On the cotangent cohomology of rational surface singularities with almost reduced fundamental cycle

We prove dimension formulas for the cotangent spaces $T^{1}$ and $T^{2}$ for a class of rational surface singularities by calculating a correction term in the general dimension formulas. We get that it is zero if the dual graph of the rational surface singularity $X$ does not contain a particular type of configurations, and this generalizes a result of Theo de Jong stating that the correction term $c(X)$ is zero for rational determinantal surface singularities. In particular our result implies that $c(X)$ is zero for Riemenschneiders quasi-determinantal rational surface singularities, and this also generalise results for qoutient singularities.Comment: 11 pages, one figur

Scale-Dependent Habitat Selection of Nesting Great Egrets and Snowy Egrets

Foraging habitat selection of nesting Great Egrets ( Ardea alba ) and Snowy Egrets ( Egretta thula ) was investigated within an estuary with extensive impounded salt marsh habitat. Using a geographic information system, available habitat was partitioned into concentric bands at five, ten, and 15 km radius from nesting colonies to assess the relative effects of habitat composition and distance on habitat selection. Snowy Egrets were more likely than Great Egrets to depart colonies and travel to foraging sites in groups, but both species usually arrived at sites that were occupied by other wading birds. Mean flight distances were 6.2 km (SE = 0.4, N = 28, range 1.8-10.7 km) for Great Egrets and 4.7 km (SE = 0.48, N = 31, range 0.7-12.5 km) for Snowy Egrets. At the broadest spatial scale both species used impounded (mostly salt marsh) and estuarine edge habitat more than expected based on availability while avoiding unimpounded (mostly fresh water wetland) habitat. At more local scales habitat use matched availability. Interpretation of habitat preference differed with the types of habitat that were included and the maximum distance that habitat was considered available. These results illustrate that caution is needed when interpreting the results of habitat preference studies when individuals are constrained in their choice of habitats, such as for central place foragers

Vegetation Effects on Fish Distribution in Impounded Salt Marshes

We compared the density and biomass of resident fish in vegetated and unvegetated flooded habitats of impounded salt marshes in the northern Indian River Lagoon (IRL) Estuary of east-central Florida. A 1-m2 throw trap was used to sample fish in randomly located, paired sample plots (n = 198 pairs) over 5 seasons in 7 impoundments. We collected a total of 15 fish taxa, and 88% of the fishes we identified from the samples belonged to three species: Cyprinodon variegatus (Sheepshead Minnow), Gambusia holbrooki (Eastern Mosquitofish), and Poecilia latipinna (Sailfin Molly). Vegetated habitat usually had higher density and biomass of fish. Mean fish density (and 95% confidence interval) for vegetated and unvegetated sites were 8.2 (6.7–9.9) and 2.0 (1.6–2.4) individuals m-2, respectively; mean biomass (and 95% confidence interval) for vegetated and unvegetated sites were 3.0 (2.5–3.7) and 1.1 (0.9–1.4) g m-2, respectively. We confirmed previous findings that impounded salt marshes of the northern IRL Estuary produce a high standing stock of resident fishes. Seasonal patterns of abundance were consistent with fish moving between vegetated and unvegetated habitat as water levels changed in the estuary. Differences in density, mean size, and species composition of resident fishes between vegetated and unvegetated habitats have important implications for movement of biomass and nutrients out of salt marsh by piscivores (e.g., wading birds and fishes) via a trophic relay

Phase-locking in Multi-Frequency Brillouin Oscillator via Four Wave Mixing

Stimulated Brillouin scattering (SBS) and Kerr-nonlinear four wave-mixing (FWM) are among the most important and widely studied nonlinear effects in optical fibres. At high powers SBS can be cascaded producing multiple Stokes waves spaced by the Brillouin frequency shift. Here, we investigate the complex nonlinear interaction of the cascade of Stokes waves, generated in a Fabry-Perot chalcogenide fibre resonator through the combined action of SBS and FWM. We demonstrate the existence of parameter regimes, in which pump and Stokes waves attain a phase-locked steady state. Real-time measurements of 40ps pulses with 8GHz repetition rate are presented, confirming short-and long-term stability. Numerical simulations qualitatively agree with experiments and show the significance of FWM in phase-locking of pump and Stokes waves. Our findings can be applied for the design of novel picosecond pulse sources with GHz repetition rate for optical communication systems

Birefringence and polarisation mode-dispersion in spun single-mode fibres

A theoretical and experimental analysis of the polarization properties of twisted single-mode fibers is presented. It is shown that whereas a conventionally twisted fiber possesses considerable optical rotation, a fiber which has a permanent twist imparted by spinning the preform during fiber drawing exhibits almost no polarization anisotropy. It is thus possible to virtually eliminate the commonly observed fiber linear birefringence. As a consequence, fibers made in this way are ideally suited for use in the Faraday-effect current transducer. It is further shown that a permanent twist of a few turns/meter effectively eliminates polarization mode-dispersion. The technique therefore appears attractive for enhancing the bandwidth of very long unrepeatered telecommunication links

All-fiber optical parametric oscillator pumped by an all-fiber Yb-based MOPA

We report on an all-fiber PCF-based optical parametric oscillator, synchronously pumped by an all-fiber Yb-doped MOPA. A pump-to-anti-Stokes conversion efficiency of 8.6% is reached at a frequency-shift of 142 THz

Deterministic Raman crosstalk effects in amplified wavelength division multiplexing transmission

We study the deterministic effects of Raman-induced crosstalk in amplified wavelength division multiplexing (WDM) optical fiber transmission lines. We show that the dynamics of pulse amplitudes in an N-channel transmission system is described by an N-dimensional predator-prey model. We find the equilibrium states with non-zero amplitudes and prove their stability by obtaining the Lyapunov function. The stability is independent of the exact details of the approximation for the Raman gain curve. Furthermore, we investigate the impact of cross phase modulation and Raman self and cross frequency shifts on the dynamics and establish the stability of the equilibrium state with respect to these perturbations. Our results provide a quantitative explanation for the robustness of differential-phase-shift-keyed WDM transmission against Raman crosstalk effects.Comment: 34 pages and 12 figures. Revised paper. Submitted to Optics Communication