Closures of positive braids and the Morton-Franks-Williams inequality

We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is an orthonormal basis for the inner product of the Hecke algebra of the braid group defined by Kálmán, who first obtained this result by using an interesting connection with Contact Topology. We also introduce a new technique to study the Homflypt polynomial for closures of positive braids, namely resolution trees whose leaves are simple braids. In terms of these simple resolution trees, we characterize closed positive braids for which the Morton-Franks-Williams inequality is strict. In particular, we determine explicitly the positive braid words on three strands whose closures have braid index three.

Juvenile–adult tree associations in a continental Mediterranean ecosystem: no evidence for sustained and general facilitation at increased aridity

Question: How do tree species identity, microhabitat and water availability affect inter- and intra-specific interactions between juvenile and adult woody plants? Location: Continental Mediterranean forests in Alto Tajo Natural Park, Guadalajara, Spain. Methods: A total of 2066 juveniles and adults of four co-occurring tree species were mapped in 17 plots. The frequency of juveniles at different microhabitats and water availability levels was analysed using log-linear models. We used nearest-neighbour contingency table analysis of spatial segregation and J-functions to describe the spatial patterns. Results: We found a complex spatial pattern that varied according to species identity and microhabitat. Recruitment was more frequent in gaps for Quercus ilex, while the other three species recruited preferentially under shrubs or trees depending on the water availability level. Juveniles were not spatially associated to conspecific adults, experiencing segregation from them inmany cases. Spatial associations, both positive and negative, were more common at higher water availability levels. Conclusions: Our results do not agree with expectations from the stressgradient hypothesis, suggesting that positive interactions do not increase in importance with increasing aridity in the study ecosystem. Regeneration patterns are species-specific and depend on microhabitat characteristics and dispersal strategies. In general, juveniles do not look for conspecific adult protection. This work contributes to the understanding of species co-existence, proving the importance of considering a multispecies approach at several plots to overcome limitations of simple pair-wise comparisons in a limited number of sites.

Seismic modelling and ava analysis of hidrocarbon traps

In this study, forward seismic modelling of four geological models with Hydrocarbon (HC) traps were performed by ray tracing method to produce synthetic seismogram of each model. The idea is to identify the Hydrocarbon Indicators (HCI‟s) such as bright spot, flat spot, dim spot and Bottom Simulating Reflector (BSR) in the synthethic seismogram. The modelling was performed in DISCO/FOCUS 5.0 seismic data processing programme. Strong positive and negative reflection amplitudes and some artifact reflection horizons were observed on produced seismograms due to rapid changes in subsurface velocity and geometry respectively Additionally, Amplitude-versus-angle (AVA) curves of each HCIs was calculated by the Crewes Zoeppritz Explorer programme. AVA curves show that how the reflection coefficients change with the density and the P and S wave velocities of each layer such as oil, gas, gas hydrate or water saturated sediments. Due to AVA curves, an increase in reflection amplitude with incident angle of seismic waves corresponds to an indicator of a hydrocarbon reservoir