Vinylogous Nicholas Reactions in the Synthesis of Icetexane, Faveline, and Related Ring Systems

The intramolecular vinylogous Nicholas reactions of aryl substituted acetoxy enyne-Co(2)(CO)(6) complexes afford tricyclic 6,7,6-ring systems and related systems in good yield

The frequency map for billiards inside ellipsoids

The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\lambda_1},...,Q_{\lambda_n}$, so the caustic parameters $\lambda=(\lambda_1,...,\lambda_n)$ are integrals of the billiard map. The frequency map $\lambda \mapsto \omega$ is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of $\omega$. The map $\omega$ can be continuously extended to singular values of the caustic parameters, although it becomes "exponentially sharp" at some of them. Finally, we study triaxial ellipsoids of \Rset^3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure

Examining the Underlying Structure of Adult Literacy Practices at Home and Work

Adults have similar literacy habits as children, such as reading to gain knowledge or for enjoyment. However, when workplace literacy skills are considered, these practices are not always book related and usually involve informal communication such as collaboration between workers. This study used data from the 2012 Program for the International Assessment of Adult Competencies to examine adults’ literacy skills. A total of 39 adult literacy skills were examined to explore patterns among them, effectively reducing them to nine interpretable factors. Each factor focused on an area of literacy skills, such as work-related reading, educating others, and writing. The nine factors that consisted of 37 variables accounted for 59.2% of the total variance in the adults’ literacy habits

Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

AMP peptide targets tight junctions to protect and heal barrier structure and function in models of IBD.

Background: A peptide derived from Antrum Mucosal Protein (AMP)-18 (gastrokine-1) reduces the extent of mucosal erosions and clinical severity in mice with dextran sulfate sodium (DSS)-induced colonic injury. The present study set out to determine if AMP peptide was also therapeutic for immune- and cytokine-mediated mouse models of intestinal injury and inflammatory bowel diseases (IBD) by enhancing and stabilizing tight junctions (TJs). Methods: Therapeutic effects of AMP peptide were examined in interleukin-10 deficient and a T cell adoptive transfer models of colitis in immunodeficient recombinase activating gene-1 knock-out (RAG-1−/−) mice. Mechanisms by which AMP peptide enhances barrier function and structure were studied ex vivo using intestine and colon from mice given lipopolysaccharide (LPS), and in AMP-18 deficient mice given DSS. Results: In interleukin-10 deficient mice given piroxicam, AMP peptide enhanced recovery after weight loss, protected against colon shortening and segmental dilation, and reduced the colitis activity score. In the T cell transfer model, treatment with the peptide protected against colon shortening. In mice given LPS in vivo to induce gut injury, AMP peptide prevented the onset of, and reversed established intestinal hyperpermeability by targeting TJ proteins and perijunctional actin

Observation of individual molecules trapped on a nanostructured insulator

For the first time, ordered polar molecules confined in monolayer-deep rectangular pits produced on an alkali halide surface by electron irradiation have been resolved at room temperature by non-contact atomic force microscopy. Molecules self-assemble in a specific fashion inside pits of width smaller than 15 nm. By contrast no ordered aggregates of molecules are observed on flat terraces. Conclusions regarding nucleation and ordering mechanisms are drawn. Trapping in pits as small as 2 nm opens a route to address single molecules