One-sided Hopf algebras and quantum quasigroups

We study the connections between one-sided Hopf algebras and one-sided quantum quasigroups, tracking the four possible invertibility conditions for the left and right composite morphisms that combine comultiplications and multiplications in these structures. The genuinely one-sided structures exhibit precisely two of the invertibilities, while it emerges that imposing one more condition often entails the validity of all four. A main result shows that under appropriate conditions, just one of the invertibility conditions is su?cient for the existence of a one-sided antipode. In the left Hopf algebra which is a variant of the quantum special linear group of two-dimensional matrices, it is shown explicitly that the right composite is not injective, and the left composite is not surjective.     

Phase Separation in the Advective Cahn–Hilliard Equation

The Cahn–Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn–Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing, then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection–hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection–diffusion equation.

     

Charge transport in polythiophene:fullerene:nanotube bulk heterojunction photovoltaic devices investigated by impedance spectroscopy

P3HT:PCBM bulk heterojunction devices incorporating SWNTs, which are predominantly metallic in character, have been analyzed using impedance spectroscopy to understand the effect of SWNTs on their charge carrier transport properties. SWNTs reduce the effective lifetime of injected charge carriers. Frequency dependence of capacitance and conductance of P3HT:PCBM devices show monotonic variations without any clear peak positions. Simulations of the complex admittance of the P3HT:PCBM devices under trap free space charge limited current within the framework of Scher–Montrol theory are used to qualitatively show that such characteristics are a signature of charge transport which is highly dispersive in nature. The position of peak τ_peak in the imaginary part of impedance Im(Z), which is essentially same as the first transition frequency of Cole–Cole plot, has a direct relation with the effective dc mobility of charge carriers which varies with dispersion parameters. Using the dc mobility values and the voltage variation of peak frequency of Im(Z), the ratio of τ_dc to τ_peak has been calculated. The magnitude of this ratio is indicative of the degree of dispersiveness in transport. It has been shown that, SWNTs at low concentrations tend to reduce the dispersiveness in charge transport.     

Effect of the total galactose content on complement-dependent cytotoxicity of the therapeutic anti-CD20 IgG1 antibodies under temperature stress conditions

The degree of monoclonal antibody galactosylation is known to affect complement-dependent cytotoxicity (CDC) activity by affecting C1q binding, suggesting that galactose is associated with CDC bioactivity. However, whether this association also exists under temperature stress conditions is not known. This study highlights the impact of variations in the terminal galactose content of an anti-CD20 monoclonal antibody on CDC bioactivity under high-temperature stress conditions compared with storage conditions at 2–8?°C. Drug product samples with a total galactose content of >38% showed stable CDC bioactivity at higher temperatures (45?°C), while those with 16% galactose content showed reduced CDC activity.     

Influence of divalent ions on composition and viscoelasticity of polyelectrolyte complexes

The addition of monovalent salts to polyelectrolyte complexes (PECs) comprising oppositely charged polyelectrolytes results in diminishing propensity for complexation, leading to complexes with higher water contents and lower moduli. However, the corresponding influence of multivalent ions on polyelectrolyte complexation has not yet been explored beyond enhanced screening effects. Here, we elucidate the significant impact of the valency of the salt cation on the composition, ion partitioning, and viscoelasticity of charge-matched PECs comprising sodium salt of poly(acrylic acid) and poly(allylamine hydrochloride). Notably, preferential partitioning of divalent cations (Ca²⁺ and Sr²⁺) into the complexes is observed, in stark contrast to the depletion of monovalent ions (Na⁺) from the complexes. Concomitantly, electrostatic bridging of polyanion chains by divalent ions is found to hinder their relaxation, manifesting as a non-monotonic evolution of the shear moduli of the complexes with increasing divalent salt concentrations. Relatedly, a failure of time-salt and time-ionic strength superposition approaches in presence of divalent ions is demonstrated, highlighting the nontrivial influence of these ions on chain relaxation behavior.     

Influence of surface morphology on the oxidation of metal electrodes studied by in-situ grazing incidence x-ray diffractometry

The successful application of in-situ grazing incidence x-ray diffractometry (GIXD) for the investigation of oxidation processes at copper electrodes in pH 12 electrolytes is demonstrated. A penetration/escape depth of about 1 μm could be detected for a smooth polycrystalline copper foil and an x-ray incidence angle of 1.7°. Oxide layers generated at overpotentials less than about 0.5 V in respect to the equilibrium formation potentials of Cu₂O or CuO, respectively, showed a dependence of the crystalline oxide formation on the defect density of the copper substrate. Highly disordered ground or polished specimens exhibited an order of magnitude higher GIXD reflexes from crystalline Cu₂O than electrodeposited copper. Beyond overpotentials of 0.5 V, this epitaxial information for the Cu₂O crystal growth became irrelevant. Further, GIXD turned out to be an appropriate tool to monitor atmospheric corrosion processes under thin humidity films with oxygen access. When oxygen diffusion through the polymer window membrane is allowed, oxygen reduction led to the concurrent formation of a crystalline CuO phase coexisting with amorphous Cu(OH)₂ and Cu₂O, though the potential was kept in the region of Cu₂O. Received: 30 July 1997 / Revised: 28 May 1998 / Accepted: 13 July 1998     

Synthesis of poly(urethane‐imide) using aromatic secondary amine‐blocked polyurethane prepolymer

A set of poly(urethane‐imide)s were prepared using blocked Polyurethane (PU) prepolymer and pyromellitic dianhydride (PMDA). The PU prepolymer was prepared by the reaction of polyether glycol and 2,4‐tolylene diisocyanate, and end capped with N‐methyl aniline. The PU prepolymer was reacted with PMDA until the evolution of carbon dioxide ceased. The effect of tertiary amine catalysts, organo tin catalysts, solvents, and reaction temperature were studied and compared with the poly(urethane‐imide) prepared using phenol‐blocked PU prepolymer. N‐methyl aniline blocked PU prepolymer gave a higher molecular weight poly(urethane‐imide) at a lower reaction temperature in a shorter time. Amine catalysts were found to be more efficient than organo tin catalysts. The reaction was favorable in particular with N‐ethylmorpholine and diazabicyclo(2.2.2)octane (DABCO) as catalysts, and dimethylpropylene urea as a reaction medium. The poly(urethane‐imide)s were characterized by FTIR, GPC, TGA, and DSC analyses. The molecular weight decreased with an increase in reaction temperature. The thermal stability of the PU was found to increase by the introduction of imide component. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4032–4037, 2000     

Self‐Healing Colloidal Crystals

Healing hands : A complex interplay between colloidal and polymeric energetics in microgel self‐assembly behavior results in soft colloidal assemblies with self‐healing properties. Repulsive soft spheres can adopt highly compressed conformations in colloidal crystalline lattices without directly contacting the nearest neighbors (see picture). This distant action is directly responsible for the self‐healing of the assemblies.

     

Chern–Simons classes for a superconnection

In this note we define the Chern–Simons classes of a flat superconnection, D+L$D+L$, on a complex Z/2Z$\mathbb{Z}/2\mathbb{Z}$-graded vector bundle E$E$ on a manifold such that D$D$ preserves the grading and L$L$ is an odd endomorphism of E$E$. As an application, we obtain a definition of Chern–Simons classes of a (not necessarily flat) morphism between flat vector bundles on a smooth manifold. An application of Reznikov's theorem shows the triviality of these classes when the manifold is a compact Kähler manifold or a smooth complex quasi-projective variety in degrees >1$>1$.