The Groupoidal Analogue \widetilde{{\Theta}} to Joyal’s Category Θ is a Test Category

We introduce the groupoidal analogue $\widetilde{\Theta}$ to Joyal’s cell category Θ and we prove that $\widetilde{\Theta}$ is a strict test category in the sense of Grothendieck. This implies that presheaves on $\widetilde{\Theta}$ model homotopy types in a canonical way. We also prove that the canonical functor from Θ to $\widetilde{\Theta}$ is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on $\widetilde{\Theta}$ to weak equivalences of presheaves on Θ. Our proofs apply to other categories analogous to Θ.     

Efficacy of End-Only-Functionalized Oligo(arylene-ethynylene)s in Killing Bacterial Biofilms

Cationic end-only-functionalized oligo(arylene-ethynylene)s (EO-OPEs) have recently been found to be broad-spectrum and effective antimicrobial agents because of their unique structure and optical properties. In this study, we investigated their potential use for preventing and reducing Escherichia coli (E. coli) biofilms. The Calgary biofilm device (CBD) was used to form bacterial biofilms of E. coli; in these studies, the minimum inhibitory concentration (MIC) and the minimum biofilm eradication concentration (MBEC) were determined. E. coli biofilms uniformly grow on pegs of the CBD device lid. The MIC values determined for EO-OPEs are comparable to those found for standard antibiotics such as kanamycin (MIC = 11.2 μg/mL). About 10-30 times the concentration of EO-OPEs was required to eradicate E. coli biofilms and prevent regrowth in the dark. Near-UV irradiation of EO-OPEs enhanced their efficacy in killing biofilms.     

Quantum gray solitons in confining potentials

We define and study holelike excitations (the Lieb II mode) in a weakly interacting Bose liquid subject to external confinement. These excitations are obtained by semiclassical quantization of gray solitons propagating on top of a Thomas-Fermi background. Radiation of phonons by an accelerated gray soliton leads to a finite lifetime of these excitations. It is shown that, for a large number of trapped atoms, most of the Lieb II levels can be experimentally resolved.     

Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations

We have implemented the sweep algorithm for the variational optimization of SU(2) U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are presented. This allows to assess the performance of other quantum chemical methods. For small basis sets, MPS calculations in the saturation regime of the optical response properties can be performed. These results are extrapolated to the thermodynamic limit.     

Moduli of symplectic instanton vector bundles of higher rank on projective space ℙ<Superscript>3</Superscript>

Symplectic instanton vector bundles on the projective space ℙ³ constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space I _n;r of rank-2r symplectic instanton vector bundles on ℙ³ with r ≥ 2 and second Chern class n ≥ r, n ≡ r (mod 2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus I _n;r ^* of tame symplectic instantons is irreducible and has the expected dimension, equal to 4n(r + 1) −r(2r + 1).     

Physical and Chemical Characterization of Therapeutic Iron Containing Materials: A Study of Several Superparamagnetic Drug Formulations with the β-FeOOH or Ferrihydrite Structure

The effectiveness of therapeutically used iron compounds is related to their physical and chemical properties. Four different iron compounds used in oral, intravenous, and intramuscular therapy have been examined by X-ray powder diffraction, iron-57 Mössbauer spectroscopy, transmission electron microscopy, BET surface area measurement, potentiometric titration and studied through dissolution kinetics determinations using acid, reducing and chelating agents. All compounds are nanosized with particle diameters, as determined by X-ray diffraction, ranging from 1 to 4.1 nm. The superparamagnetic blocking temperatures, as determined by Mössbauer spectroscopy, indicate that the relative diameters of the aggregates range from 2.5 to 4.1 nm. Three of the iron compounds have an akaganeite-like structure, whereas one has a ferrihydrite-like structure. As powders the particles form large and dense aggregates which have a very low surface area on the order of 1 m²?g^?1. There is evidence, however, that in a colloidal solution the surface area is increased by two to three orders of magnitude, presumably as a result of the break up of the aggregates. Iron release kinetics by acid, chelating and reducing agents reflect the high surface area, the size and crystallinity of the particles, and the presence of the protective carbohydrate layer coating the iron compound. Within a physiologically relevant time period, the iron release produced by acid or large chelating ligands is small. In contrast, iron is rapidly mobilized by small organic chelating agents, such as oxalate, or by chelate-forming reductants, such as thioglycolate.

     

Dark solitons in mode-locked lasers

Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model that incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve (mode-lock) into dark solitons under appropriate requirements also met in experimental observations. The resulting pulses are essentially dark solitons of the unperturbed nonlinear Schr?dinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers.     

On the geometry of O’N

We classify the rank two BCDL ₂₀₀₃-geometries of O’Nan and show that the maximal rank of a BCDL ₂₀₀₃-geometry for O’Nan is 4. This bound is sharp since it is satisfied by the rank four geometry given by Buekenhout (Contemp Math 45:1–32, 1985).     

Solitary waves in Abelian Gauge Theories with strongly nonlinear potentials

We study the existence of radially symmetric solitary waves for a system of a nonlinear Klein–Gordon equation coupled with Maxwell's equation in presence of a positive mass. The nonlinear potential appearing in the system is assumed to be positive and with more than quadratical growth at infinity.