The Intersection of Pseudovarieties of Central Simple Semigroups

The problem of computing a finite semigroup generating the intersection of two finitely generated pseudovarieties is considered. A solution to this problem is presented for central simple semigroups.     

Lower limits on R-parity-violating couplings in supersymmetric models with light squarks

We interpret the results of searches for strongly interacting massive particles to place absolute lower limits on R-parity-violating couplings for squarks with mass (m(q) below 100 GeV. Recent searches for anomalous isotopes require that there be a baryon-number-violating or lepton-number-violating coupling larger than 10(-22)-10(-21) if m(q)>18 GeV. Using data from searches for stable particles at the CERN Large Electron Positron Collider (LEP) we demonstrate that this lower limit increases by 14 orders of magnitude, to an R-parity-violating coupling larger than 10(-8)-10(-7) for any squarks of mass less than 90 GeV. In the presence of an R-parity-violating coupling of this magnitude, neutralinos cannot explain the dark matter density in the Universe.     

Relaxation of an optimal control problem involving a perturbed sweeping process

We establish first, in the setting of infinite dimensional Hilbert space, a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are Lipschitz single-valued maps. Then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes. Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday     

Applications of a quantum virial theorem to kronig and penney's model and to a diatomic molecule in static approximation

Kronig and Penney's model is used to test a new formulation of quantum virial theorem for periodic systems. It is shown that the corrective term to the usual formulation of the virial theorem corresponding to boundary conditions is of importance and gives correct energy values for the system. Application of the virial theorem to a diatomic molecule also shows an important boundary condition correction if the distance of the nuclei is slightly different from equilibrium position, in accordance with the above correction.     

Key fragmentation patterns of aporphine alkaloids by electrospray ionization with multistage mass spectrometry

This work reports a detailed study of the fragmentations of aporphine alkaloids by electrospray ionization with multistage mass spectrometry (ESI-MS(n)) in positive mode. In a first step the loss of the amino group and its substituent is observed. Further steps display the loss of the peripheral groups. Losses of methanol and CO are observed if an OH is vicinal to an OCH(3) on the aromatic ring. Otherwise the spectra show radical losses of CH(3)* or CH(3)O* as the main fragmentations. If a methylenedioxy group is present losses of formaldehyde followed by CO are observed. These fragmentations yield important information on the structures of aporphines.     

Identity Bases for Some Non-exact Varieties

Let A₂ be the variety generated by the five-element non-orthodox 0-simple semigroup. This paper presents the identity bases for several subvarieties of A₂ that are not generated by any completely 0-simple or completely simple semigroups. It will be shown that several subvarieties of A₂, including the variety generated by the five-element Brandt semigroup, are hereditarily finitely based.     

A new class of functionalized terpyridyl ligands as building blocks for photosensitized supramolecular architectures. Synthesis, structural, and electronic characterizations

A new class of triarylpyridinio-derivatized [4'-(p-phenyl)(n)]terpyridyl ligands, R(1)(2)R(2)TP(+)-(p)(n)tpy, was designed as a novel category of electron-acceptor (A)-substituted proto-photosensitizing molecules. The first elements of this versatile family of ligands (i.e., n = 0, 1 and R(1) = R(2) = H), H(3)TP(+)-tpy and H(3)TP(+)-ptpy, were synthesized as well as their Ru(II) and Os(II) complexes to form the related acceptor-functionalized M(tpy)(2)(2+) and M(ptpy)(2)(2+) photosensitizer components denoted P0 and P1, respectively. Within the P1 series of compounds, an electron-donor (D)-substituted ligand, Me(2)N-ptpy, was also involved and associated with H(3)TP(+)-ptpy, giving rise to various combinations (up to 10 polyad systems). The two resulting series of nanometer-scale rigid rod-like photosensitized supramolecular architectures are of potential interest for long-range photoinduced electron transfer purposes. The main structural features of such supermolecules were determined by comparing the results obtained from (i) single-crystal X-ray analysis of the two free ligands together with that of the P0A/Ru and P1A(2)/Ru complexes and (ii) a detailed solution (1)H NMR study of the P0 series and, more specifically, of the P0A/Ru dyad (ROESY experiment). It is shown that the pseudoperpendicular conformation of the covalently linked A and P subunits found in the solid state is persistent in fluid medium; i.e., A is not conjugated with P (P0 and P1). The first insights regarding the consequences upon intercomponent couplings of combined substituent effects and conjugation (case of D-based polyads)-or absence of conjugation-are discussed in the light of ground-state electronic properties of the compounds.