Homolytic alkylation of chromones in micellar solution

Treatment of an aqueous solution of chromone, the detergent sodium dodecylbenzenesulfonate, silver nitrate and an alkanoic acid, with ammonium peroxydisulfate gives 2-R-chromone [R = i-C₃H₇ (47%), R = t-C₄H₉ (65%) and R = 1-adamantyl (78%)]. In addition 2-R-4-chromanone [R = i-C₃H₇ (40%), R = t-C₄H₉ (5%) and R-1-adamantyl (10%)] is formed. It is proposed that the reaction involves as intermediate the relatively stable 2-R-4-chromanon-3-yl radical and that the detergent has a micellar catalytic activity on the free radical alkylation process.     

Ω-Invariance in control systems with bounded controls

The concepts of weakly Ω-invariant sets and strictly weakly Ω-invariant sets in control systems with bounded controls are defined and analyzed. Computable conditions for weak Ω-invariance are derived, and the question of existence of rest points and stationary points in weakly Ω-invariant sets is considered. For linear dynamics, properties of weakly Ω-invariant sets are studied, and questions of constrained reachability are investigated.     

Ethers of indoxylie acid

O-alkylations of indoxylie acid (2b) to produce 3-indolyl-alkyl ethers and a synthesis of 5-melhoxy-2-earboxyindol-3-oxyaeetic acid (25) are described.     

The use of jacobi's lemma in unimodularity theory

The paper applies Jacobi's fundamental result on minors of the adjoint matrix to obtain properties on determinants of unimodular matrices.     

Multiple Čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure

We report simultaneous generation of multiple conical second-harmonic waves in a two-dimensional nonlinear photonic structure when illuminated by two overlapping noncollinear fundamental beams. We show that this phenomenon is caused by the nonlinear ?erenkov radiation emitted due to the interaction of photons from each constituent fundamental beam as well as the virtual one propagating along the bisector of the two beams. In addition, by studying the asymmetric geometry of the interaction, we uniquely verify the effects of reciprocal vectors on the ?erenkov-type second-harmonic generation in nonlinear photonic structures.     

Structural and electrical properties of granular metal films

Granular metal films (50–200,000 Å thick) were prepared by co-sputtering metals (Ni, Pt, Au) and insulators (SiO₂, Al₂O₃), where the volume fraction of metal, x, was varied from x = 1 to x = 0.05. The materials were characterized by electron micrography, electron and X-ray diffraction, and measurements of composition, density and electrical resistivity at electric fields ε up to 10⁶ V/cm and temperatures T in the range of 1.3 to 291 K. In the metallic regime (isolated insulator particles in a metal continuum) and in the transition regime (metal and insulator particles in a metal continuum) and in the transition regime (metal and insulator labyrinth structure) the conduction is due to percolation with a percolation threshold at x?0.5. Tunnelling measurements on superconductor-insulator-granular metal junctions reveals that the transition from the metallic regime to the dielectric regime (10–50 Å size isolated metal particles in an insulator continuum) is associated with the breaking up of a metal continuum into isolated metal particles. In the dielectric regime the temperature dependence of the low-field resistivity is given by ρL = ρo exp [2√(C/kT)], and the field dependence of the high-field, low-temperature resistivity is given by ρH = ρ∞ exp (εo/ε), where ρo, ρ∞, C, and εo are material constants. A simple theory based on the assumption that the ratio s/d (d-metal particle size and s-separation between particles) is a function only of composition yields expressions for ρ(ε, T) in excellent agreement with experiment. Furthermore, the theory predicts the experimental finding that the resistivity can be expressed in terms of a universal function of the reduced variables kT/C and ε/εo. The inter-relationship between all the important physical properties of granular metals and their structure is also discussed.     

Nonmonotonicity in the quantum-classical transition: chaos induced by quantum effects

The classical-quantum transition for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative variant Planck's over 2pi is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the double-well Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective variant Planck's over 2pi is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantum-classical transition in this case is nonmonotonic in variant Planck's over 2pi.     

Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO<Subscript>3</Subscript>

We present wavelength- and temperature-dependent refractive index equations for 5% MgO-doped congruent PPLN and for 1% MgO-doped stoichiometric PPLN crystals valid for a wide spectral and temperature range. The dispersion equations were derived from quasi-phase-matched nonlinear interactions with these two crystal compositions in the near and mid-infrared. The results show a good agreement with previously published frequency conversion experiments. PACS 42.65.Ky; 42.65.Yj; 42.70.Mp