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.     

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.     

Mechanical exfoliation of epitaxial graphene on Ir(111) enabled by Br2 intercalation

We show here that Br(2) intercalation is an efficient method to enable exfoliation of epitaxial graphene on metals by adhesive tape. We exemplify this method for high-quality graphene of macroscopic extension on Ir(111). The sample quality and the transfer process are monitored using low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), scanning electron microscopy (SEM) and Raman spectroscopy. The developed process provides an opportunity for preparing graphene of strictly monatomic thickness and well-defined orientation including the transfer to poly(ethylene terephthalate) (PET) foil.     

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.     

Influence of triplet state multidimensionality on excited state lifetimes of bis-tridentate RuII complexes: a computational study

Calculated triplet excited state potential energy surfaces are presented for a set of three bis-tridentate Ru(II)-polypyridyl dyes covering a wide range of room temperature excited state lifetimes: [Ru(II)(tpy)(2)](2+), 250 ps; [Ru(II)(bmp)(2)](2+), 15 ns; and [Ru(II)(dqp)(2)](2+), 3 μs (tpy is 2,2':6',2″-terpyridine, bmp is 6-(2-picolyl)-2,2'-bipyridine, and dqp is 2,6-di(quinolin-8-yl)pyridine). The computational results provide a multidimensional view of the (3)MLCT-(3)MC transition for the investigated complexes. Recently reported results of significantly prolonged (3)MLCT excited state lifetimes of bis-tridentate Ru(II)-complexes, for example [Ru(II)(dqp)(2)](2+), are found to correlate with substantial differences in their triplet excited state multidimensional potential energy surfaces. In addition to identification of low-energy transition paths for (3)MLCT-(3)MC conversion associated with simultaneous elongation of two or more Ru-N bonds for all investigated complexes, the calculations also suggest significant differences in (3)MLCT state volume in the multidimensional reaction coordinate space formed from various combinations of Ru-N bond distance variations. This is proposed to be an important aspect for understanding the large differences in experimentally observed (3)MLCT excited state lifetimes. The results demonstrate the advantage of considering multidimensional potential energy surfaces beyond the Franck-Condon region in order to predict photophysical and photochemical properties of bis-tridentate Ru(II)-polypyridyl dyes and related metal complexes.     

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.