Stable categories of higher preprojective algebras

We introduce (n+1)$(n+1)$-preprojective algebras of algebras of global dimension n$n$. We show that if an algebra is n$n$-representation-finite then its (n+1)$(n+1)$-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)$(n+1)$-preprojective algebra is (n+1)$(n+1)$-Calabi–Yau, and, more precisely, it is the (n+1)$(n+1)$-Amiot cluster category of the stable n$n$-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)$(n+1)$-cluster tilting object. We show that even if the (n+1)$(n+1)$-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}$n\in \{1,2\}$) the results above still hold for the stable category of Cohen–Macaulay modules.     

1‐Factor and Cycle Covers of Cubic Graphs

Let G be a bridgeless cubic graph. Consider a list of k 1‐factors of G. Let be the set of edges contained in precisely i members of the k 1‐factors. Let be the smallest over all lists of k 1‐factors of G. Any list of three 1‐factors induces a core of a cubic graph. We use results on the structure of cores to prove sufficient conditions for Berge‐covers and for the existence of three 1‐factors with empty intersection. Furthermore, if , then is an upper bound for the girth of G. We also prove some new upper bounds for the length of shortest cycle covers of bridgeless cubic graphs. Cubic graphs with have a 4‐cycle cover of length and a 5‐cycle double cover. These graphs also satisfy two conjectures of Zhang 18 . We also give a negative answer to a problem stated in 18 .     

Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets

We study Minkowski contents and fractal curvatures of arbitrary self-similar tilings (constructed on a feasible open set of an IFS) and the general relations to the corresponding functionals for self-similar sets. In particular, we characterize the situation, when these functionals coincide. In this case, the Minkowski content and the fractal curvatures of a self-similar set can be expressed completely in terms of the volume function or curvature data, respectively, of the generator of the tiling. In special cases such formulas have been obtained recently using tube formulas and complex dimensions or as a corollary to results on self-conformal sets. Our approach based on the classical Renewal Theorem is simpler and works for a much larger class of self-similar sets and tilings. In fact, generator type formulas are obtained for essentially all self-similar sets, when suitable volume functions (and curvature functions, respectively) related to the generator are used. We also strengthen known results on the Minkowski measurability of self-similar sets, in particular on the question of non-measurability in the lattice case.     

On lower bounds for cohomology growth in p-adic analytic towers

Let \(p\) and \(\ell \) be two distinct prime numbers and let \(\Gamma \) be a group. We study the asymptotic behaviour of the mod- \(\ell \) Betti numbers in \(p\) -adic analytic towers of finite index subgroups. If \(\Theta \) is a finite \(\ell \) -group of automorphisms of \(\Gamma \) , our main theorem allows to lift lower bounds for the mod- \(\ell \) cohomology growth in the fixed point group \(\Gamma ^\Theta \) to lower bounds for the growth in \(\Gamma \) . We give applications to \(S\) -arithmetic groups and we also obtain a similar result for cohomology with rational coefficients.     

Ultrafast ring-closure reaction of photochromic indolylfulgimides studied with UV-pump-IR-probe spectroscopy

The ring-opening and ring-closure reactions of a photochromic indolylfulgimide are investigated with femtosecond vibrational spectroscopy. Spectral signatures due to excited-state decay and vibrational cooling are seen in the mid-IR region. For the ring-opening reaction triggered with visible pulses, a lifetime of the excited electronic state of 4 ps was obtained in polar solution. In a nonpolar solvent, this time constant is reduced to 2 ps. The ring-closure reaction induced with UV pulses displays an excited-state lifetime and thus a building of the photoproduct of roughly 0.5 ps. For all processes, the subsequent cooling occurs on a 15-ps time scale lasting up to approximately 50 ps. The time-resolved IR measurements do not support the existence of any long-living intermediate states.     

Kristallstrukturen von Säurehydraten und Oxoniumsalzen. XX. Die Oxoniumtetrafluoroborate H3OBF4, [H5O2]BF4 und [H(CH3OH)2]BF4

Crystal Structures of Acid Hydrates and Oxonium Salts. XX. Oxonium Tetrafluoroborates H₃OBF₄, [H₅O₂]BF₄, and [H(CH₃OH)₂]BF₄ The crystal structures of three oxonium tetrafluoroborates were determined. H₃OBF₄, oxonium tetrafluoroborate proper, is triclinic with space group P1 , Z = 2 and the unit cell dimensions a = 4.758, b = 6.047, c = 6.352 Å and α = 80.40, β = 79.48, γ = 88.25° at ?26°C. Cations H₃O⁺ and anions BF₄^? are linked by hydrogen bonds O? H…?F into ribbons of condensed rings. In [H₅O₂]BF₄ (diaquohydrogen tetrafluoroborate, monoclinic, P2₁/c, Z = 4, a = 6.584, b = 9.725, c = 7.084 Å, β = 95.15° at ?100°C) the hydrogen bond in the cation H₅O₂⁺ is 2.412 Å short, asymmetric and approximately centered and the linking of cations and anions three-dimensional. In [H(CH₃OH)₂]BF₄ (Bis(methanol)hydrogen tetrafluoroborate, monoclinic, P2₁/c, Z = 4, a = 5.197, b = 14.458, c = 9.318 Å, β = 94.61° at ?50°C) the cation [H(CH₃OH)₂]⁺ is characterized for the first time in a crystal structure with an again very short (2.394 Å), asymmetric and effectively centered hydrogen bond. By further hydrogen bonds cations and anions form only dimers of the formula unit of centrosymmetric cyclic structure.     

Routes to unique palladium A-frame complexes with a bridging fluoro-ligand

Treatment of a toluene solution of [PdMe(2)(Cy(2)PCH(2)PCy(2))](1) with pentafluoropyridine in the presence of traces of water affords the generation of the A-frame complexes [(PdMe)(2){mu-kappa(2)(P,P)Cy(2)PCH(2)PCy(2)}(2)(mu-F)][SiMeF(4)]() and [(PdMe)(2){mu-kappa(2)(P,P)Cy(2)PCH(2)PCy(2)}(2)(mu-F)][OC(5)NF(4)](2b). If the reaction is performed in an NMR tube equipped with a PFA inliner, complex 2b is produced, only. Treatment of 1 with pentafluoropyridine in the presence of an excess water yields the pyridyloxy complex [PdMe(OC(5)NF(4))(Cy(2)PCH(2)PCy(2))](3). Compound [(PdMe)(2){mu-kappa(2)(P,P)Cy(2)PCH(2)PCy(2)}(2)(mu-F)][FHF](2c) bearing a bifluoride anion instead of SiMeF(4)(-) or OC(5)NF(4)(-) can be generated by reaction of 1 with substoichiometric amounts of Et(3)N.3HF. The analogous complex [(PdMe)(2){mu-kappa(2)(P,P)Ph(2)PCH(2)PPh(2)}(2)(mu-F)][FHF] (5c) has been synthesized by addition of Ph(2)PCH(2)PPh(2) to a solution of [PdMe(2)(Me(2)NCH(2)CH(2)NMe(2))](4) in THF and subsequent treatment of the reaction mixture with Et(3)N.3HF. The structure of the A-frame complex 5c has been determined by X-ray crystallography.     

Hydrogen Production by Water Dissociation in Surface‐Modified BaCoxFeyZr1−x−yO3−δ Hollow‐Fiber Membrane Reactor with Improved Oxygen Permeation

A porous perovskite BaCo_xFe_yZr_0.9?x?yPd_0.1O_3?δ (BCFZ‐Pd) coating was deposited onto the outer surface of a BaCo_xFe_yZr_1?x?yO_3?δ (BCFZ) perovskite hollow‐fiber membrane. The surface morphology of the modified BCFZ fiber was characterized by scanning electron microscopy (SEM), indicating the formation of a BCFZ‐Pd porous layer on the outer surface of a dense BCFZ hollow‐fiber membrane. The oxygen permeation flux of the BCFZ membrane with a BCFZ‐Pd porous layer increased 3.5 times more than that of the blank BCFZ membrane when feeding reactive CH₄ onto the permeation side of the membrane. The blank BCFZ membrane and surface‐modified BCFZ membrane were used as reactors to shift the equilibrium of thermal water dissociation for hydrogen production because they allow the selective removal of the produced oxygen from the water dissociation system. It was found that the hydrogen production rate increased from 0.7 to 2.1 mL H₂ min^?1 cm^?2 at 950 °C after depositing a BCFZ‐Pd porous layer onto the BCFZ membrane.     

Improved particle-packed HPLC/MS microchips for proteomic analysis

The influence of packing process parameters (packing pressure, application of ultrasound) and the stationary phase particle size (3.5 and 5 μm) on the chromatographic performance of HPLC/MS chips was systematically investigated for proteomic samples. First, reproducibility and detection limits of the separation were evaluated with a low‐complexity sample of tryptic BSA peptides. The influence of adsorbent packing quality on protein identification was then tested with a typical proteomics sample of high complexity, a human plasma protein fraction (Cohn fraction IV‐4). All HPLC/MS chips provided highly reproducible separations of these proteomic samples, but improved packing conditions and smaller particle sizes resulted in chromatograms with narrower peaks and correspondingly higher signal intensities. Improved separation performance increased the peak capacity, the number of identified peptides, and thus the sequence coverage in the proteomic samples, particularly for low sample amounts.     

Photoinduced electron transfer between a donor and an acceptor separated by a capsular wall

The efficient photoinduced electron transfer from a stilbene derivative incarcerated within a negatively charged organic nanocapsule to positively charged acceptors (methyl viologen and a pyridinium salt) adsorbed outside and the back electron transfer were controlled by supramolecular effects.