The picard group of a category of graded modules

For R a G-graded ring, we study Pic(R-gr), the group of isomorphism classes of autoequivalences of the category of graded left R-modules. For G infinite, this requires generalizing the classical sequences involving Pic(A), A a fc-algebra, to A a ring with local units. Then for G either finite or infinite, we characterize the inner automorphisms in some subgroups H of the automorphism group of the smash product R#PG and thus obtain some subgroups of Pic(R-gr).     

Techniques for Classifying Hopf Algebras and Applications to Dimension p 3

Classifying Hopf algebras of a given finite dimension n over ? is a challenging problem. If n is p, p², 2p, or 2p² with p prime, the classification is complete. If n = p³, the semisimple and the pointed Hopf algebras are classified, and much progress on the remaining cases was made by the second author but the general classification is still open. Here we outline some results and techniques which have been useful in approaching this problem and add a few new ones. We give some further results on Hopf algebras of dimension p³ and finish the classification for dimension 27.     

Adsorption of modified dextrins on molybdenite: AFM imaging, contact angle, and flotation studies

The adsorption of three dextrins (a regular wheat dextrin, Dextrin TY, carboxymethyl (CM) Dextrin, and hydroxypropyl (HP) Dextrin) on molybdenite has been investigated using adsorption isotherms, tapping mode atomic force microscopy (TMAFM), contact angle measurements, and dynamic bubble-surface collisions. In addition, the effect of the polymers on the flotation recovery of molybdenite has been determined. The isotherms revealed the importance of molecular weight in determining the adsorbed amounts of the polymers on molybdenite at plateau coverage. TMAFM revealed the morphology of the three polymers, which consisted of randomly dispersed domains with a higher area fraction of surface coverage for the substituted dextrins. The contact angle of polymer-treated molybdenite indicated that polymer layer coverage and hydration influenced the mineral surface hydrophobicity. Bubble-surface collisions indicated that the polymers affected thin film rupture and dewetting rate differently, correlating with differences in the adsorbed layer morphology. Direct correlations were found between the surface coverage of the adsorbed layers, their impact on thin film rupture time, and their impact on flotation recovery, highlighting the paramount role of the polymer morphology in the bubble/particle attachment process and subsequent flotation.     

The Antipode of a Dual Quasi-Hopf Algebra with Nonzero Integrals is Bijective

For a Hopf algebra A of arbitrary dimension over a field K, it is well-known that if A has nonzero integrals, or, in other words, if the coalgebra A is co-Frobenius, then the space of integrals is one-dimensional and the antipode of A is bijective. Bulacu and Caenepeel recently showed that if H is a dual quasi-Hopf algebra with nonzero integrals, then the space of integrals is one-dimensional, and the antipode is injective. In this short note we show that the antipode is bijective.     

The coalescence of polystyrene in correlated binary solvents

The solution behavior of solvophobic polymers is crucial to the development of polymer coatings and polymeric drug delivery vehicles. In this article, the role of dipolar interactions is investigated in the solvophobic coalescence of polystyrene in binary correlated polar solvent mixtures. A simple model for coalescence thermodynamics is derived from correlations between thermally rotating dipole moments in the solvent. The stabilizing correlations lost to the solvent due to a solute's presence give rise to a driving force for the coalescence of solutes. This stabilization is offset by the entropy of mixing that favors the dispersion of solutes. Predictions are compared to the measured point of coalescence of polystyrene in acetone when different alcohols are titrated. The model is shown to capture this point of coalescence and conformation for a variety of systems. Our results suggest the significant property determining the solubility of nonpolar polymers in a polar liquid is a free energy resulting from attractive dispersion interactions between thermally rotating solvent dipole moments. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 948–955     

Synchrotron scanning photoemission microscopy of homogeneous and heterogeneous metal sulfide minerals

Scanning photoemission microscopy (SPEM) has been applied to the investigation of homogeneous and heterogeneous metal sulfide mineral surfaces. Three mineral samples were investigated: homogeneous chalcopyrite, heterogeneous chalcopyrite with bornite, and heterogeneous chalcopyrite with pyrite. Sulfur, copper and iron SPEM images, i.e. surface‐selective elemental maps with high spatial resolution acquired using the signal from the S 2p and Cu and Fe 3p photoemission peaks, were obtained for the surfaces after exposure to different oxidation conditions (either exposed to air or oxidized in pH 9 solution), in addition to high‐resolution photoemission spectra from individual pixel areas of the images. Investigation of the homogeneous chalcopyrite sample allowed for the identification of step edges using the topography SPEM image, and high‐resolution S 2p spectra acquired from the different parts of the sample image revealed a similar rate of surface oxidation from solution exposure for both step edge and a nearby terrace site. SPEM was able to successfully distinguish between chalcopyrite and bornite on the heterogeneous sample containing both minerals, based upon sulfur imaging. The high‐resolution S 2p spectra acquired from the two regions highlighted the faster air oxidation of the bornite relative to the chalcopyrite. Differentiation between chalcopyrite and pyrite based upon contrast in SPEM images was not successful, owing to either the poor photoionization cross section of the Cu and Fe 3p electrons or issues with rough fracture of the composite surface. In spite of this, high‐resolution S 2p spectra from each mineral phase were successfully obtained using a step‐scan approach.     

Austrocolorone B and austrocolorin B1, cytotoxic anthracenone dimers from the Tasmanian mushroom Cortinarius vinosipes Gasparini

The yellow dihydroanthracenone dimer, austrocolorin B₁ and the unique violet-red 1,4-anthraquinone dimer, austrocolorone B, were isolated from the Tasmanian mushroom Cortinariusvinosipes and their structures and stereochemistry were determined from spectroscopic data. Austrocolorin B₁ and austrocolorone B were found to exhibit potent cytotoxic activity in vitro against the murine lymphoblast (P388D₁) cell line with IC₅₀ values in the range 10-31 μg/mL.     

Continuous convergence and functional analysis

The usual setting for Functional Analysis is the category LCS of locally convex topological vector spaces. There are, however, advantages in working in a larger setting, the category CVS of convergence vector spaces—even if one's interest is restricted to LCS. In CVS, one has access to a dual structure, continuous convergence, unavailable in LCS.

We show that theorems such as Grothendieck's completion theorem, Ptak's closed graph and open mapping theorems and the Banach-Steinhaus theorem are transformed from technical results in LCS to transparent and elegant results when examined in CVS with continuous convergence. In the theory of distributions, important bilinear mappings such as evaluations, multiplication and convolution, which are separately continuous when viewed in LCS, become jointly continuous in CVS.     

Unexpected Vulnerability of DPEphos to C−O Activation in the Presence of Nucleophilic Metal Hydrides

C−O bond activation of DPEphos occurs upon mild heating in the presence of [Ru(NHC)₂(PPh₃)₂H₂] (NHC=N-heterocyclic carbene) to form phosphinophenolate products. When NHC=IEt₂Me₂, C−O activation is accompanied by C−N activation of an NHC ligand to yield a coordinated N-phosphino-functionalised carbene. DFT calculations define a nucleophilic mechanism in which a hydride ligand attacks the aryl carbon of the DPEphos C−O bond. This is promoted by the strongly donating NHC ligands which render a trans dihydride intermediate featuring highly nucleophilic hydride ligands accessible. C−O bond activation also occurs upon heating cis-[Ru(DPEphos)₂H₂]. DFT calculations suggest this reaction is promoted by the steric encumbrance associated with two bulky DPEphos ligands. Our observations that facile degradation of the DPEphos ligand via C−O bond activation is possible under relatively mild reaction conditions has potential ramifications for the use of this ligand in high-temperature catalysis.