral 5-substituted 2(5H)-furanones mainly by the less hindered side.     

Relativistic holonomic fluids

The notion of holonomic fluid in relativity is reconsidered. An intrinsic characterization of holonomic fluids, involving only the unit velocity, is given, showing that in spite of its dynamical appearance the notion of holonomic fluid is a kinematical notion. The relations between holonomic and thermodynamic perfect fluids are studied.     

Iron(III) complexes withN-Methyl-4-mercaptopiperidine

Summary Complexes of iron(III), containingN-methyl-4-mercaptopiperidine in its zwitterionic form (HRS), of stoichiometry Fe(HRS)₄XA₄ · nD, Fe(HRS)₃(BPh₄)₃ · 3DMF and (Fe(HRS)SO₄)₂SO₄ · 3MeOH · 2H₂O (X=Cl or NO₃; A=BPh₄ or PF₆; D=H₂O, MeOH or DMF) have been prepared and characterized by i.r. and electronic spectra, magnetic susceptibilities at room temperature and by cyclic voltammetry measurements.     

Backreaction Effects of Dissipation in Neutrino Decoupling

Dissipative effects during neutrino decoupling in the early universe create a small backreaction on the Hubble rate, and lead to a small rise in temperature and entropy. We use a simplified thermo-hydrodynamic model, which provides a causal approximation to kinetic theory, in order to estimate the backreaction effects and the entropy production.     

The Frobenius traces distribution for modular Abelian surfaces

We prove that there exist at least 15 pairs of measures for which the two normalized Frobenius traces on modular Abelian surfaces are equidistributed. Under an assumption about stochastic independence, we prove that there are exactly 18 such pairs of measures. Moreover, we describe all of them by giving their moments and distributions.     

On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices

In this paper, we characterize the games in which Johnston, Shapley-Shubik and Penrose-Banzhaf-Coleman indices are ordinally equivalent, meaning that they rank players in the same way. We prove that these three indices are ordinally equivalent in semicomplete simple games, which is a newly defined class that contains complete games and includes most of the real-world examples of binary voting systems. This result constitutes a twofold extension of Diffo Lambo and Moulen’s result (Diffo Lambo and Moulen, 2002) in the sense that ordinal equivalence emerges for three power indices (not just for the Shapley-Shubik and Penrose-Banzhaf-Coleman indices), and it holds for a class of games strictly larger than the class of complete games.     

A Koszul complex over skew polynomial rings

We construct a Koszul complex in the category of left skew polynomial rings associated with a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequence.     

The picard group of the variety of plane cuspidal cubics of ?3

We give a compactification of the varietyU of non-degenerate plane cuspidal cubics of ℙ³. We construct this compactification by means of the projective bundleX of a suitable vector bundleE. We describe the intersection ring ofX and, as a consequence, we obtain the intersection numbers ofU that satisfy 10 conditions of the following kinds:ρ, that the plane determined by the cuspidal cubic go through a point;c, that the cusp be on a plane;q, that the cuspidal tangent intersect a line;μ, that the cuspidal cubic intersect a line. Moreover, we prove that the Picard group of the varietyU is a product of two infinite cyclic groups generated byρ andc−q.