An exact homology sequences approach to the controllability of systems

Some results are given on the homology groups of the abstract simplicial complex associated to a multivariable control system, as an extension of the central result of J. Casti (J. Math. Anal. Appl.68 (1979), 347–370) to the multivariable case. The method used is “polyhedral dynamics” as termed by J. Casti, who introduced it. A given control system is mapped into a simplicial complex and then its homological structure is studied. These results, obtained in the multivariable case by the use of the Mayer-Vietoris homology sequence and of the relative homology sequence, present topological invariants for control systems thus creating the possibility of a new topological classification of multivariable systems. An example is given to clarify the approach.     

Crystal and molecular structure of the coordination compound of O-phenanthroline thiosemicarbazide diacetate of cadmium(II) monohydrate

Institute for Applied Physics, Moldavian Academy of Sciences. Moldavian Institute of Chemistry. Lazo Polytechnic Institute of Kishinev. Translated from Zhurnal Strukturnoi Khimii, Vol. 133, No. 6, pp. 197–201, November–December, 1992.     

The regioselectivity of α,β-enone photoannelation with monosubstituted acetylenes: a possible effect of dipole-dipole interactions

The Raman and ¹H NMR-spectra of mixtures of 2-cyclopentenone and 2cyclohexenone with 1-hexyne show that the enone-alkyne association in the ground state is weak and cannot account for the difference in the regioselectivity observed in photocycloadditions of enones to alkynes and alkenes. The comparison of dipole moments and the calculation of π-electronic charges on the interacting orbitals of both enone and substrate lead to the conclusion that the regioselectivity of enone-alkyne photoannelation may be controlled by the dipole-dipole interactions between the ₃(π, π^*) state of the enone and the ground state of the substrate. This effect is the stronger, the weaker are π-donating capacity and polarization of the multiple bond in the substrate.     

Electric field modulated Raman scattering in CdS

We have observed electric field modulated Raman scattering by A₁ LO phonons in CdS. The field induced scattering is observed with a geometry in which Raman scattering by A₁ LO phonons is normally allowed. The interference of the field induced and allowed terms in the transition susceptibility leads to a modulated Raman scattering intensity proportional to the applied field. This is contrasted with data previously reported on field induced Raman scattering by E₁ LO phonons in a configuration in which the Raman scattering is normally forbidden and in which there is no interference between linear wavevector dependent and field induced terms in the transition susceptibility. Electric field effects on Raman scattering by TO phonons and by 2 LO phonons is also discussed.     

Restricted Dumont Permutations

We analyze the structure and enumerate Dumont permutations of the first and second kinds avoiding certain patterns or sets of patterns of length 3 and 4. Some cardinalities are given by Catalan numbers, powers of 2, little Schr?der numbers, and other known or related sequences. Received June 21, 2004     

Blei

Ohne Zusammenfassung