How to recognize convexity of a set from its marginals

We investigate the regularity of the marginals onto hyperplanes for sets of finite perimeter. We prove, in particular, that if a set of finite perimeter has log-concave marginals onto a.e. hyperplane then the set is convex. Our proof relies on measuring the perimeter of a set through a Hilbertian fractional Sobolev norm, a fact that we believe has its own interest.     

Säurealizarinschwarz SN als Reagens für extraktionsphotometrische Metallbestimmungen

Zusammenfassung Säurealizarinschwarz SN ist ein empfindliches Reagens zur spektralphotometrischen Bestimmung von Cu, U, Bi, Th, Fe, Mo und V. Arbeits-vorschriften für die einzelnen Metalle sowie Maskierungsmittel zur Ausschaltung von Störungen werden angegeben. Mit n-Butanol lassen sich alle Metallchelate aus wäßriger Lösung extrahieren und photometrieren. Zugabe eines C₁-bis C₃-Alkohols zum Metall-Farbstoffchelat in wäßriger Lösung bewirkt verschieden starke Erhöhung der Extinktion.

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Acid alizarin black SN as reagent for extraction photometric determinations of metals

Summary Acid alizarin Black SN is a sensitive reagent for the spectrophotometric determination of Cu, U, Bi, Th, Fe, Mo and V. Procedures are given for the individual metals and also for masking agents to avert interferences. All metal chelates can be extracted from aqueous solution and then determined photometrically. The addition of a C₁-C₃-alcohol to the metal dyestuff chelate in aqueous solution results in an increase of the extinction to varying degrees.

     

Transition Metal Promoted Cascade Heterocycle Synthesis through C−H Functionalization

Sequential, domino and tandem reactions could be defined as a sequence of synthetic transformations that occur one after the other, in the same reaction flask. This Review highlights recent advances at the overlap of two worlds: transition-metal mediated C−H activation as a trigger of cascade reaction, for the heterocycles synthesis. To shed some light on this intricate “middle-earth”, focus was put on the reaction mechanism rather than the type of metal or the chronological order of the reaction. The aim is to separate, and then highlight, the true domino reactions initiated by C−H activation, compared to other examples of C−H functionalization for heterocycle syntheses.     

Understanding the orientation and dynamic motion of planar heterocyclic N-donor ligands by exploiting the symmetry properties of mixed-ligand mu-oxorhenium(V) dinuclear complexes

Factors influencing the orientation and dynamic motions of planar N-donor heterocyclic ligands (L) are of interest since such features have broad relevance in metallobiochemistry [Marzilli, L. G.; Marzilli, P. A.; Alessio, E. Pure Appl. Chem. 1998, 70, 961-968]. We found that mu-oxorhenium(V) dinuclear complexes [ReOCl2LsLt]-O-[ReOCl2LsLt] bearing either symmetrical (L = py = pyridine; 3,5-lut = 3,5-lutidine) or lopsided (L = Me3-Bzm = 1,5,6-trimethylbenzimidazole) cis L ligands are particularly useful for studying these factors. NMR data showed that terminal (Lt) and stacked (Ls) ligands were exchanged by approximately 180 degrees rotation about the Re-O-Re bond system. Such exchange occurred, however, between degenerate chiral conformers. Here we report a combined X-ray structural and solution NMR investigation of the AA + CC (racemic) and AC (meso) forms of two mixed-ligand mu-oxorhenium dimers that bear one lopsided and one symmetrical ligand on each Re atom, namely, Re2O3-Cl4(py)2(Me3Bzm)2 (1rac and 1meso) and Re2O3Cl4(3,5-lut)2(Me3Bzm)2 (2rac and 2meso). The presence of two different cis L ligands in 1 and 2 breaks the local symmetry at each Re atom, so that, in the racemic dimers, the exchange of terminal and stacked ligands leads to nondegenerate conformers. Overall, NMR data showed that the unsymmetrical dimers 1 and 2 undergo two dynamic processes contemporaneously, namely, 180 degrees rotation about the Re-N(py or 3,5-lut) bond and coupled rotation about the Re-O-Re/Re-N bonds. Both processes reach the slow exchange limit below -80 degrees C. Rotation of py in 1 occurs faster than that of 3,5-lut in 2; this difference is attributed to the higher steric demands of 3,5-lut compared to py. For both dimers NMR data provided compelling evidence of the preferred conformers in solution, including ligand orientations. The low-T solution structure of 1meso and 2meso is chiral, the same as that found in the solid state for 2meso, where the Me3Bzm on one Re atom is stacked with the 3,5-lut on the other Re atom. The remaining Me3Bzm and 3,5-lut, one on each Re atom, are both terminal. In solution the coupled Re-O-Re/Re-N rotations interconvert the two halves of each meso dimer to yield the same overall stable chiral conformation. For the racemic dimers, however, this process does not interconvert one enantiomer into the other, but instead interconverts two rotamers, R1 and R2, each of which is chiral. We found that, in the case of both 1rac and 2rac, the conformer with stacking symmetrical ligands (R1) is roughly 1 order of magnitude more stable than that with stacking Me3Bzm ligands (R2). Moreover, the solution conformation of R1 is the same as that found in the solid state of 1rac. Solution- and solid-state data indicate that the key interaction favoring the observed conformations is very likely the electrostatic attraction between the delta+ H2 atoms on the Me3Bzm ligands and the negative O and Cl groups in the core of the dimers. Finally, for both meso and racemic dimers we were also able to elucidate the preferred pathways of the coupled dynamic motions and establish that, very likely, the two halves of the dimers swing back and forth by approximately 130 degrees through the anti eclipsed form.     

Promiscuity of carbonic anhydrase II. Unexpected ester hydrolysis of carbohydrate-based sulfamate inhibitors

Carbonic anhydrases (CAs) are enzymes whose endogenous reaction is the reversible hydration of CO(2) to give HCO(3)(-) and a proton. CA are also known to exhibit weak and promiscuous esterase activity toward activated esters. Here, we report a series of findings obtained with a set of CA inhibitors that showed quite unexpectedly that the compounds were both inhibitors of CO(2) hydration and substrates for the esterase activity of CA. The compounds comprised a monosaccharide core with the C-6 primary hydroxyl group derivatized as a sulfamate (for CA recognition). The remaining four sugar hydroxyl groups were acylated. Using protein X-ray crystallography, the crystal structures of human CA II in complex with four of the sulfamate inhibitors were obtained. As expected, the four structures displayed the canonical CA protein-sulfamate interactions. Unexpectedly, a free hydroxyl group was observed at the anomeric center (C-1) rather than the parent C-1 acyl group. In addition, this hydroxyl group is observed axial to the carbohydrate ring while in the parent structure it is equatorial. A mechanism is proposed that accounts for this inversion of stereochemistry. For three of the inhibitors, the acyl groups at C-2 or at C-2 and C-3 were also absent with hydroxyl groups observed in their place and retention of stereochemistry. With the use of electrospray ionization-Fourier transform ion cyclotron resonance-mass spectrometry (ESI-FTICR-MS), we observed directly the sequential loss of all four acyl groups from one of the carbohydrate-based sulfamates. For this compound, the inhibitor and substrate binding mode were further analyzed using free energy calculations. These calculations suggested that the parent compound binds almost exclusively as a substrate. To conclude, we have demonstrated that acylated carbohydrate-based sulfamates are simultaneously inhibitor and substrate of human CA II. Our results suggest that, initially, the substrate binding mode dominates, but following hydrolysis, the ligand can also bind as a pure inhibitor thereby competing with the substrate binding mode.     

Gold-mediated synthesis of α-ionone

A simple and convenient synthesis of α-ionone, an important component of flowers and fragrances, is reported. The key step in the formation of the α,β-unsaturated ketone moiety involves an NHC-Au^I catalyzed Meyer-Schuster-like rearrangement of readily prepared propargylic esters. The complex [{Au(IPr)}₂(μ-OH)][BF₄] proved to be the most efficient catalyst leading to α-ionone in 70% yield from a propargylic benzoate. This optimized procedure represents a valuable and attractive alternative to classical methods leading to α,β-unsaturated ketones, such as the Wittig or aldol reactions.     

Synthesis and structural,spectroscopic, and electrochemical characterization of new ruthenium dimethyl sulfoxide nitrosyls

The reactivity of ruthenium(II)- and ruthenium(III)-chloride-dimethyl sulfoxide precursors and of the antimetastatic drug [ImH][trans-RuCl(4)(dmso-S)(Im)] (NAMI-A, Im = imidazole, dmso = dimethyl sulfoxide) toward NO was investigated. Treatment of [(dmso)(2)H][trans-RuCl(4)(dmso-S)(2)] and mer-RuCl(3)(dmso)(3) with gaseous NO yielded [(dmso)(2)H][trans-RuCl(4)(dmso-O)(NO)] (1) and mer,cis-RuCl(3)(dmso-O)(2)(NO) (2), respectively. Thus, coordination of the strong pi-acceptor NO induces a S to O linkage isomerization of the dmso trans to it to avoid competition for pi-electrons. In light-protected nitromethane solutions, complex 2 equilibrates slowly with the two isomers mer-RuCl(3)(dmso-S)(dmso-O)(NO) (3), with NO trans to Cl, and mer-RuCl(3)(dmso-S)(dmso-O)(NO) (4), with NO trans to dmso-O; the equilibrium mixture consists of ca. 64% 2, 3% 3, and 33% 4. Treatment of the Ru(II) precursor trans-RuCl(2)(dmso-S)(4) with gaseous NO in CH(2)Cl(2) solution yielded the nitrosyl-nitro derivative trans,cis,cis-RuCl(2)(dmso-O)(2)(NO)(NO(2)) (5). Finally, [(Im)(2)H][trans-RuCl(4)(Im)(NO)] (6) was prepared by treatment of [ImH][trans-RuCl(4)(dmso-O)(NO)] (1Im) with an excess of imidazole in refluxing acetone. The spectroscopic features are consistent with the [Ru(NO)](6) formulation for all complexes, that is, a diamagnetic Ru(II) nucleus bound to NO(+). Compounds 1, 2, 5, and 6 were characterized also by X-ray crystallography; they all show a linear nitrosyl group, with short Ru-NO bond distances consistent with a strong d(pi) --> pi NO back-bonding. An unusual inertness of O-bonded dmso was observed in compound 1. Complexes 1, 2, 3, 5, and 6 are all redox active in DMF solutions showing irreversible reductions whose peak potentials depend on the other ligands attached to the Ru metal center. The site of reduction is the NO(+) moiety. The reduced complexes are not stable and release a Cl(-) or NO(2)(-) ligand followed by the NO(*) radical. The chemical reactions following electron transfer are all fast (rate constant >100 s(-1) at 293 K). The Ru product species are not redox active within the DMF window.