Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems

We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrödinger system, which are systems in two variables and . The Zakharov system is known to be locally well-posed in and the Klein-Gordon-Schrödinger system is known to be locally well-posed in . Here, we show that the Zakharov and Klein-Gordon-Schrödinger systems are globally well-posed in these spaces, respectively, by using an available conservation law for the norm of and controlling the growth of via the estimates in the local theory.

     

Weighted enumeration of spanning subgraphs in locally tree‐like graphs

Using the theory of negative association for measures and the notion of unimodularity for random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree‐like graphs. Specifically, the normalized logarithm of the associated partition function (free energy) is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton–Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitly. As an illustration, we provide a new asymptotic formula for the maximum size of a b‐matching in the Erd?s–Rényi random graph with fixed average degree and diverging size, for any $b\in\mathbb{N}Using the theory of negative association for measures and the notion of unimodularity for random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree‐like graphs. Specifically, the normalized logarithm of the associated partition function (free energy) is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton–Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitly. As an illustration, we provide a new asymptotic formula for the maximum size of a b‐matching in the Erd?s–Rényi random graph with fixed average degree and diverging size, for any $b\in\mathbb{N}$. To the best of our knowledge, this is the first time that correlation inequalities and unimodularity are combined together to yield a general proof of uniqueness of Gibbs measures on infinite trees. We believe that a similar argument is applicable to other Gibbs measures than those over spanning subgraphs considered here. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

An interface comprising molecular wires and poly(ethylene glycol) spacer units self-assembled on carbon electrodes for studies of protein electrochemistry

The characterization and application of a modified electrode interface for protein electrochemistry is reported. This generic interface is composed of a mixed monolayer of oligo(phenylethynylene) molecular wires (MWs) and poly(ethylene glycol) (PEG) deposited on glassy carbon electrodes by reductive adsorption of the respective aryl diazonium salts. Electrochemistry and scanning electron microscopy demonstrate that the PEG component exhibits a distinct decrease in nonspecific adsorption of blood serum and the proteins bovine serum albumin (BSA) and horseradish peroxidase (HRP) relative to a bare glassy carbon electrode. The ability of the MWs to facilitate efficient electron transfer through the PEG layer to the underlying electrode was demonstrated by covalently attaching ferrocenemethylamine to the end of the MWs. The calculated rate constant for this system was 229 +/- 30 s(-1). Covalent attachment of HRP to the MWs allowed direct electron transfer to the redox protein with almost ideal electrochemistry, indicating a specific interaction between the MW and HRP, with a rate constant of 13.4 +/- 2.3 s(-1). This rate constant is more rapid than previously reported for HRP shown to still be catalytically active. Retained catalytic activity of HRP was demonstrated by the enzyme responding to the addition of hydrogen peroxide. Similarly, by attaching myoglobin to the end of the MWs, a rate constant for this protein of 2 s(-1) was measured. The rigidity of the MWs, as well as it being longer than the PEG diluent, means this generic interface can be employed to investigate the electrochemistry of a wide range of redox proteins.     

Reaction mechanisms and kinetics for the oxidations of dimethyl sulfide, dimethyl disulfide, and methyl mercaptan by the nitrate radical

This study examines the initial oxidation routes of the three major reduced sulfur compounds (CH(3)SH, CH(3)SCH(3), and CH(3)SSCH(3)) by the nitrate radical using density functional and ab initio methods. Stationary points along each reaction pathway are examined using different levels of theory and basis sets to ensure the convergence of the results. Kinetics calculations follow on the determined reaction pathways to obtain the rate constants. This study shows that sulfur compounds exhibit a general trend of hydrogen abstraction following the formation of an initial sulfur-nitrate complex. The results are in agreement with experimental work on CH(3)SCH(3) and CH(3)SH, while refuting a proposal of several previous studies that oxygen addition is the dominant oxidation pathway in the case of CH(3)SSCH(3). The rate constants obtained from kinetics calculations are consistent with experimental findings and exhibit negative temperature dependence. Overall, this study confirms the importance of nitrate in the oxidation of reduced sulfur compounds in the atmosphere.     

Synthesis, NMR conformational analysis and pharmacological evaluation of 7,7a,13,14-tetrahydro-6H-cyclobuta[b]pyrimido[1,2-a:3,4-a']diindole analogues as melatonin receptor ligands

A structure for the self-condensation product of 2-(1H-indol-2-yl)ethyl tosylate 2a, previously proposed as 6,7,14,15-tetrahydro-15aH-azocino[1,2-a:6,5-b]diindole 3a, was revised based on the (13)C-2D-INADEQUATE experiment, and proved to be 7,7a,13,14-tetrahydro-6H-cyclobuta[b]pyrimido[1,2-a:3,4-a']diindole 4a. A mechanism for the unexpected formation of this novel hexacyclic heterocycle was proposed and its NMR solution structure was elucidated. Five derivatives of the title ring skeleton 12-16 designed as melatonin receptor ligands were synthesized and their affinities for the human MT(1) and MT(2) receptors were determined. Both butyramides 13 and 15, as well as the non-methoxy acetamide 12 exhibited micromolar binding affinities for both receptors being slightly MT(2) selective. The methoxy acetamide 14 showed the best pharmacological profile exhibiting a five times higher affinity for MT(1) (K(i) = 49 nM) than for MT(2) (K(i) = 246 nM) receptor.     

Ring-borylated 15-electron and 17-electron ansa-chromocene complexes, their physical properties and molecular structures

A detailed study of the thermal decomposition of the zwitterionic, ring-borylated ansa-chromocene hydrido carbonyl complex [Cr(CO)H{Me(4)C(2)(C(5)H(4))[C(5)H(3)B(C(6)F(5))(3)]}] (2) is described. This complex is formed in the reaction between [Cr(CO){Me(4)C(2)(C(5)H(4))(2)}] (1) and B(C(6)F(5))(3) in toluene at -78 degrees C. Above -25 degrees C, 2 decomposes to a 50:50 mixture of the low-spin, 17e Cr(III) complexes [Cr(CO){Me(4)C(2)(C(5)H(4))[C(5)H(3)B(C(6)F(5))(3)]}] (3b) and [Cr(CO){Me(4)C(2)(C(5)H(4))(2)}][HB(C(6)F(5))(3)] (4). Carbon monoxide elimination from 3 b generates high-spin, 15 e [Cr{Me(4)C(2)(C(5)H(4))[C(5)H(3)B(C(6)F(5))(3)]}] (3a), which coordinates two other electron-donating ligands, such as xylyl isocyanide, PMe3, and PPh(2)Me to form the low-spin, 17 e electron complexes 3c, 3d, and 3e, respectively. High-spin, 15 e [Cr{Me(4)C(2)(C(5)H(4))(2)}][HB(C(6)F(5))(3)] (5) is generated by heating 3 b in toluene at 100 degrees C and periodically removing the evolved CO. Efforts to isolate more than a few X-ray quality crystals of 5 were thwarted by its tendency to form an insoluble precipitate (6) with the same molecular formula. Heating the solution of 5 at 120 degrees C results in its partial conversion (ca. 28 %) to 3a, thereby allowing the formation of 3a in yields as high as 74 % from the reaction between 1 and B(C(6)F(5))(3). The X-ray crystal structures of 3 b-e and 5 are described. Cyclic voltammetry measurements on 3 a-e reveal a dramatic reduction in the redox potentials of the complexes relative to their non-borylated analogues. DFT calculations show that this is due primarily to electrostatic stabilization of the oxidized species by the negatively charged borylate group. EPR and 19F NMR spectroscopy allow 3a to be distinguished from its Lewis base adducts 3 b-e and reveal the relative affinities of different Lewis bases for the chromium.     

Amine-functionalised SBA-15 of tailored pore size for heavy metal adsorption

This study examines the synthesis of SBA-15 with tailored pore sizes through controlled thermal treatment for the adsorption of Pb and Cd ions. The aim is to produce a material that can adsorb heavy metals at both high and low concentrations. The materials were characterised by means of N(2) physisorption, powder X-ray diffraction (PXRD), diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), microanalysis and transmission electron microscopy (TEM). The surface areas ranged from 410 to 871 m(2)g(-1), and pore diameter was increased from 5.9 to 10.8 nm. This method allows for maximum adsorption of metal ions at very low concentrations. Metal ion adsorption was determined using an Atomic Absorption Spectrophotometer. The effects of pH were found to play a major role in the precipitation and, therefore, adsorption of metal ions. This method proved to be efficient at adsorbing large quantities of both metals (39 and 41 mg g(-1) for Pb and Cd, respectively).     

A magnetic resonance imaging contrast agent capable of detecting hydrogen peroxide

The redox-active ligand N-(2-hydroxy-5-methylbenzyl)-N,N',N'-tris(2-pyridinylmethyl)-1,2-ethanediamine (Hptp1) was prepared and complexed to manganese(II). The isolated [Mn(Hptp1)(MeCN)](2+) serves as a magnetic resonance imaging contrast agent, with an r(1) value comparable to those of other mononuclear gadolinium(III) and manganese(II) complexes. The metal and ligand are stable in aerated aqueous solutions, but the addition of H(2)O(2) causes the complex to oxidatively couple to itself through a bimolecular reaction involving the phenol groups of two Hptp1 ligands. The binuclear product is less paramagnetic per manganese(II) than its mononuclear precursor, lowering the measured r(1) per manganese(II). The manganese(II) complex with Hptp1 can thereby serve as a sensor for oxidative stress.     

Properties of the polyhydride anions [WH5(PMe2Ph)3]- and [ReH4(PMePh2)3]- and periodic trends in the acidity of polyhydride complexes

The new anionic complexes [K(18-crown-6)][WH5(PMe2Ph)3], [K(1,10-diaza-18-crown-6)][WH5(PMe2Ph)3], [K(2,2,2-crypt)][ReH4(PMePh2)3], and [K(1,10-diaza-18-crown-6)][ReH4(PMePh2)3] were prepared by reaction of KH/crown or KH/crypt with the appropriate neutral polyhydride WH6(PMe2Ph)3 or ReH5(PMePh2)3. The rate of deprotonation of the rhenium hydride in THF is much greater for the reaction involving crypt compared with that of crown. The structure of [ReH4(PMePh2)3]- is distorted pentagonal bipyramidal as determined by an X-ray diffraction study of the crypt salt. No hydridic-protonic M-H...HN bonding is detected between the hydrides of the anionic hydrides and the amino hydrogens of the cations [K(1,10-diaza-18-crown-6)]+ suggesting that stronger M-H...K interactions are present. Acid dissociation constants Ka of polyhydride complexes in THF, approximately corrected for ion pairing, are determined by NMR in order to better understand the periodic trends of metal hydrides. The pKalphaTHF of (WH6(PMe2Ph)3/[WH5(PMe2Ph)3]-) is 42+/-4 according to the equilibrium set up by reacting WH6(PMe2Ph)3 with [K(2,2,2-crypt)][ReH6(PCy3)2]. The pKalphaTHF for ReH5(PMePh2)3 can be estimated as greater than the pKalphaTHF of 38 for HNPh2 and less than the pKalphaTHF of 41 for ReH7(PCy3)2. Reaction of the phosphazene base P4-tBu with ReH7(PCy3)2 gave an equilibrium with [HP4-tBu]+[ReH6(PCy3)2]- whereas reaction with WH6(PMe2Ph)3 gave an equilibrium with [HP4-tBu]+[WH5(PMe2Ph)3]-. From these and a related equilibrium, the pKalphaTHF of [HP4-tBu]+ is found to be 40+/-4. In general, neutral complexes MHx(PR3)n (M=W, Re, Ru, Os, Ir; n=3, 2) studied to date have pKalphaTHF values from 30 to 44 on going from phenyl-substituted to alkyl-substituted phosphine ligands whereas MHx(PR3)n+ (M=Re, Fe, Ru, Os, Co, Rh, Ni, Pd, Pt; n=4, 3), including diphosphine ligands ((PR3)2=PR2-PR2), have values from 12 to 23. From the equilibrium established from the reaction of [HP2-tBu][BPh4] and [K(2,2,2-crypt)][OP(OEt)2NPh], [HP2-tBu]+ was calculated to have a pKalphaTHF of 30+/-4. The equilibrium constant for the similar deprotonation reaction with [K(18-crown-6)][{ReH2(PMePh2)2}2(mu-H)3] confirmed this value.