Nonmetrizable ANR's admitting a group structure are manifolds

It is shown that a nonmetrizable ANR-space of weight τ>ω, admitting a group structure, is (topologically) an Rτ-manifold.     

Weakly dependent chains with infinite memory

We prove the existence of a weakly dependent strictly stationary solution of the equation _Xt=F(_Xt−1,_Xt−2,_Xt−3,…;_ξt)$X_t=F(X_{t-1},X_{t-2},X_{t-3},\dots ;{\xi }_t)$ called a chain with infinite memory. Here the innovations  _ξt${\xi }_t$ constitute an independent and identically distributed sequence of random variables. The function F$F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments, the rate of decay of the Lipschitz coefficients of the function F$F$ and the weak dependence properties. From these weak dependence properties, we derive strong laws of large number, a central limit theorem and a strong invariance principle.     

Local-to-global spectral sequences for the cohomology of diagrams

We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings.     

One-parameter toric deformations of cyclic quotient singularities

In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions introduced by Altmann [Minkowski sums and homogeneous deformations of toric varieties, Tohoku Math. J. (2) 47 (2) (1995) 151-184.]. In particular, we show how to induce each deformation from a versal family, describe exactly to which reduced versal base space components each such deformation maps, describe the singularities in the general fibers, and construct the corresponding partial simultaneous resolutions.     

Multiplicity-free representations of symmetric groups

Building on work of Saxl, we classify the multiplicity-free permutation characters of all symmetric groups of degree 66 or more. A corollary is a complete list of the irreducible characters of symmetric groups (again of degree 66 or more) which may appear in a multiplicity-free permutation representation. The multiplicity-free characters in a related family of monomial characters are also classified. We end by investigating a consequence of these results for Specht filtrations of permutation modules defined over fields of prime characteristic.     

On the multiplicity and the Cohen-Macaulayness of fiber cones of graded algebras

Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J. Let S=?_n≥0S_n be a finitely generated standard graded algebra over A. Set S⁺=?_n>0S_n. Denote by F_J(S)=?_n≥0→(S_n/JS_n) the fiber cone of S with respect to J. The paper characterizes the multiplicity and the Cohen-Macaulayness of F_J(S) in terms of minimal reductions of S⁺.     

A new amino amidine derivative from the wood-decaying fungus Xylaria cf. cubensis SWUF08-86

The secondary metabolites of Xylaria cf. cubensis SWUF08-86 fungus were investigated, and the chromatographic separation of the crude extracts yielded seventeen compounds. The structure elucidation by spectroscopic analysis including 1D and 2D NMR and the comparison of these data with literature, along with HREIMS spectrometry, revealed one new amino amidine derivative (1), together with five known simple cyclic dipeptide analogs, diketopiperazines (2–6) and eleven other known compounds, including one hemi-cycline (10), three aromatic derivatives (11–13), one sesquiterpene (14) and three sterols (15–17). The isolated compounds were screened for anticancer and anti-pathogenic bacterial and fungal activities. Based on this work, Xylaria cf. cubensis SWUF08-86 has proven to be a diverse secondary metabolites producer.     

A novel phenylspirodrimane dimer from cultures of the fungus Stachybotrys chartarum

Stachartone A (1), a novel phenylspirodrimane dimer, was isolated from cultures of the tin mine tailings-associated fungus Stachybotrys chartarum. Its structure was elucidated by means of spectroscopic methods. At the same time, compound (1) was tested for its cytotoxicity against five human cancer cell lines.     

Helix Induction by Dirhodium: Access to Biocompatible Metallopeptides with Defined Secondary Structure

The use of carboxylate side chains to induce peptide helicity upon binding to dirhodium centers is examined through experimental and computational approaches. Dirhodium binding efficiently stabilizes α helicity or induces α helicity in otherwise unstructured peptides for peptides that contain carboxylate side chains with i, i+4 spacing. Helix induction is furthermore possible for sequences with i, i+3 carboxylate spacing, though in this case the length of the side chains is crucial: ligating to longer glutamate side chains is strongly helix inducing, whereas ligating the shorter aspartate side chains destabilizes the helical structure. Further studies demonstrate that a dirhodium metallopeptide complex persists for hours in cellular media and exhibits low toxicity toward mammalian cells, enabling exploitation of these metallopeptides for biological applications.