On the derived category of the classical Godeaux surface

We construct an exceptional sequence of length 11 on the classical Godeaux surface X$X$ which is the Z/5Z$\mathbb{Z}/5\mathbb{Z}$-quotient of the Fermat quintic surface in P³${\mathbb{P}}^3$. This is the maximal possible length of such a sequence on this surface which has Grothendieck group Z¹¹⊕Z/5Z${\mathbb{Z}}^{11}\oplus \mathbb{Z}/5\mathbb{Z}$. In particular, the result answers Kuznetsov’s Nonvanishing Conjecture, which concerns Hochschild homology of an admissible subcategory, in the negative. The sequence carries a symmetry when interpreted in terms of the root lattice of the simple Lie algebra of type _E8$E_8$. We also produce explicit nonzero objects in the (right) orthogonal to the exceptional sequence.     

Ion chemistry of OV(OCH3)3 in the gas phase: molecular cations and anions and their primary fragmentations

Trimethyl vanadate(V), OV(OCH(3))(3) (1), is examined by various mass spectrometric means. Photoionization experiments yield an ionization energy of IE(OV(OCH(3))(3)) = 9.54 +/- 0.05 eV for the neutral molecule. The primary fragmentation of the molecular cation 1(+), i.e., loss of neutral formaldehyde, can occur via two independent routes of hydrogen migrations to afford the formal V(IV) compounds HOV(OCH(3))(2)(+) and OV(OCH(3))(CH(3)OH)(+), respectively. These two pathways are associated with low-lying activation barriers of almost identical height. At elevated energies, direct V-O bond cleavage of 1(+) allows for expulsion of a methoxy radical concomitant with the generation of the cationic fragment OV(OCH(3))(2)(+), a formal V(V) compound. Trimethyl vanadate can also form a molecular anion, 1(-), whose most abundant dissociation channel involves loss of a methyl radical, thereby leading to the formal V(V) compound OV(OCH(3))(2)O(-). Various mass spectrometric experiments and extensive theoretical studies provide detailed insight into the ion structures and the relative energetics of the primary dissociation reactions of the molecular cations and anions of 1.     

BRST Cohomology and Phase Space Reduction in Deformation Quantization

In this article we consider quantum phase space reduction when zero is a regular value of the momentum map. By analogy with the classical case we define the BRST cohomology in the framework of deformation quantization. We compute the quantum BRST cohomology in terms of a "quantum" Chevalley-Eilenberg cohomology of the Lie algebra on the constraint surface. To prove this result, we construct an explicit chain homotopy, both in the classical and quantum case, which is constructed out of a prolongation of functions on the constraint surface. We have observed the phenomenon that the quantum BRST cohomology cannot always be used for quantum reduction, because generally its zero part is no longer a deformation of the space of all smooth functions on the reduced phase space. But in case the group action is "sufficiently nice", e.g. proper (which is the case for all compact Lie group actions), it is shown for a strongly invariant star product that the BRST procedure always induces a star product on the reduced phase space in a rather explicit and natural way. Simple examples and counterexamples are discussed.     

Ultrasonic extraction of veterinary antibiotics from soils and pig slurry with SPE clean-up and LC-UV and fluorescence detection

A simple and rapid analytical method is presented in which the three veterinary antibiotics oxytetracycline (OTC), sulfachloropyridazine (SCP) and tylosin (TYL) are simultaneously extracted and determined in four different soils. Extractions were carried out by a combination of ultrasonic agitation and vortex mixing using a mixture of methanol, EDTA and McIlvaine buffer at pH 7 as the extractant solution. The extracts were then cleaned-up by a tandem solid phase extraction (SPE) method using an Isolute SAX anion exchange cartridge to remove natural organic matter and an Oasis HLB polymeric cartridge to retain the study compounds. Analysis was by HPLC-UV with additional fluorescence detection for SCP. Recoveries were in the range 68-85% for SCP in all soil types, 58-75% for OTC in sandy soils, 27-51% for OTC in clay containing soils, 74-105% for TYL and 47-61% in a clay soil. OTC and SCP were also extracted from liquid pig manure using a mixture of EDTA and McIlvaine buffer at pH 7 with ultrasonic agitation and vortex mixing with SPE clean-up and HPLC-UV analysis. Recoveries were greater than 77% and 58% for OTC and SCP, respectively. Limits of detection were 18 μg kg⁻¹ for OTC and SCP and 40 μg kg⁻¹ for TYL in soils and 70 μg L⁻¹ for OTC and 140 μg L⁻¹ for SCP in pig slurry.     

The role of electric current in the formation of white-etching-cracks

ABSTRACT

Material failure by white-etching-cracks (WECs) can cause enormous economic costs. The formation of WECs emerges from the decomposition of the original, usually cementite-containing, microstructure. As small amounts of electric current can trigger this failure mechanism, we investigate the contribution of electric current to cementite decomposition. We applied ～700 A/cm² for two weeks at 60°C to a pearlitic Fe-0.74C (wt%) specimen. The comparison of the microstructure before and after showed no differences. Theoretical considerations support the conclusion that at this low temperature such electric current densities cannot directly cause cementite decomposition. Electric current could play an indirect role in the formation of WECs, however, by generating hydrogen from the lubricant which is known to accelerate WECs formation.     

On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions

We discuss BFV deformation quantization (Bordemann et al. in A homological approach to singular reduction in deformation quantization, singularity theory, pp. 443–461. World Scientific, Hackensack, 2007) in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms and Gotay (Adv Math 79(1):43–103, 1990) for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.      

Convex Defining Functions for Convex Domains

We give three proofs of the fact that a smoothly bounded, convex domain in ℝ ⁿ has defining functions whose Hessians are non-negative definite in a neighborhood of the boundary of the domain.     

HS-SPME-GC-MS analysis of antioxidant degradation products migrating to drinking water from PE materials and PEX pipes

Polyethylene (PE) and cross-linked polyethylene (PEX) pipes are frequently used in water supply systems. Such pipes contain added antioxidants with phenolic structures, e.g. Irgafos 168, Irganox 1010 and 1076, in order to improve durability. However, phenol, ketone and quinone antioxidant degradation products may leach and enter drinking water. The aim of this investigation was to develop a method for measuring these degradation products with a performance meeting the drinking water quality criteria of 20?µg?L^?1. Using headspace solid phase microextraction coupled to a gas chromatograph with a mass spectrometer, a method was established revealing limits of detection and quantification less than 0.4 and 1?µg?L^?1 respectively. The method was applied to migration experiments for two PEX pipes and one PE material, quantifying the release of two degradation products. Highest concentrations were observed for 2,6-di-tert-butyl-p-benzoquinone which in one of the two pipes was found in concentrations of 18–57?µg?L^?1 in each of eight consecutive release experiments.