Electronic structure and Fermi surface tolopogy of Nax_xCoO2_2

We construct an effective Hamiltonian for the motion of T2g highly correlated states in NaxCoO2. We solve exactly a multiband model in a CoO6 cluster with electronic occupation corresponding to a nominal Co valence of either +3 or +4. Using the ensuing ground states, we calculate the effective O mediated hopping t=0.10 eV between many-body T2g states, and estimate the direct hopping t'~0.04 eV. The trigonal splitting 3D=0.315 eV is taken from recent quantum chemistry calculations. The resulting effective Hamiltonian is solved using a generalized slave-boson mean-field approximation. The results show a significant band renormalization and a Fermi surface topology that agrees with experiment, in contrast to predictions using the local-density approximation.Comment: 4 pages, 2 figure

An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification

Highly efficient synthesis of the tricyclic core of Taxol by cascade metathesis

An efficient enantioselective synthesis of the ABC tricyclic core of the anticancer drug Taxol is reported. The key step of this synthesis is a cascade metathesis reaction, which leads in one operation to the required tricycle if appropriate fine-tuning of the dienyne precursor is performed

Weak and strong fillability of higher dimensional contact manifolds

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor edits. v3: exposition improved using referee's comments. Published by Invent. Mat

Évaluation du débit réservé par méthodes hydrologiques et hydrobiologiques

Plusieurs méthodes existent pour calculer le débit réservé d'un cours d'eau. Dans la présente étude deux approches sont analysées, soit les approches par méthodes hydrologiques et hydrobiologiques. Cinq méthodes hydrologiques d'évaluation du débit réservé ont été appliquées au ruisseau Catamaran au Nouveau-Brunswick (Canada), ainsi qu'une méthode hydrobiologique. Parmi les méthodes hydrologiques, on retrouve la méthode de Tennant, celle de 25% du débit moyen annuel (DMA), la méthode du débit médian (Q50) mensuel, 90% du débit classé (Q90) et la méthode basée sur l'analyse statistique de fréquence des débits faibles (7Q10). La méthode hydrobiologique utilisée dans la présente étude fut l'application du modèle PHABSIM pour le saumon Atlantique juvénile. Ce modèle est calibré en utilisant les données de vitesse d'écoulement (V), profondeur d'eau (D) et grosseur du substrat (S) pour trois différents débits. L'application des méthodes hydrologiques a démontré que certaines méthodes telle que la méthode Tennant, 25% DMA et la méthode du débit médian, donnent des résultats similaires surtout en période d'étiage. D'autre part, deux méthodes en particulier, soit la méthode de 90% du débit classé et celle basée sur une analyse statistique des débits faibles prédisent un débit réservé très faible en période d'étiage.Une modélisation de l'habitat physique du ruisseau Catamaran démontre que l'habitat disponible maximal se trouve généralement aux environs du débit moyen. De plus, il a été observé qu'en appliquant les modèles hydrologiques, l'habitat disponible était réduit par rapport à l'habitat maximum prédit par PHABSIM. En effet, l'habitat résultant de l'application de Tennant (30% DMA) et du 25% DMA représente environ 70% de l'habitat disponible maximum. Le débit calculé par la méthode du débit médian correspond à un habitat qui n'est que de 50% de l'habitat disponible maximum, tandis que les méthodes basées sur 90% du débit classé et l'analyse statistique des débits faibles ne représentent plus que des habitats de l'ordre de 20% à 40% de l'habitat disponible maximum. L'application de ces deux dernières méthodes laisse beaucoup de doute sur le niveau de protection des habitats aquatiques qu'elles procurent et il a été jugé utile de ne pas les recommander pour l'évaluation du débit réservé dans la région d'étude. Les autres méthodes (Tennant, 25% DMA et Q50) peuvent être utilisées. Cependant, l'application de la méthode du débit médian, qui peut donner des résultats proches de 50% de l'habitat disponible maximum, doit être appliquée avec précaution.Many techniques exist to calculate instream flow requirements. This study considers hydrologically-based techniques and hydrobiological or habitat preference methods. The hydrologically-based techniques use only historical streamflow data, and require little or no field work. Conversely, the habitat preference methods require knowledge of the specific hydraulic conditions of the studied water course and the habitat preferences of the relevant fish species.Five hydrologically-based methods and one habitat preference method were applied to Catamaran Brook, a small drainage basin in New Brunswick, Canada. The hydrologically-based techniques included the Tennant Method, the 25% Mean Annual Flow (MAF), the median monthly flow (Q50), the 90% flow duration method (Q90) and a low-flow frequency method (7Q10). The habitat preference method studied was the PHABSIM model applied for Atlantic salmon.The PHABSIM model was calibrated using the hydraulic characteristics of water depth (D), velocity (V) and substrate (S) for three flows. It was then used to calculate the same physical habitat parameters (D,V,S) for other discharges. The hydraulic results were used with habitat preference (suitability curves) to calculate the potential habitat or weighted usable area (WUA).The application of hydrologically-based in-stream flow techniques showed that methods such as Tennant, 25% MAF and the median monthly flow method provided similar results, especially during low flow periods. The in-stream flow requirement calculated by Tennant Method (30% MAF) was 0.20 m3·s-1, and the 25% MAF represented a value of 0.16 m3·s-1. The application of the Q50 approach yielded results of 0.13 m3·s-1 for the month of August with higher values for other months. In contrast, the 90% flow duration and the low-flow frequency methods established very low discharge for in-stream flow requirements during low-flow periods. The lowest Q90 observed was in September at 0.050 m3·s-1 whereas the months of August, July, October, February and March all showed results slightly higher than September but still lower than 0.10 m3·s-1. The method that calculated the lowest in-stream flow value was the 7Q10 (low-flow frequency) Method with a discharge of only 0.037 m3·s-1. These results (Q90 and 7Q10) represent significantly lower in-stream flow values compared to the Tennant, 25% MAF and the Q50 methods.The application of a habitat model (PHABSIM) at Catamaran Brook showed that the maximum available habitat, expressed as weighted usable area (WUA), was observed at a discharge close to the mean annual flow. Results also showed more habitat for salmon parr than for fry at maximum available habitat (optimal habitat), and this optimal habitat was at a higher flow for parr than for fry. The results from hydrologically-based methods were compared to the maximum value derived from the PHABSIM method. This comparative study showed that habitat was reduced by 30% to 80% of the maximum WUA calculated by PHABSIM depending upon which hydrologically-based in-stream flow technique was applied. Habitat (WUA) resulting from the Tennant and the 25% MAF methods derived flows represents approximately 70% of the maximum available habitat. Results from the application of the median monthly flow method (Q50) showed in-stream flow providing over 50% of maximum available habitat. The 90% flow duration method and low-flow frequency method (7Q10) showed habitat values in the range of 20% to 40% of maximum. The application of these latter two methods clearly limits the available habitat for the protection of aquatic resources and they were therefore not recommended for use in in-stream flow studies in this region. Instead, methods such as Tennant and 25% MAF should be used. The Q50 method may be used with caution as its use results in habitat availability slightly over 50% of maximum WUA

New obstructions to symplectic embeddings

In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.Comment: 80 pages, 3 figures, v2: improved exposition and minor corrections, v3: Final version, expanded and improved exposition and minor corrections. The final publication is available at link.springer.co

Specific Heat Signature of the Berezinskii-Kosterlitz-Thouless Transition in Ultrathin Superconducting Films

The Berezinskii-Kosterlitz-Thouless (BKT) transition is expected to have a clear signature on the specific heat. The singularity at the transition temperature $T_{BKT}$ is predicted to be immeasurable, and a broad non-universal peak is expected at $T>T_{BKT}$. Up to date this has not been observed in two-dimensional superconductors. We use a unique highly sensitive technique to measure the specific heat of ultrathin Pb films. We find that thick films exhibit a specific heat jump at $T_C$ that is consistent with BCS theory. As the film thickness is reduced below the superconducting coherence length and the systems enters the 2D limit the specific heat reveals BKT-like behavior. We discuss these observations in the framework of the continuous BCS-BKT crossover as a function of film thickness.Comment: 5 pages, 4 figure