Evolution Systems for Differential Equations with Variable Time Lags

We consider nonautonomous retarded functional differential equations under hypotheses which are designed for the application to equations with variable time lags, which may be unbounded, and construct an evolution system of solution operators which are continuously differentiable. These operators are defined on manifolds of continuously differentiable functions. The results apply to pantograph equations and to nonlinear Volterra integro-differential equations, for example. For linear equations we also provide a simpler evolution system with solution operators on a Banach space of continuous functions.     

Comparison of irreversible and reversible cluster formation

Covalent and reversible cluster molecules were synthesized by an A₃B₂ type gelation. Crosslinking of three-arm hydroxyl-terminated star polymers with 2,4-toluenediisocyanate gave branched polymers, while the reversible analogue was made by crosslinking of tertiary amine-terminated star polymers with bis(4-hydroxy-3,5-dinitrophenyl) adipate. Gelation process was followed by static and dynamic light scattering. The extent of reacted groups was measured with UV spectroscopy. Growth of the covalent clusters could be described in terms of percolation scaling laws. The experimental gel point (P_{OH, cr} = 0.70) was shifted significantly from the theoretical predicted gel point (P_{OH, cr} = 0.50), indicating extensive ring formation during the gelation. The reversible endlinking reaction gave no macroscopic gelation, though increase of the cluster dimensions was observed. Ring formation proved to be an important side reaction in both cases; however, the ring formation ability seems to change in a different manner during the course of a gelation.     

OH sensor based on ultraviolet, continuous-wave absorption spectroscopy utilizing a frequency-quadrupled, fiber-amplified external-cavity diode laser

The development of an all-solid-state cw laser system for optical absorption measurements of the OH radical in the UV spectral range is described. The tunable output of a 1064-nm external-cavity diode laser is amplified by use of a Nd:doped, double-clad fiber amplifier. The amplified near-IR radiation is frequency doubled by a periodically poled lithium niobate crystal and then quadrupled in a beta-barium borate crystal. The design and operation of the system and measurements of OH absorption in the (2, 0) band of the A(2)?(+)- X(2)? electronic transition are discussed.     

CH...O and CH...F links form the cage structure of dioxane-trifluoromethane

The molecular beam Fourier transform microwave spectrum of 1,4-dioxane-trifluoromethane has been assigned and measured. The two subunits form a cage stabilized by one C-H...O and two C-H...F weak hydrogen bonds. The C-H...O link involves the axial lone pair of one of the two equivalent ring oxygens, while the two C-H...F bridges connect trifluoromethane to the two axial hydrogens in positions 3 and 5. The dissociation energy has been estimated from the D(J) centrifugal distortion parameter to be approximately 6.8 kJ/mol.