Eigenvalue amplitudes of the Potts model on a torus

We consider the Q-state Potts model in the random-cluster formulation, defined on finite   two-dimensional lattices of size L×N$L\times N$ with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N)$Z(L,N)$ cannot be written simply as a trace of the transfer matrix TL${\mathrm{T}}_L$. Using a combinatorial method, we establish the decomposition Z(L,N)=_∑l,Dkb(l,Dk)K_l,Dk$Z(L,N)={\sum }_{l,D_k}{b}^{(l,D_k)}{K}_{l,D_k}$, where the characters K_l,Dk=i_∑N(λi)$K_{l,D_k}={\sum }_i{({\lambda }_i)}^N$ are simple traces. In this decomposition, the amplitudes b(l,Dk)$b^{(l,D_k)}$ of the eigenvalues λi${\lambda }_i$ of TL${\mathrm{T}}_L$ are labelled by the number l=0,1,…,L$l=0,1,\dots ,L$ of clusters which are non-contractible with respect to the transfer (N  ) direction, and a representation Dk$D_k$ of the cyclic group Cl$C_l$. We obtain rigorously a general expression for b(l,Dk)$b^{(l,D_k)}$ in terms of the characters of Cl$C_l$, and, using number theoretic results, show that it coincides with an expression previously obtained in the continuum limit by Read and Saleur.     

Terminal Ligand and Packing Effects on Slow Relaxation in an Isostructural Set of [Dy(H2dapp)X2]+ Single Molecule Magnets**

We report three structurally related single ion Dy compounds using the pentadentate ligand 2,6-bis((E)-1-(2-(pyridin-2-yl)-hydrazineylidene)ethyl)pyridine (H₂dapp) [Dy(H₂dapp)(NO₃)₂]NO₃ ( 1 ), [Dy(H₂dapp)(OAc)₂]Cl ( 2 ) and [Dy(H₂dapp)(NO₃)₂]Cl_0.92(NO₃)_0.08 ( 3 ). The (H₂dapp) occupies a helical twisted pentagonal equatorial arrangement with two anionic ligands in the axial positions. Further influence on the electronic and magnetic structure is provided by a closely associated counterion interacting with the central N−H group of the (H₂dapp). The slow relaxation of the magnetisation shows that the anionic acetates give the greatest slowing down of the magnetisation reversal. Further influence on the relaxation properties of compounds 1 and 2 is the presence of short nitrate-nitrate intermolecular ligand contact opening further lattice relaxation pathways.     

Platinum‐Promoted Ga/Al2O3 as Highly Active,Selective, and Stable Catalyst for the Dehydrogenation of Propane

A novel catalyst material for the selective dehydrogenation of propane is presented. The catalyst consists of 1000 ppm Pt, 3 wt % Ga, and 0.25 wt % K supported on alumina. We observed a synergy between Ga and Pt, resulting in a highly active and stable catalyst. Additionally, we propose a bifunctional active phase, in which coordinately unsaturated Ga³⁺ species are the active species and where Pt functions as a promoter.     

Counting of Oxygen Defects versus Metal Surface Sites in Methanol Synthesis Catalysts by Different Probe Molecules

Different surface sites of solid catalysts are usually quantified by dedicated chemisorption techniques from the adsorption capacity of probe molecules, assuming they specifically react with unique sites. In case of methanol synthesis catalysts, the Cu surface area is one of the crucial parameters in catalyst design and was for over 25 years commonly determined using diluted N₂O. To disentangle the influence of the catalyst components, different model catalysts were prepared and characterized using N₂O, temperature programmed desorption of H₂, and kinetic experiments. The presence of ZnO dramatically influences the N₂O measurements. This effect can be explained by the presence of oxygen defect sites that are generated at the Cu‐ZnO interface and can be used to easily quantify the intensity of Cu‐Zn interaction. N₂O in fact probes the Cu surface plus the oxygen vacancies, whereas the exposed Cu surface area can be accurately determined by H₂.     

Quantification of Structural Integrity and Stability Using Nanograms of Protein by Flow-Induced Dispersion Analysis

In the development of therapeutic proteins, analytical assessment of structural stability and integrity constitutes an important activity, as protein stability and integrity influence drug efficacy, and ultimately patient safety. Existing analytical methodologies solely rely on relative changes in optical properties such as fluorescence or scattering upon thermal or chemical perturbation. Here, we present an absolute analytical method for assessing protein stability, structure, and unfolding utilizing Taylor dispersion analysis (TDA) and LED-UV fluorescence detection. The developed TDA method measures the change in size (hydrodynamic radius) and intrinsic fluorescence of a protein during in-line denaturation with guanidinium hydrochloride (GuHCl). The conformational stability of the therapeutic antibody adalimumab and human serum albumin were characterized as a function of pH. The simple workflow and low sample consumption (40 ng protein per data point) of the methodology make it ideal for assessing protein characteristics related to stability in early drug development or when having a scarce amount of sample available.     

Simultaneous extraction of tetracycline, macrolide and sulfonamide antibiotics from agricultural soils using pressurised liquid extraction, followed by solid-phase extraction and liquid chromatography-tandem mass spectrometry

The veterinary antibacterial agents chlortetracycline (CTC), oxytetracycline (OTC), sulfadiazine (SDZ), erythromycin (ERY) and tylosin (TYL A, B, C and D) were extracted from soil using pressurized liquid extraction (PLE). Citric acid (pH 4.7) and methanol was used as extraction buffer, followed by tandem-solid-phase extraction (SPE) clean-up (SAX + HLB) for all compounds. For quantification two slightly different methods were employed using LC-MS-MS with MRM detection. The soil extraction method was validated using a loamy sand soil and a sandy soil, representing two typical Danish agricultural soils. Recoveries were 50-80% for the tetracyclines (CTC and OTC) and sulfadiazine (SDZ) and 60-100% for the macrolides (TYL and ERY). Limits of detection for the soil extraction method (LOD(soil)) were 0.6-5.6 microg kg(-1) soil for CTC and OTC, 0.9-2.9 microg kg(-1) soil for SDZ and 2.4-5.5 microg kg(-1) soil for TYL A and ERY. Furthermore, the method was applied to field samples taken from two agricultural fields fertilised with liquid manure containing CTC and TYL A. These results showed a decline in the content of antibacterial agents throughout the sampling period of 155 days from 10 to 15 microg CTC kg(-1) soil and 20-55 microg TYL A kg(-1) soil to below or near the LOD(soil) listed above. Finally, the method was applied to barley grains harvested from the fields. None of the antibacterial agents were measured in grain samples, but recoveries for spiked grain samples were similar to soil recoveries.     

The Liouville-Bratu-Gelfand Problem for Radial Operators

We determine precise existence and multiplicity results for radial solutions of the Liouville-Bratu-Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.