Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space

We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceH _? ⁿ . We show that there exists a Γ-invariant real hypersurfaceF ?H _? ⁿ such that the Dirichlet fundamental polyhedron for Γ centered at z₀ has two sides (resp. infinitely many sides) if and only ifz ₀ ∈F (resp.z ₀ ?F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofH _? ⁿ is developed in terms of these horospherical coordinates.     

Regioselectivity of rhodium nitrene insertion. Syntheses of protected glycals of l-daunosamine, d-saccharosamine, and l-ristosamine

[reaction: see text] The carbamate-protected glycals of naturally occurring 3,4-cis-3-amino-2,3,6-trideoxyhexoses (l-daunosamine, d-saccharosamine, and l-ristosamine) were prepared from noncarbohydrate starting materials. The short, high-yield syntheses are based on the chemoselective insertion of a rhodium nitrene in an allylic C-H bond rather than in a C-H bond that is alpha to an oxygen substituent.     

Lanthanide macrocyclic quinolyl conjugates as luminescent molecular-level devices.

The Eu(III) tetraazamacrocyclic complexes [Eu.1] and [Eu.2], and the Tb(III) and Yb(III) complexes [Tb.1] and [Yb.2], have been synthesized as luminescent molecular-level devices. The Eu complexes exhibit unique dual pH switching behavior in water under ambient conditions. The delayed Eu emission is reversibly switched on in acid, with an enhancement factor of several hundred for [Eu.1]. These observations are consistent with the protonation of the quinoline aryl nitrogen moiety (pK(a) approximately equal to 5.9 for [Eu.1]). The fluorescence emission spectra of these complexes are unaffected by acid, but pronounced changes occur in alkaline solution due to the deprotonation of the aryl amide nitrogen (pK(a) approximately 9.4 for [Eu.1]). [Tb.1] shows a more intriguing pH dependence; Tb emission is switched "on" only in the presence of H+ and in the absence of molecular oxygen, whereas the fluorescence emission properties are similar to those observed with [Eu.1]. This behavior can be conveniently described as a molecular-level logic gate, corresponding to a two-input INHIBIT function, A wedge B'. The analogous [Yb.2] complex shows no such pH or O(2) dependence.     

Study of hadronic events inpp collisions at\sqrt s = 62GeV and comparison with hadronic events ine + e − collisions

We present an analysis of minimum bias events from proton-proton collisions at \(\sqrt s = 7GeV\) in the CERN ISR. We remove the effects of both the leading protons and compare theB=0 mesonic residue of the events to the hadronic events of similar energy produced ine ⁺ e ^? collisions. This comparison is presented in terms of the standard jet-type analyses involving quantities such as sphericity and aplanarity. We find significant differences between these data and the data frome ⁺ e ^? annihilations. The data of this experiment are consistent with the predictions of a longitudinal phase space model.     

Scaling laws in simple and complex proteins: size scaling effects associated with domain number and folding class

The native states of the most compact globular proteins have been described as being in the so-called “collapsed-polymer regime,” characterized by the scaling law R _g ~ n ^ν, where R _g is radius of gyration, n is the number of residues, and ν ≈ 1/3. However, the diversity of folds and the plasticity of native states suggest that this law may not be universal. In this work, we study the scaling regimes of: (i) one to four-domain protein chains, and (ii) their constituent domains, in terms of the four major folding classes. In the case of complete chains, we show that size scaling is influenced by the number of domains. For the set of domains belonging to the all-α, all-β, α/β, and α?+?β folding classes, we find that size-scaling exponents vary between 0.3?≤?ν?≤?0.4. Interestingly, even domains in the same folding class show scaling regimes that are sensitive to domain provenance, i.e., the number of domains present in the original intact chain. We demonstrate that the level of compactness, as measured by monomer density, decreases when domains originate from increasingly complex proteins.     

Proper Orthogonal Decomposition of Flexible Clap and Fling Elastic Motions via High-Speed Deformation Measurements

Many complex unsteady mechanisms are thought to facilitate the high efficiency and agility commonly observed in small biological flyers. One of these, the flexible clap and fling maneuver, has not been extensively studied; an experimental characterization is the focus of this work. The clap–fling mechanism is approximated with a single flexible membrane flapping wing, replacing the symmetry plane between two wings with a splitter plate simulating the pair wing. This produces a complex vibro-impact aeroelastic problem, the deformation resulting from which is measured with a high-speed visual image correlation system. A low-dimensional representation of the ensuing large data set is obtained with proper orthogonal decomposition. The POD modes, and the relative importance of each, can help elucidate crucial mechanisms and relationships within the flapping system, and are computed for various membrane wing structures and flapping frequencies, with or without the presence of the splitter plate.     

Exploded manifolds

This paper provides an introduction to exploded manifolds. The category of exploded manifolds is an extension of the category of smooth manifolds with an excellent holomorphic curve theory. Each exploded manifold has a tropical part which is a union of convex polytopes glued along faces. Exploded manifolds are useful for defining and computing Gromov–Witten invariants relative to normal crossing divisors, and using tropical curve counts to compute Gromov–Witten invariants.