On pathwise uniqueness for reflecting Brownian motion in C1+γC^{1+\gamma} domains

Pathwise uniqueness holds for the Skorokhod stochastic differential equation in $C^{1+\gamma}$ domains in $\mathbb{R}^d$ for $\gamma >1/2$ and $d\geq3$.Comment: Published in at http://dx.doi.org/10.1214/08-AOP390 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Pump-probe detuning dependence of four-wave mixing pulse in an SOA

Four-wave mixing (FWM) between 2-ps pulses in a multiquantum-well semiconductor optical amplifier (SOA) is presented. The conjugate pulses are fully characterized using the frequency-resolved optical gating technique. The detuning between the pump and probe is varied, leading to a compression of the FWM signal from 3.71 to 2.77 ps as the detuning is increased from 5 to 25 nm. The output conjugate pulse is always broader than the injected probe signal due to gain saturation effects. A reshaping of the conjugate pulse is also measured. However, large nonlinearities are introduced to the frequency chirp across the pulse for large detunings which may degrade the performance of four-wave-mixing-based all-optical processing applications in SOAs

Probing spatial homogeneity with LTB models: a detailed discussion

Do current observational data confirm the assumptions of the cosmological principle, or is there statistical evidence for deviations from spatial homogeneity on large scales? To address these questions, we developed a flexible framework based on spherically symmetric, but radially inhomogeneous Lemaitre-Tolman-Bondi (LTB) models with synchronous Big Bang. We expanded the (local) matter density profile in terms of flexible interpolation schemes and orthonormal polynomials. A Monte Carlo technique in combination with recent observational data was used to systematically vary the shape of these profiles. In the first part of this article, we reconsider giant LTB voids without dark energy to investigate whether extremely fine-tuned mass profiles can reconcile these models with current data. While the local Hubble rate and supernovae can easily be fitted without dark energy, however, model-independent constraints from the Planck 2013 data require an unrealistically low local Hubble rate, which is strongly inconsistent with the observed value; this result agrees well with previous studies. In the second part, we explain why it seems natural to extend our framework by a non-zero cosmological constant, which then allows us to perform general tests of the cosmological principle. Moreover, these extended models facilitate explorating whether fluctuations in the local matter density profile might potentially alleviate the tension between local and global measurements of the Hubble rate, as derived from Cepheid-calibrated type Ia supernovae and CMB experiments, respectively. We show that current data provide no evidence for deviations from spatial homogeneity on large scales. More accurate constraints are required to ultimately confirm the validity of the cosmological principle, however.Comment: 18 pages, 12 figures, 2 tables; accepted for publication in A&

Pulse pedestal suppression using four-wave mixing in an SOA

Experimental results are presented demonstrating how four-wave mixing in a semiconductor optical amplifier can be used to remove pulse pedestals introduced due to nonlinearities which occur upon pulse propagation in an optical system. Such pedestals would degrade the performance of an optical time-division-multiplexed system due to coherent interaction between channels. An improvement of the temporal pulse suppression ratio to greater than 30 dB is achieved regardless of the level of the pulse pedestal on the input signal. This improvement takes place simultaneously with wavelength conversion and compression of the optical pulse

Recursion relations for Hylleraas three-electron integral

Recursion relations for Hylleraas three-electron integral are obtained in a closed form by using integration by parts identities. Numerically fast and well stable algorithm for the calculation of the integral with high powers of inter-electronic coordinates is presented.Comment: 12 pages, requires RevTeX4, submitted to Phys. Rev.

Correlated exponential functions in high precision calculations for diatomic molecules

Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional integral representation is found, which is suited for the numerical evaluation. Together with recurrence relations, it makes possible the calculation of the two-center two-electron integral with arbitrary powers of electron distances. Alternative approach via the Taylor series in the internuclear distance is also investigated. Although numerically slower, it can be used in cases when recurrences lose stability. Separate analysis is devoted to molecular integrals with integer powers of interelectronic distances $r_{12}$ and the vanishing corresponding nonlinear parameter. Several methods of their evaluation are proposed.Comment: 26 pages, includes two tables with exemplary calculation

Extended Hylleraas three-electron integral

A closed form expression for the three-electron Hylleraas integral involving the inverse quadratic power of one inter-particle coordinate is obtained, and recursion relations are derived for positive powers of other coordinates. This result is suited for high precision calculations of relativistic effects in lithium and light lithium-like ions.Comment: Submited to Phys. Rev.