Ueber die allgemeine Auflösung von Gleichungen durch Kettenbrüche

Ohne Zusammenfassung     

Multilayer resonances sharpened by grating waveguide resonance

A multilayer planar structure comprising a highly reflective multilayer dielectric mirror and a corrugated waveguide is proposed for use as a narrow passband optical filter. The proposed filter has a much narrower linewidth than a usual Fabry–Perot cavity with two multilayer dielectric mirrors. It is shown that the narrowing of the linewidth is due to the strong spectral dependence of the phase of the wave reflected from the waveguide grating mirror. The shape of the pass band can be made symmetrical by a proper choice of the grating groove profile.     

Enhancing the CO2 Electroreduction of Fe/Ni-Pentlandite Catalysts by S/Se Exchange

The electrochemical reduction of CO₂ is an attractive strategy towards the mitigation of environmental pollution and production of bulk chemicals as well as fuels by renewables. The bimetallic sulfide Fe_4.5Ni_4.5S₈ (pentlandite) was recently reported as a cheap and robust catalyst for electrochemical water splitting, as well as for CO₂ reduction with a solvent-dependent product selectivity. Inspired by numerous reports on monometallic sulfoselenides and selenides revealing higher catalytic activity for the CO₂ reduction reaction (CO₂RR) than their sulfide counterparts, the authors investigated the influence of stepwise S/Se exchange in seleno-pentlandites Fe_4.5Ni_4.5S_8-YSe_Y (Y=1–5) and their ability to act as CO₂ reducing catalysts. It is demonstrated that the incorporation of higher equivalents of selenium favors the CO₂RR with Fe_4.5Ni_4.5S₄Se₄ revealing the highest activity for CO formation. Under galvanostatic conditions in acetonitrile, Fe_4.5Ni_4.5S₄Se₄ generates CO with a Faradaic Efficiency close to 100 % at applied current densities of −50 mA cm⁻² and −100 mA cm⁻². This work offers insight into the tunability of the pentlandite based electrocatalysts for the CO₂ reduction reaction.     

Approximations of Parabolic Equations at the Vicinity of Hyperbolic Equilibrium Point

This article is devoted to the numerical analysis of the abstract semilinear parabolic problem u′(t) = Au(t) + f(u(t)), u(0) = u ⁰, in a Banach space E. We are developing a general approach to establish a discrete dichotomy in a very general setting and prove shadowing theorems that compare solutions of the continuous problem with those of discrete approximations in space and time. In [3 W.-J. Beyn and S. Piskarev ( 2008 ). Shadowing for discrete approximations of abstract parabolic equations . Discrete Contin. Dyn. Syst., B 10 : 19 – 42 .[Crossref], [Web of Science ®] , [Google Scholar]] the discretization in space was constructed under the assumption of compactness of the resolvent. It is a well-known fact (see [10 S. Larsson ( 1999 ). Numerical analysis of semilinear parabolic problems . In: The Graduate Student's Guide to Numerical Analysis ’98 ( M. Ainsworth , ed.). Lecture Notes from the 8th EPSRC Summer School in Numerical Analysis . Leicester , UK , July 5–17. 1998. Ser. Comput. Math. 26:83–117; Springer, Berlin .[Crossref] , [Google Scholar], 11 S. Larsson and J. M. Sanz-Serna (1994). The behavior of finite element solutions of semilinear parabolic problems near stationary points. SIAM J. Numer. Anal. 31:1000–1018.[Crossref], [Web of Science ®] , [Google Scholar]]) that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value problems with exponential bounded solutions on the corresponding subspaces. We show that such a decomposition of the flow persists under rather general approximation schemes, utilizing a uniform condensing property. The main assumption of our results are naturally satisfied, in particular, for operators with compact resolvents and condensing semigroups and can be verified for finite elements as well as finite differences methods.     

Low-temperature sealed tube combustion of gaseous,liquid and solid organic compounds for 13C/12C and 14C analysis

A new, low-temperature sealed tube technique for combustion of organic carbon prior to subsequent off-line isotope analysis is proposed. Complete oxidation is achieved with potassium peroxodisulfate and silver permanganate as oxidants at temperatures not exceeding 500 °C. The combustion of gaseous (methane), solid (cane sugar, vanilla, N-thiazolyl-2-sulfamide, ascorbic acid, phenanthrene, thiourea, polyethylenefilm, tetrafluoropolyethylene, polyetheretherketone, graphite, and Suwannee River Fulvic Acid), and liquid (tetrachloroethene, toluene, and oil) model compounds and international standards was tested. A 24 h combustion at 500 °C was sufficient for complete oxidation in all cases. The time required for complete oxidation of Suwannee River Fulvic Acid, typical of refractory freshwater dissolved organic carbon, as a function of combustion temperature was 2 h at 500 °C, 6 h at 400 °C, and 24 h at 300 °C. Preparation of saline solution parallels of cane sugar, vanilla, N-thiazolyl-2-sulfanilamide, and ascorbic acid gave consistent results. For reproducible δ¹³C analyses using a Thermoquest MAT 252 MS, a minimum of 5 µg C had to be combusted. Reliable ¹⁴C results, measured at an accelerator mass spectrometer facility, were obtained from coal and from cane sugar combusted for 24 h at 500 °C by the proposed method.     

Aspochalasin H1: A New Cyclic Aspochalasin from Hawaiian Plant-Associated Endophytic Fungus Aspergillus sp. FT1307

Aspergillus is one of the most diverse genera, and it is chemically profound and known to produce many biologically active secondary metabolites. In the present study, a new aspochalasin H1 (1), together with nine known compounds (2–10), were isolated from a Hawaiian plant-associated endophytic fungus Aspergillus sp. FT1307. The structures were elucidated using nuclear magnetic resonance (NMR) (¹H, ¹H-¹H COSY, HSQC, HMBC, ROESY and 1D NOE), high-resolution electrospray ionization mass spectroscopy (HRESIMS), and comparisons with the reported literature. The absolute configuration of the new compound was established by electronic circular dichroism (ECD) in combination with NMR calculations. The new compound contains an epoxide moiety and an adjacent trans-diol, which has not been reported before in the aspochalasin family. The antibacterial screening of the isolated compounds was carried out against pathogenic bacteria (Staphylococcus aureus, Methicillin-resistant S. aureus and Bacillus subtilis). The antiproliferative activity of compounds 1–10 was evaluated against human breast cancer cell lines (MCF-7 and T46D) and ovarian cancer cell lines (A2780).     

Unveiling Luminescent IrI and RhI N-Heterocyclic Carbene Complexes: Structure,Photophysical Specifics,and Cellular Localization in the Endoplasmic Reticulum

Complexes of Rh^I and Ir^I of the [M(COD)(NHC)X] type (where M=Rh or Ir, COD=1,5-cyclooctadiene, NHC=N-heterocyclic carbene, and X=halide) have recently shown promising cytotoxic activities against several cancer cell lines. Initial mechanism of action studies provided some knowledge about their interaction with DNA and proteins. However, information about their cellular localization remains scarce owing to luminescence quenching within this complex type. Herein, the synthesis of two rare examples of luminescent Rh^I and Ir^I [M(COD)(NHC)I] complexes with 1,8-naphthalimide-based emitting ligands is reported. All new complexes are comprehensively characterized, including with single-crystal X-ray structures. Steric crowding in one derivative leads to two distinct rotamers in solution, which apparently can be distinguished both by pronounced NMR shifts and by their respective spectral and temporal emission signatures. When the photophysical properties of these new complexes are exploited for cellular imaging in HT-29 and PT-45 cancer cell lines, it is demonstrated that the complexes accumulate predominantly in the endoplasmic reticulum, which is an entirely new finding and provides the first insight into the cellular localization of such Ir^I(NHC) complexes.