Viscosity approximation methods for pseudo-contractive semigroups in Banach spaces

We study the strong convergence of two viscosity iteration processes for pseudo-contractive semigroup and for ?$?$-strongly pseudo-contractive mapping in uniformly convex Banach spaces with uniformly Gâteaux differentiable norm. As special cases, we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain Banach spaces. The results presented in this paper extend and generalize previous results.     

Low loss propagation in slow light photonic crystal waveguides at group indices up to 60

We have designed slow light photonic crystal waveguides operating in a low loss and constant dispersion window of Δλ = 2 nm around λ = 1565 nm with a group index of n_g = 60. We experimentally demonstrate a relatively low propagation loss, of 130 dB/cm, for waveguides up to 800 μm in length. This result is particularly remarkable given that the waveguides were written on an electron-beam lithography tool with a writefield of 100 μm that exhibits stitching errors of typically 10–50 nm. We reduced the impact of these stitching errors by introducing “slow–fast–slow” mode conversion interfaces and show that these interfaces reduce the loss from 320 dB/cm to 130 dB/cm at n_g = 60. This significant improvement highlights the importance of the slow–fast–slow method and shows that high performance slow light waveguides can be realised with lengths much longer than the writing field of a given e-beam lithography tool.     

Time-resolved chirp measurement for 100GBaud test systems using an ideal frequency discriminator

In this paper we present multi-channel chirp measurements of wide-band sources, using a programmable Fourier-domain optical processor (FDOP) as a near-perfect linear frequency discriminator element followed by a fast photodiode and electrical sampling oscilloscope. The electric field of a 10.7 Gbit/s phase-encoded data source and a directly modulated laser diode are simultaneously interrogated with this measurement system. The constellation diagram of the phase-encoded data source is demonstrated, and a comparison with another phase-sensitive measurement technique is performed. Additionally, an extension to this technique is demonstrated in which the time-resolved chirp of a picosecond-duration mode-locked laser diode with a 260 GHz spectral bandwidth is characterised using the FDOP and a high-bandwidth optical sampling oscilloscope. This measurement ensemble has sufficient temporal resolution to characterise random or repetitive data signals up to 100GBaud.     

Application of the lithiation-borylation reaction to the rapid and enantioselective synthesis of the bisabolane family of sesquiterpenes

The expedient enantioselective synthesis of 5 bisabolane sesquiterpenes has been achieved using a common, one-pot lithiation-borylation reaction of secondary benzylic carbamates and either protodeboronation or oxidation to give the natural products in fewer than 5 steps, with high yield and >94?:?6 er.     

Core temperature and density profile measurements in inertial confinement fusion implosions

We have measured time-integrated and time-gated electron temperature (T_e) and density (N_e) spatial profiles from indirect-drive implosions. In our experiments, we used a multiple-pinhole two-dimensional imaging spectrometer to obtain multispectral X-ray images of the imploded core. Quantitative comparisons between quasi-monochromatic images in different energy bands allowed T_e and N_e spatial profiles to be determined using two independent and validated techniques: a multi-objective search and reconstruction analysis, and an analytical analysis. We then compared the results to a simple one-dimensional (1D) mix-free hydrodynamics simulation in order to evaluate the ability of such a model to predict our experiments. Our data show spatial T_e profiles that are qualitatively consistent with the predictions of our 1D simulations, but we observe central cores that are 10–25% cooler and emit X-rays as late as 200 ps after peak compression. We infer time-gated spatial N_e profiles that are consistent with our 1D simulations near the times of peak compression, but we find significant disagreement between time-integrated data and 1D simulation predictions at large radii. Careful analysis of the time-gated and time-integrated T_e and N_e spatial profiles, together with streaked X-ray emission spectra from core and shell dopants, suggests mixing of shell material into the core is an important process that our 1D hydrodynamics simulations fail to capture, and comparison between image data and a simple analytical model suggests that 2–5 μm of the initial inner shell thickness mixes into the core during the time period of significant X-ray emission. This mix width is consistent with the predictions of a growth-factor analysis that treats instability growth seeded by capsule surface roughness, and points to the need to consider time-dependent mixing effects when interpreting T_e and N_e spatial profiles derived from multispectral X-ray image data, particularly at large radii where mixing effects will be most significant.     

A new μs isomer in 136Sb produced in the projectile fission of 238U

Rapidity correlations in 800 GeV proton interactions with emulsion nuclei are investigated for different targets and multiplicity regions. To study the energy dependence, the results have been compared with proton interactions at 200 GeV and 400 GeV. A common feature of all the interactions is the existence of strong, short-range correlations. However, no dependence of cluster parameters on primary energy or target mass is found. A marginal increase of correlation strength with multiplicity is observed. Received: 30 March 2001 / Accepted: 18 September 2001     

cis‐Tetra­carbonyl­[(4‐fluoro­phenyl)di­phenyl­phosphine‐P](piperidine‐N)molybdenum(0)

The title mol­ecule, [Mo{P(C₆H₅)₂(C₆H₄F)}(HNC₅H₁₀)(CO)₄] or [Mo(C₁₈H₁₄FP)(C₅H₁₁N)(CO)₄], has irregular octahedral geometry about the Mo atom. The mol­ecules form a complicated hydrogen‐bonded network comprising C—H?O, C—H?F and C—H?π hydrogen bonds and π–π interactions. The C—H?π and π–π interactions form chains containing C—H?π/π–π dimers linked via C—H?π interactions and the chains are linked into a three‐dimensional network via C—H?O and C—H?F hydrogen bonds.     

Yrast band spectroscopy of132Sm and130Nd

The states in the yrast band of¹³² Sm have been identified for the first time up to J^π=16⁺. The yrast band of¹³⁰Nd has also been extended from J^π=16⁺ to 24⁺. The energy of the first 2⁺ state in¹³²Sm indicates that the quadrupole deformation ε₂ ～ 0.3 and is still increasing as the neutron number N decreases across the samarium isotopes. The results for¹³⁰Nd allow the (h_2/11)² proton crossing frequency to be determined as ω=0.325 ± 0.005 MeV/?. This result is compared with cranked shell model predictions.