Forcing Linearity Numbers of Semisimple Modules over Integral Domains

In this paper we determine the forcing linearity numbers for semisimple modules over integral domains.     

Diffuse-reflectance laser flash photolysis of 16-(1-pyrene)-hexadecanoic acid adsorbed on silica

The absorption and fluorescence of 16-(1-pyrene)-hexadecanoicacid adsorbed on silica have been investigated. Time-resolved transient diffuse reflectance spectra were recorded following pulsed nanosecond laser excitation at 355 nm of pyrene, 1-methylpyrene and 16-(1-pyrene)-hexadecanoicacid adsorbed on silica. In addition to a rapidly decaying transient, absorbing at 420 nm assigned as the triplet state, and of the radical cation, absorbing at 460 nm, another long living transient species absorbing at 420 nm was observed for 16-(1-pyrene)-hexadecanoic acid. The decay is reversible but complete recovery takes several hours. Although no definitive assignment could be made for this transient several possibilities are discussed. The radical cations of the investigated molecules are formed by a biphotonic process. The non-exponential decay of the radical cations could be analyzed in the framework of a Gaussian distribution of free energy barriers.     

Fermi resonances in the Raman spectra of alkali halide/BH4−

Raman spectra of a series of alkali-halide/BH^?₄ (and BD^?₄ crystals have been obtained. These spectra show some interesting examples of Fermi resonance type interactions between the stretching mode levels and overtone and combination band levels of the bending modes. Two resonances will be considered: (i) that between ν₁ and 2ν₄(A₁), and (ii) that between ν₃, 2ν₄ (F₂) and (ν₂+ν₄) (F₂).The F₂ resonance between ν₃, 2ν₄ and ν₂+ν₄ appears in the infrared spectrum and it has been studied on several occasions. However the equivalent Raman spectrum is of interest because the relative intensities of the bands are significantly different to those shown by the infrared spectrum.In the A₁ (and E) Raman spectrum of the stretching mode region there are two strong bands for each for the ¹⁰B and ¹¹B isotopes. The ν₁ would not be expected to show any ¹⁰B and ¹¹B splitting, but the observed bands are both closely resonating mixtures of ν₁ and 2ν₄(A₁). In fact the analysis shows that the stronger band has the higher proportion of 2ν₄ character, and the larger isotopic shift of the more intense band can then be seen to be reasonable.     

Laser-Induced Electron-Transfer Processes in a Pyrene–β-Cyclodextrin Complex in Titanosilicate Systems

We have used fluorescent spectroscopy and laser flash photolysis to investigate the photonics of pyrene molecules in a pyrene–-cyclodextrin inclusion complex in various media. We have observed a protective effect of -cyclodextrin relative to solubilized pyrene molecules during quenching of fluorescence by Ti ions (or titanium dioxide particles) in mixed colloids. In the presence of a precursor of silica (a TEOS solution), the pyrene molecules react with the colloidal silica particles formed, and the reaction is accompanied by decomposition of the pyrene–-cyclodextrin inclusion complex and efficient photoionization of pyrene.     

Effect of inter-miniband tunneling on current resonances due to the formation of stochastic conduction networks in superlattices

We study the effects of inter-miniband electron tunneling and electric field domains on the current–voltage and conductance–voltage curves of biased semiconductor superlattices under the action of a magnetic field that is tilted relative to the plane of the layers. For this geometry, electrons in the superlattice minibands exhibit a unique type of stochastic semiclassical motion. At certain critical values of the electric field within the superlattice layers, the stochastic trajectories change abruptly from fully localized to completely unbounded, and map out an intricate web-like mesh of conduction channels in phase space. Delocalization of the electron paths produces a series of strong resonant peaks in the electron drift velocity versus electric field curves. We use these drift velocity characteristics to make self-consistent drift-diffusion calculations of the current–voltage and differential conductance–voltage curves of the superlattices, which reveal strong resonant features originating from the sudden delocalization of the stochastic single-electron paths. We show that this delocalization has a pronounced effect on the distribution of space charge and electric field domains within the superlattices. Inter-miniband tunneling greatly reduces the amount of space-charge buildup, thus enhancing the domain structure and both the strength and number of the current resonances.