Periodic Solutions for Completely Resonant Nonlinear Wave Equations with Dirichlet Boundary Conditions

We consider the nonlinear string equation with Dirichlet boundary conditions u_tt–u_xx=(u), with (u)=u³+O(u⁵) odd and analytic, 0, and we construct small amplitude periodic solutions with frequency for a large Lebesgue measure set of close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). The proof is based on combining the Lyapunov-Schmidt decomposition, which leads to two separate sets of equations dealing with the resonant and non-resonant Fourier components, respectively the Q and the P equations, with resummation techniques of divergent powers series, allowing us to control the small divisors problem. The main difficulty with respect to the nonlinear wave equations u_tt–u_xx+Mu=(u), M0, is that not only the P equation but also the Q equation is infinite-dimensional.     

Electrochemical deposition and structural characterization of Au-Sn alloys

In the present work the electrochemical deposition of Au-Sn alloys is addressed and a cyanide-free process is presented. The electrolyte is an acidic thiourea solution containing gold as a Au[CS(NH₂)₂]⁺ complex and tin as stannous ions. Results concerning the plating process development and deposit characterization are reported. Au-Sn alloy films with a Sn content up to 50 at% and a single-phase structure can be obtained from the acidic thiourea–Au(I) solution under pulsed current plating conditions. Alloy deposits show three main crystal structures: a face centred cubic (fcc) Au(Sn) solid solution, extending up to 7 at% Sn; a hexagonal close-packed structure, of the same type as the metallurgical phase, up to about 18 at% Sn; and a NiAs-type structure, corresponding to the phase of the equilibrium diagram, with an enlarged homogeneity range. Mechanical properties of thin layers of Au-Sn alloys derived from micro-indentation measurements follow the structural modification with the alloy composition. The ordered intermetallic phases occurring in the equilibrium binary system, in particular the and phases at 8 at% and 16 at% Sn, respectively, are not detected in the electrodeposited alloys. The main factors controlling electrochemical phase formation are pointed out, considering the differences between the phase structure of the electrodeposited alloys and the equilibrium phase diagram.Presented at the 3rd International Symposium on Electrochemical Processing of Tailored Materials held at the 53rd Annual Meeting of the International Society of Electrochemistry, 15–20 September 2002, Düsseldorf, Germany     

Phase-locked, time-delayed harmonic pulses for high spectral resolution in the extreme ultraviolet

We present experiments in the time and frequency domains aimed at confirming the measured mutual phase coherence of time-delayed, collinear harmonic pulses. We show that pairs of phase-locked harmonic pulses of medium order can be generated for peak intensities up to ~1.5 10(14)W/cm(2) in xenon, demonstrating the possibility of performing high-resolution spectroscopy in the extreme ultraviolet with Ramsey-like techniques.     

trans‐Decahydronaphthalene (decalin) from powder diffraction data

The title compound, C₁₀H₁₈, a decalin stereoisomer, crystallizes with Z′ = 0.5 in the space group P2₁/n. The trans‐decalin molecule is located on an inversion centre with both rings in a chair conformation, making for a quasi‐flat overall shape. Despite the absence of hydrogen bonds, it crystallizes easily. In this work the unknown crystal structure of trans‐decalin has been solved and refined using X‐ray powder diffraction data.     

Pressure broadening and shift of transitions of the first overtone of HCl

High-resolution spectroscopic measurements were made using distributed feedback diode lasers. We measured line strength and pressure-induced broadening and shift for two lines, R(3) and P(4), of the first overtone (2?0) ro-vibrational band, for the two isotopomers H³⁵Cl and H³⁷Cl, according to their natural abundances; measurements were also made in the presence of foreign gases. Comparison was made with available data when possible. Received: 29 February 2000 / Published online: 8 November 2000     

Catalytic enantioselective alkene epoxidation using novel spirocyclic N-carbethoxy-azabicyclo[3.2.1]octanones

A general synthetic route allowing access to several spirocyclic N-carbethoxy-azabicyclo[3.2.1]octanones is developed. These novel ketones efficiently catalyse alkene epoxidation using Oxone^® with up to 91.5% ee.