A note on a symmetry result for traveling waves in cylinders

We prove in this note that all bounded traveling waves, in cylinders, of some -dimensional viscous conservation laws are symmetric.

     

Spontaneous trans‐Selective Transfer Hydrogenation of Apolar Boron–Boron Double Bonds

The transfer hydrogenation of N‐heterocyclic carbene (NHC)‐supported diborenes with dimethylamine borane proceeds with high selectivity for the trans‐1,2‐dihydrodiboranes. DFT calculations, supported by kinetic studies and deuteration experiments, suggest a stepwise proton‐first‐hydride‐second reaction mechanism via an intermediate μ‐hydrodiboronium dimethylaminoborate ion pair.     

Scattering Below Critical Energy for the Radial 4D Yang-Mills Equation and for the 2D Corotational Wave Map System

Given g and f  =  gg′, we consider solutions to the following non linear wave equation :

New oxacalix[4]arene carboxylate detects viologen in protic media

ABSTRACT

We demonstrate that Ullman fragment-coupling can be used to synthesise an oxacalix[4]arene monocarboxylic acid, which provides easy access to its water-soluble carboxylato derivatives. Crystallographic and computational data suggest that the new carboxyl-substituted oxacalix[4]arene adopts a 1,3-alternate conformation both in the solid-state and in methanol solution. Its water-soluble tetrabutylammonium derivate can detect the herbicide paraquat at neutral pH in aqueous media (K _a = 111 ± 3 M^–1) and in methanol (K _a = 2020 ± 70 M^–1).     

Bottleable Neutral Analogues of [B2H5]− as Versatile and Strongly Binding η2 Donor Ligands

Herein we report the discovery that two bottleable, neutral, base‐stabilized diborane(5) compounds are able to bind strongly to a number of copper(I) complexes exclusively through their B?B bond. The resulting complexes represent the first known complexes containing unsupported, neutral σ_B?B diborane ligands. Single‐crystal X‐ray analyses of these complexes show that the X?Cu moiety (X=Cl, OTf, C₆F₅) lies opposite the bridging hydrogen atom of the diborane and is near perpendicular to the B?B bond, interacting almost equally with both boron atoms and causing a B?B bond elongation. DFT studies show that σ donation from and π backdonation to the pseudo‐π‐like B?B bond account for their formation. Astoundingly, these copper σ_B?B complexes are inert to ligand exchange with pyridine under either heating or photoirradiation.     

Concentric glucose/O2 biofuel cell

A concentric glucose/O₂ biofuel cell has been developed. The device is constituted of two carbon tubular electrodes, one in the other, and combines glucose electrooxidation at the anode and oxygen electroreduction at the cathode. The anodic catalyst is glucose oxidase co-immobilized with the mediator 8-hydroxyquinoline-5-sulfonic acid hydrate, and the cathodic catalyst is bilirubin oxidase co-immobilized with the mediator 2,2′-azinobis (3-ethylbenzothiazoline-6-sulfonate) diammonium salt. Both enzymes and mediators are entrapped at the surface of the tubular electrodes by an electrogenerated polypyrrole polymer. The originality of the concentric configuration is to compartmentalize the anode and cathode electrodes and to supply dissolved oxygen separate from the electrolyte in order to avoid secondary reactions. The dissolved oxygen circulates through the inside of the cathode tube and diffuses from the inner to the external surface of the tube to react directly with the immobilized bilirubin oxidase. The assembled biofuel cell is studied at 37 °C in phosphate buffer pH 7.4. We show the influence of the thickness of the polypyrrole polymer on the electrochemical activity of the biocathodes. We also demonstrate the effect of the chemical reticulation of the enzymes by glutaraldehyde within the polymer on the performances of the bioelectrodes. The maximum power density delivered by the assembled glucose/O₂ biofuel cell reaches 42 μW cm⁻², evaluated from the geometric area of the electrodes, at a cell voltage of 0.30 V with 10 mM glucose. The results demonstrate that the concentric design of the BFC based on compartmented electrodes is a promising architecture for further development of micro electronic devices.     

Synthesis of the 2,4,5-tri-tert-butyl-1,3-diphospholide anion by phosphinidene elimination from 2,4,6-tri-tert-butyl-1,3,5-triphosphabenzene on treatment with the amide Li[NPh(SiMe3)

Treatment of the lithium amide Li[NPh(SiMe3)] with 2,4,6-tri-tert-butyl-1,3,5-triphosphabenzene, P(3)C(3)tBu(3), in a 1:2 ratio afforded equimolar amounts of the lithium salt of the five-membered 2,4,5-tri-tert-butyl-1,3-diphospholide anion, LiP(2)C(3)tBu(3) (isolated as its N,N,N',N'-tetramethylethylenediamine (TMEDA) adduct), and the tricyclic compound 6-[phenyl(trimethylsilyl)amino]-3,5,7-tri-tert-butyl-1,2,4,6-tetraphosphatricyclo[3.2.0.0(2,7)]hept-3-ene. Both compounds have been structurally characterised by single-crystal X-ray diffraction studies. The mechanism of this remarkable reaction has been elucidated by theoretical methods at the B3LYP/6-311+G** level of theory. The reaction involves a hitherto unobserved aminophosphinidene, which was formed by abstraction of a phosphorus atom from triphosphabenzene. The intermediate aminophosphinidene, which is further stabilised by the solvent THF, shows, in agreement with previous theoretical predictions, enhanced stability and reacts then with a second molecule of triphosphabenzene.     

Radiative transmission of lepton flavor hierarchies

We discuss a one loop model for neutrino masses which leads to a seesaw-like formula with the difference that the charged lepton masses replace the unknown Dirac mass matrix present in the usual seesaw case. This is a considerable reduction of parameters in the neutrino sector and predicts a strong hierarchical pattern in the right handed neutrino mass matrix that is easily derived from a U(1)_H family symmetry. The model is based on the left–right gauge group with an additional Z₄ discrete symmetry which gives vanishing neutrino Dirac masses and finite Majorana masses arising at the one loop level. Furthermore, it is one of the few models that naturally allow for large (but not necessarily maximal) mixing angles in the lepton sector. A generalization of the model to the quark sector requires three iso-spin singlet vector-like down type quarks, as in E₆. The model predicts an inert doublet type scalar dark matter.