Amination of ethers using chloramine-T hydrate and a copper(I) catalyst

Amination of C-H bonds activated by ether oxygen atoms is facile with chloramine-T as nitrene source and copper(I) chloride in acetonitrile as catalyst. For cyclic ethers the hemiaminal products are generally stable and can be isolated pure. For acyclic ethers, the hemiaminal products, as expected, fragment with elimination of alcohol to yield imines. When activation of benzylic positions is remote through a conjugated system, stable benzylamine derivatives are isolated. Mechanistic studies are consistent with concerted insertion of an electrophilic nitrenoid into the C-H bond in the rate-determining step, though in an asynchronous manner with a more activated substrate.     

Powers of Euler's Product and Related Identities

Ramanujan's partition congruences can be proved by first showing that the coefficients in the expansions of (q; q) ^r satisfy certain divisibility properties when r = 4, 6 and 10. We show that much more is true. For these and other values of r, the coefficients in the expansions of (q; q) ^r satisfy arithmetic relations, and these arithmetic relations imply the divisibility properties referred to above. We also obtain arithmetic relations for the coefficients in the expansions of (q; q) ^r (q ^t; q ^t) ^s , for t = 2, 3, 4 and various values of r and s. Our proofs are explicit and elementary, and make use of the Macdonald identities of ranks 1 and 2 (which include the Jacobi triple product, quintuple product and Winquist's identities). The paper concludes with a list of conjectures.     

Invariant circles for the piecewise linear standard map

We investigate invariant circles for a one-parameter family of piecewise linear twist homeomorphisms of the annulus. We show that invariant circles of all types and rotation numbers occur and we classify them into families. We compute parameter ranges in which there are no invariant circles.     

Force-Free States, Relative Strain, and Soft Elasticity in Nematic Elastomers

The remarkable ability of nematic elastomers to exhibit large deformations under small applied forces is known as soft elasticity. The recently proposed neo-classical free-energy density for nematic elastomers, derived by molecular-statistical arguments, has been used to model soft elasticity. In particular, the neo-classical free-energy density allows for a continuous spectrum of equilibria, which implies that deformations may occur in the complete absence of force and energy cost. Here we study the notion of force-free states in the context of a continuum theory of nematic elastomers that allows for isotropy, uniaxiality, and biaxiality of the polymer microstructure. Within that theory, the neo-classical free-energy density is an example of a free-energy density function that depends on the deformation gradient only through a nonlinear strain measure associated with the deformation of the polymer microstructure relative to the macroscopic continuum. Among the force-free states for a nematic elastomer described by the neo-classical free energy density, there is, in particular, a continuous spectrum of states parameterized by a pair of tensors that allows for soft deformations. In these force-free states the polymer microstructure is material in the sense that it stretches and rotates with the macroscopic continuum. Limitations of and possible improvements upon the neo-classical model are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Engineering enzyme specificity using computational design of a defined-sequence library

Engineered biosynthetic pathways have the potential to produce high-value molecules from inexpensive feedstocks, but a key limitation is engineering enzymes with high activity and specificity for new reactions. Here, we developed a method for combining structure-based computational protein design with library-based enzyme screening, in which inter-residue correlations favored by the design are encoded into a defined-sequence library. We validated this approach by engineering a glucose 6-oxidase enzyme for use in a proposed pathway to convert D-glucose into D-glucaric acid. The most active variant, identified after only one round of diversification and screening of only 10,000 wells, is approximately 400-fold more active on glucose than is the wild-type enzyme. We anticipate that this strategy will be broadly applicable to the discovery of new enzymes for engineered biological pathways.     

Microviscoelasticity of soft repulsive sphere dispersions: tracer particle microrheology of triblock copolymer micellar liquids and soft crystals

Tracer particle microrheology using diffusing wave spectroscopy-based microrheology is demonstrated to be a useful method to study the dynamics of aqueous Pluronic? F108 solutions, which are viewed as solutions of repulsive soft spheres. The measured zero-shear microviscosity of noncrystallizing micellar dispersions indicates micelle corona dehydration upon increasing temperature. Colloidal sphere thermal motion is shown to be exquisitely sensitive to the onset of crystallization in these micellar dispersions. High temperature dynamics are dominated by an apparent soft repulsive micelle-micelle interaction potential indicating the important role played by lubrication forces and ultimately micelle corona interpenetration and compression at sufficiently high concentrations. The measured microscopic viscoelastic storage and loss moduli are qualitatively similar to those experimentally observed in mechanical measurements on colloidal dispersions and crystals, and calculated from mode coupling theory of colloidal suspensions. The observation of subdiffusive colloidal sphere thermal motion at short time-scales is strong evidence that the observed microscopic viscoelastic properties reflect the dynamics of individual micelles rather than a dispersion of micellar crystallites.     

Bioflocculant production by Virgibacillus sp. Rob isolated from the bottom sediment of Algoa Bay in the Eastern Cape, South Africa

A bioflocculant-producing marine bacterium previously isolated from marine sediment of Algoa Bay was screened for flocculant production. Comparative analysis of 16S rDNA sequence identified the isolate to have 99% similarity to Virgibacillus sp. XQ-1 and it was deposited in the GenBank as Virgibacillus sp. Rob with accession number HQ537127. The bacterium produced biflocculants optimally in glucose (70.4%) and peptone (70.4%) as sole sources of carbon and nitrogen, alkaline pH (12) (74%); and the presence of Fe2+ (74%). Chemical analysis of the bioflocculant revealed it to be a polysaccharide.     

A sulfone-based strategy for the preparation of 2,4-disubstituted furan derivatives

2,4-Disubstituted furans are prepared by treating 2,3-dibromo-1-phenylsulfonyl-1-propene (DBP, 2) with 1,3-diketones under basic conditions. The furan-forming step involves a deacetylation, and the selectivity of this process depends upon the steric demand of the R group. The substituent in position 4 is elaborated by reaction of sulfonyl carbanions with alkyl halides, acyl halides, and aldehydes. Oxidative or reductive desulfonylation produces the 2,4-disubstituted furans in 60-92% yield. This strategy has been used to prepare rabdoketone A (12) and the naturally occurring nematotoxic furoic acid 13.     

Semisimple strata for p-adic classical groups

Let F₀ be a non-archimedean local field, of residual characteristic different from 2, and let G be a unitary, symplectic or orthogonal group defined over F₀. In this paper, we prove some fundamental results towards the classification of the representations of G via types [8]. In particular, we show that any positive level supercuspidal representation of G contains a semisimple skew stratum, that is, a special character of a certain compact open subgroup of G. The intertwining of such a stratum has been calculated in [19].     

Electronic structure and properties of NbS3 and Nb3S4

Electronic structure calculations for NbS₃ and Nb₃S₄ are reported. The NbS₃ structure is closely related to that of ZrSe₃. In the undistorted ZrSe₃ atomic arrangement, NbS₃ would be a metal; it is shown that the observed distortion, a pairing of Nb atoms along the b-axis relative to ZrSe₃, stabilizes the NbS₃ crystal by inducing a 0.5-eV semiconducting gap. Nb₃S₄ is found to be a metal with the Fermi level lying near a deep minimum in the density of electron states.