The convergence rate of continued fractions representing solutions of a Riccati equation

The aim of this note is to generalize and apply results on matrix continued fractions representing the solution of discrete matrix Riccati equations. Assuming uniform bounds for the norm of the matrix coefficients of the continued fraction, the minimal and maximal solutions of the corresponding algebraic Riccati equation can be accurately enclosed.     

Lifetimes of Hg(3P0) complexes with methanol,ammonia, and water

Lifetimes of Hg(³P₀) complexes were determined by simultaneous observation of Hg(³P₀) optical absorption and complex emission, using a modulation technique and phase sensitive detection. The lifetimes of the mercury complexes with methanol, (1.4 ± 0.7) × 10^-8 s, and water, ? 8 × 10^-8 s, were found to be much shorter than reported in earlier work. For the ammonia complex, however a lifetime was measured which is in good agreement with previous determinations. Reasons for the large errors in earlier work where the methanol and water complex lifetimes were determined from complex emission data alone are discussed, and these data are reinterpreted. In the reaction rate of Hg(³P₀) with methanol no detectable contribution from the termolecular process Hg(³P₀) + 2CH₃OH → (Hg·CH₃OH)^* + CH₃OH could be observed.     

Template synthesis of a tetraazamacrocyclic ligand with two pendant pyridinyl groups: properties of the isomers of the metal-free ligand and of their first-row transition metal compounds

The one-step reaction of [Cu(en)(2)](2+) (en = 1,2-diaminoethane) with formaldehyde, ethyl 2-pyridyl acetate, and base produces a mixture of [Cu(s-pypymac)](2+) and [Cu(a-pypymac)](2+) (s-pypymac = syn-6,13-bis(2-pyridinyl)-1,4,8,11-tetraazacyclotetradecane, a-pypymac = anti-6,13-bis(2-pyridinyl)-1,4,8,11-tetraazacyclotetradecane; syn-to-anti ratio approximately 1:9) in low yield (6%). Ion exchange chromatography is used for isomer separation, and the two isomers of the metal-free ligand are obtained by reduction of the copper(II) complexes and subsequent ion exchange chromatography. Crystal structure analyses of the metal-free a-pypymac ligand, of two isomeric copper(II) compounds of a-pypymac and one of s-pypymac, and of the cobalt(III) complexes of a- and s-pypymac and nickel(II), as well as zinc(II) complexes of a-pypymac, are reported and discussed on the basis of the expectations from force field calculations and from published experimental data of the transition metal compounds of the bis-pendant amine derivative diammac.     

Saturated high-repetition-rate 18.9-nm tabletop laser in nickellike molybdenum

We report saturated operation of an 18.9-nm laser at 5-Hz repetition rate. An amplification with a gain-length product GL of 15.5 is obtained in the 4d 1S0-4p 1P1 laser line of Ni-like Mo in plasmas heated at grazing incidence with approximately 1-J pulses of 8.1-ps duration from a tabletop laser system. Lasing is obtained over a broad range of time delays and pumping conditions. We also measure a GL of 13.5 in the 22.6-nm transition of the same ion. The results are of interest for numerous applications requiring high-repetition-rate lasers at wavelengths below 20 nm.     

Demonstration of a 100 Hz repetition rate gain-saturated diode-pumped table-top soft x-ray laser

We demonstrate the operation of a gain-saturated table-top soft x-ray laser at 100?Hz repetition rate. The laser generates an average power of 0.15?mW at λ=18.9 nm, the highest laser power reported to date from a sub-20-nm wavelength compact source. Picosecond laser pulses of 1.5?μJ energy were produced at λ=18.9 nm by amplification in a Mo plasma created by tailoring the temporal intensity profile of single pump pulses with 1?J energy produced by a diode-pumped chirped pulse amplification Yb:YAG laser. Lasing was also obtained in the 13.9?nm line of Ni-like Ag. These results increase by an order of magnitude the repetition rate of plasma-based soft x-ray lasers opening the path to milliwatt average power table-top lasers at sub-20?nm wavelengths.