A note on flux limiting for diffusion discretizations

In this note, a limiting technique is presented to enforcemonotonicity for higher-order spatial diffusion discretizations.The aim is to avoid spurious oscillations and to improve thequalitative behaviour on coarse grids. The technique is relatedto known ones for convection equations, using limiters to boundthe numerical fluxes. Applications arise in pattern formationproblems for reaction–diffusion equations.     

Spectral Characterizations of Some Distance-Regular Graphs

When can one see from the spectrum of a graph whether it is distance-regular or not? We give some new results for when this is the case. As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2,1), (3,1) and (4,1), the Biggs-Smith graph, the M ₂₂ graph, and the coset graphs of the doubly truncated binary Golay code and the extended ternary Golay code.     

Spatial extent of random laser modes

We have experimentally studied the distribution of the spatial extent of modes and the crossover from essentially single-mode to distinctly multimode behavior inside a porous gallium phosphide random laser. This system serves as a paragon for random lasers due to its exemplary high index contrast. In the multimode regime, we observed mode competition. We have measured the distribution of spectral mode spacings in our emission spectra and found level repulsion that is well described by the Gaussian orthogonal ensemble of random-matrix theory.     

Light‐Controlled Histone Deacetylase (HDAC) Inhibitors: Towards Photopharmacological Chemotherapy

Cancer treatment suffers from limitations that have a major impact on the patient’s quality of life and survival. In the case of chemotherapy, the systemic distribution of cytotoxic drugs reduces their efficacy and causes severe side effects due to nonselective toxicity. Photopharmacology allows a novel approach to address these problems because it employs external, local activation of chemotherapeutic agents by using light. The development of photoswitchable histone deacetylase (HDAC) inhibitors as potential antitumor agents is reported herein. Analogues of the clinically used chemotherapeutic agents vorinostat, panobinostat, and belinostat were designed with a photoswitchable azobenzene moiety incorporated into their structure. The most promising compound exhibits high inhibitory potency in the thermodynamically less stable cis form and a significantly lower activity for the trans form, both in terms of HDAC activity and proliferation of HeLa cells. This approach offers a clear prospect towards local photoactivation of HDAC inhibition to avoid severe side effects in chemotherapy.     

Elucidation of the chemical and morphological structure of double-network (DN) hydrogels by high-resolution magic angle spinning (HRMAS) NMR spectroscopy

(1)H HRMAS NMR spectroscopy is applied to gain insight into the chemical and morphological structure of double-network (DN) hydrogels, prepared from poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAMPS) and poly(acrylamide) (PAAm). The method enables one to obtain detailed information at the molecular level about the formation of covalent bonds between the two polymer networks through non-reacted double bonds of the cross-linker N,N'-methylene bis(acrylamide) (MBAA). Evidence to the existence of strong hydrogen-bond interactions based on the N-H group of the PAMPS as a hydrogen-bond donor and the C=O group of the PAAm as a hydrogen-bond acceptor is also provided. These findings clarify the origin of the toughening mechanism and the exceptionally strong mechanical properties of DN gels, further supported by microhardness data.     

Water increases rates of epoxidation by Mn(III)porphyrins/imidazole/IO4(-) in CH2Cl2. Analogy with peroxidase and chlorite dismutase

Manganese(III)-meso-tetraphenylporphyrin [Mn(TPP)] and manganese(III)-meso-tetrakis(pentafluorophenyl)porphyrin [Mn(TPFPP)] catalyse the epoxidation of cyclooctene by IO(4)(-) in the presence of excess imidazoles, in both dry CH(2)Cl(2) and CH(2)Cl(2) saturated with H(2)O. The reaction rates of the electron deficient Mn(TPFPP) are a factor 24 less than those of Mn(TPP); however, the former increases 15-30 times in the presence of water, while those of Mn(TPP) do so by a factor of 2-3. The most striking catalytic enhancement caused by the addition of water was observed with 2-methylimidazole and Mn(TPFPP). As deprotonation of imidazoles may play a significant role in the presence of water, we found that manganese(III)-meso-tetrakis(phenyl-4-sulfonato)porphyrin [Mn(TPPS)] decreases the NH proton pK(a) of axially coordinated imidazole from 14.2 to 9.5. We conclude that the imidazole ligand is partially deprotonated in the presence of water. The latter enables the solvation of imidazolium ions that are formed simultaneously. The imidazolate form of the co-catalyst is a much stronger donor than the imidazole itself, providing electron density to Mn(III) and thus promoting oxygen transfer. The failure of N-methylimidazole to increase the reaction rates upon addition of water supports this hypothesis. A functionally related deprotonation has been shown to occur in horseradish peroxidase (J. S. de Ropp, V. Thanabal, G. N. La Mar, J. Am. Chem. Soc. 1985, 107, 8270-8272) and in chlorite dismutase (B. R. Goblirsch, B. R. Streit, J. L. Dubois, C. M. Wilmot, J. Biol. Inorg. Chem. 2010, 15, 879-888). Mn(III)porphyrins in combination with imidazoles and water constitute a functional biomimetic model of peroxidases.     

An odd characterization of the generalized odd graphs

We show that any connected regular graph with d+1 distinct eigenvalues and odd-girth 2d+1 is distance-regular, and in particular that it is a generalized odd graph.     

Synthesis of 3-amino-4-fluoropyrazoles

Fluorinated pyrazoles bearing additional functional groups that allow further functionalization are of considerable interest as building blocks in medicinal chemistry. The developed synthetic strategy for new 3-amino-4-fluoropyrazoles consists of a monofluorination of β-methylthio-β-enaminoketones using 1-(chloromethyl)-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane bis(tetrafluoroborate) (Selectfluor) toward the corresponding monofluorinated enaminoketones, followed by condensation with different hydrazines.