Examples of signature (2,2) manifolds with commuting curvature operators

We exhibit Walker manifolds of signature (2,2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the Walker metric is a Riemannian extension of an underlying affine structure A, these properties are related to the Ricci tensor of A

Density and reproductive characteristics of female brown bears in the Cantabrian Mountains, NW Spain

Here we present annual nearest-neighbour distances (as a proxy of density) between females with cubs-of-the-year (hereafter FCOY) and reproductive characteristics of brown bears Ursus arctos in the Cantabrian Mountains (NW Spain), from 1989 to 2017. FCOY nearest-neighbour distances and reproduction parameters of 19 focal females followed over several consecutive years (from 2004 to 2017) were obtained from bears inhabiting the western sector of the Cantabrian Mountains, where most of the bear population resides. In contrast, general reproductive characteristics were studied in the whole Cantabrian Mountains (western and eastern sectors together) on a sample of 362 litter sizes and 695 cubs. Mean nearest-neighbour distance between FCOY was 2559 ± 1222 m (range = 1305–4757 m). Mean litter size was significantly larger in the west (1.8 ± 0.2 cubs) than in the east (1.3 ± 0.6 cubs). Mean litter size for the whole of the Cantabrian Mountains was 1.6 ± 0.3 cubs. Litter sizes of one, two and three cubs represented 33.4, 56.1 and 10.5% of observed family groups, respectively. Interannual variations in litter size were not significant for both the western and the eastern areas. Mean cub mortality was 0.2 ± 0.5 cubs and did not vary among years. Cub mortality per litter size was 3.9% for one cub, 69.2% for two cubs and 26.9% for three cubs. Mean reproductive rate of the 19 focal females was 1.5 ± 0.6 cubs (n = 58 litters). Litter size of focal FCOY did not differ from the litter size obtained from systematic observations in the whole Cantabrian Mountains. During this period, cub mortality occurred in 24.1% of the 58 litters. Females usually bred every second year (average litter interval = 2.2 years). The estimated reproductive rate for the bear population was 0.7 young born/year/reproductive adult female

Fabry-Perot method for the characterization of integrated optical directional couplers

A method to measure the loss and the power-transfer ratio of directional couplers is presented. It is based on the Fabry-Perot resonances from end-facet reflections. The dependence of the accuracy of the measurements on the facet tilts is described. For low facet misalignments, an uncertainty <0.3 dB in the loss measurements and power-transfer-ratio measurement errors <1% are obtained. For arbitrary facet tilts the errors depend on the extinction ratios. Experimental measurements are reported to verify the method, and its application to multimode interference couplers is shown.Publicad