Twisted hopf comodule algebras

For k a commutative ring, H a k‐bialgebra and A a right H‐comodule k‐algebra, we define a new multiplication on the H‐comodule A to obtain a twisted algebra” A^T, T sumHom(H,End (A)). If ^T is convolution invertible, the categories of relative right Hopf modules over A and A^Tare isomorphic. Similarly a convolution invertible left twisting gives an isomorphism of the categories of relative left Hopf modules. We show that crossed products are invertible twistings of the tensor product, and obtain, as a corollary, a duality theorem for crossed products     

Synthesis of High χ–Low N Diblock Copolymers by Polymerization-Induced Self-Assembly

Polymerization-induced self-assembly (PISA) enables the scalable synthesis of functional block copolymer nanoparticles with various morphologies. Herein we exploit this versatile technique to produce so-called “high χ–low N” diblock copolymers that undergo nanoscale phase separation in the solid state to produce sub-10 nm surface features. By varying the degree of polymerization of the stabilizer and core-forming blocks, PISA provides rapid access to a wide range of diblock copolymers, and enables fundamental thermodynamic parameters to be determined. In addition, the pre-organization of copolymer chains within sterically-stabilized nanoparticles that occurs during PISA leads to enhanced phase separation relative to that achieved using solution-cast molecularly-dissolved copolymer chains.     

The Categories of Yetter—Drinfel’d Modules, Doi—Hopf Modules and Two-sided Two-cosided Hopf Modules

We show that the two-sided two-cosided Hopf modules are in some case generalized Hopf modules in the sense of Doi. Then the equivalence between two-sided two-cosided Hopf modules and Yetter—Drinfeld modules, proved in [8], becomes an equivalence between categories of Doi—Hopf modules. This equivalence induces equivalences between the underlying categories of (co)modules. We study the relation between this equivalence and the one given by the induced functor.     

In situ particle film ATR FTIR spectroscopy of carboxymethyl cellulose adsorption on talc: binding mechanism, pH effects, and adsorption kinetics

Carboxymethyl cellulose (CMC), in solution and adsorbed on the surface of talc, has been studied with ATR FTIR spectroscopy as a function of the solution pH. The solution spectra enable the calculation of the extent of ionization of the polymer (due to protonation and deprotonation of the carboxyl group) at various pH values, yielding a value of 3.50 for the pK(app)(1/2) (pH at which half of all carboxyl groups are ionized) in a simple electrolyte solution and a value of 3.37 for the pK(app)(1/2) in solutions containing magnesium ions (3.33 x 10(-4) M). The spectra of the adsorbed layer reveal that CMC interacts with the talc surface through a chemical complexation mechanism, via the carboxyl groups substituted on the polymer backbone. The binding mechanism is active at all pH values down to pH 2 and up to pH 11. The adsorbed layer spectra reveal that protonation and deprotonation of the polymer are affected by adsorption, with an increase in the pK(app)(1/2) to a value of 4.80. Spectra of the adsorbed polymer were also acquired as a function of the adsorption time. Adsorption kinetic data reveal that the polymer most likely has two different interactions with the talc surface, with a stronger interaction with the talc edge through chemical complexation and a weaker interaction with the talc basal plane presumably through the hydrophobic interaction.     

The Simplest Amino‐borane H2B=NH2 Trapped on a Rhodium Dimer: Pre‐Catalysts for Amine–Borane Dehydropolymerization

The μ‐amino–borane complexes [Rh₂(L^R)₂(μ‐H)(μ‐H₂B=NHR′)][BAr^F₄] (L^R=R₂P(CH₂)₃PR₂; R=Ph, ⁱPr; R′=H, Me) form by addition of H₃B?NMeR′H₂ to [Rh(L^R)(η⁶‐C₆H₅F)][BAr^F₄]. DFT calculations demonstrate that the amino–borane interacts with the Rh centers through strong Rh‐H and Rh‐B interactions. Mechanistic investigations show that these dimers can form by a boronium‐mediated route, and are pre‐catalysts for amine‐borane dehydropolymerization, suggesting a possible role for bimetallic motifs in catalysis.     

In situ determination of the size and polydispersity of concentrated emulsions

Droplet size distributions of concentrated, polydisperse oil-in-water emulsions have been measured using ultra small angle neutron scattering (USANS). The mean radii calculated by fitting a model for polydisperse hard spheres with excluded volume interactions to the USANS data were consistent with those derived from electroacoustics on diluted emulsions after correction for conductance behind the shear plane. The Porod radii measured by USANS were similarly consistent with the mean surface-area-weighted radii derived from electroacoustics, irrespective of the drop concentration or polydispersity.     

Colloid stability of thymine-functionalized gold nanoparticles

Gold nanoparticles surface-coated with thyminethiol derivatives containing long hydrocarbon chains have been prepared. The diameter of the particles is 2.2 and 7.0 nm, respectively, with a relatively narrow size distribution. Thyminethiol derivatives are attached to the gold particle surfaces with thymine moieties as the end groups. The colloid stability of the gold nanoparticles as a function of the type and concentration of monovalent salt, pH, and particle size was investigated in alkaline, aqueous solutions. The gold particles are stable in concentrated NaCl and KCl solutions, but are unstable in concentrated LiCl and CsCl solutions. The larger gold particles are more sensitive to salt concentration and aggregate at lower salt concentrations. The reversible aggregation and dispersion of the gold particles can be controlled by changing the solution pH. The larger gold particles can be dispersed at higher pH and aggregate faster than the smaller particles, due to stronger van der Waals forces between the larger particles. Hydration forces play an important role in stabilizing the particles under conditions where electrostatic forces are negligible. The coagulation of the gold nanoparticles is attributed to van der Waals attraction and reduced hydration repulsion in the presence of LiCl and CsCl.     

Effect of signal intensity normalization on the multivariate analysis of spectral data in complex ‘real‐world’ datasets

Spectral signal intensities, especially in ‘real‐world’ applications with nonstandardized sample presentation due to uncontrolled variables/factors, commonly require additional spectral processing to normalize signal intensity in an effective way. In this study, we have demonstrated the complexity of choosing a normalization routine in the presence of multiple spectrally distinct constituents by probing a dataset of Raman spectra. Variation in absolute signal intensity (90.1% of total variance) of the Raman spectra of these complex biological samples swamps the variation in useful signals (9.4% of total variance), degrading its diagnostic and evaluative potential. Using traditional spectral band choices, it is shown that normalization results are more complex than generally encountered in traditionally designed sample sets investigating limited chemical species. We demonstrate that no choice of a single band proves to be appropriate for predicting all the reference parameters, instead requiring a tailored normalization routine for each parameter. Of the reference parameters studied in the chosen system, signals from pathogenic adducts in ocular tissues called advanced glycation endproducts were most prominent when normalizing about the 1550–1690 cm⁻¹ region of the spectrum (17.5% of total variance, compared with 0.3% for unnormalized), while prediction of pentosidine and gender were optimized by normalization about the 1570 (R² = 0.97 vs 0.57 for unnormalized) and 1003 cm⁻¹ (p < 0.0000001 vs p < 0.01 for unnormalized) bands, respectively. The data obtained point to the extreme sensitivity of multivariate analysis to signal intensity normalization. Some general guidelines for making appropriate band choices are given, including the use of peak‐finding routines. Copyright © 2008 John Wiley & Sons, Ltd.     

A Survey of Hopf Algebras of Low Dimension

This short survey is based on a talk on the classification of finite dimensional Hopf algebras given at Memorial University of Newfoundland in St. John’s in May of 2008. This seminar was given in conjunction with the mini-course “Introduction to pointed Hopf algebras” offered by Professor Nicolás Andruskiewitsch which concentrated on classification methods and results for the pointed case. Here we will outline some low dimensional classifications for the general case.