A note on Reeb dynamics on the tight 3-sphere

We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. Moreover, in this case the Floquet multipliers and Conley-Zehnder indices of the two Reeb orbits agree with those of a suitable irrational ellipsoid in 4-space.Comment: 20 pages, no figure

Error training: an examination of metacognition, emotion control, intrinsic motivation, and knowledge as mediators of performance effects

Error Management Training (EMT) is a method of training that encourages trainees to make errors during training and to view those errors as beneficial for learning. Previous research has shown support for the benefits of EMT on metacognition, emotion control, intrinsic motivation and transfer performance compared to traditional error avoidant training. Also, previous research has found support for the mediating effects of metacognition and emotion control on the training type (i.e., EMT vs. error avoidant) and transfer performance relationship. However, previous research has not determined whether the increased metacognition, emotion control, and intrinsic motivation of EMT individuals has its effects on transfer performance through only increased knowledge or whether the effects are partially independent of knowledge differences. Therefore, the purpose of the current study was to examine whether the increased metacognition, emotion control, and intrinsic motivation that result from EMT influence transfer performance holding constant any differences in knowledge acquisition. The proposed investigation manipulated the knowledge that individuals acquired from the training such that participants in the EMT group and an error-tailored avoidant group were exposed to the same information during training. These two groups were compared to participants in a control group who received error avoidant training. Consistent with the hypotheses, participants in the EMT group had higher levels of metacognition, emotion control and intrinsic motivation than participants in the error-tailored avoidant group. Results of the study suggested that participants in the EMT group had more task knowledge than participants in the error avoidant group, but did not differ from participants in the error-tailored avoidant group. Similar to previous studies, the current study showed that participants in the EMT condition demonstrated higher levels of transfer performance than the error avoidant or the error-tailored avoidant training conditions. A comparison of the EMT and the error avoidant training groups showed that the effect on transfer performance was partially mediated by task knowledge and a comparison of the EMT and the error-tailored avoidant groups indicated that the effect on transfer performance was mediated by emotion control. Implications, limitations, and areas for future research are discussed

The Minimal Length of a Lagrangian Cobordism between Legendrians

To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a $1$-dimensional measurement of the non-cylindrical portion of the cobordism. Our primary tool is a set of real-valued capacities for a Legendrian submanifold, which are derived from a filtered version of Legendrian Contact Homology. Relationships between capacities of Legendrians at the ends of a Lagrangian cobordism yield lower bounds on the length of the cobordism. We apply the capacities to Lagrangian cobordisms realizing vertical dilations (which may be arbitrarily short) and contractions (whose lengths are bounded below). We also study the interaction between length and the linking of multiple cobordisms as well as the lengths of cobordisms derived from non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee comments. More general statement in Proposition 3.3 and some reorganization at the end of Section

Historical and paleo-tsunami deposits on Kamchatka, Russia: long-term chronologies and long-distance correlations

Along the eastern coast of Kamchatka, at a number of localities, we have identified and attempted to assign ages to deposits of both historic and prehistoric (paleo-) tsunamis. These deposits are dated and correlated using tephrochronology from Holocene marker tephra and local volcanic ash layers. Because the historical record of earthquakes and tsunamis on Kamchatka is so short, these investigations can make important contributions to evaluating tsunami hazards. Moreover, because even the historical record is spotty, our work helps add to and evaluate tsunami catalogues for Kamchatka. Furthermore, tsunami deposits provide a proxy record for large earthquakes and thus are important paleoseismological tools. The combined, preserved record of tsunami deposits and of numerous marker tephra on Kamchatka offers an unprecedented opportunity to study tsunami frequency. Using combined stratigraphic sections, we can examine both the average frequency of events for each locality, and also changes in frequency through time. Moreover, using key marker tephra as time lines, we can compare tsunami frequency and intensity records along the Kamchatka subduction zone. Preliminary results suggest real variations in frequency on a millennial time scale, with the period from about 0 to 1000 A.D. being particularly active at some localities

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

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