Well-posedness of the free-surface incompressible Euler equations with or without surface tension

We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. This is a free boundary problem for the motion of an incompressible perfect liquid in vacuum, wherein the motion of the fluid interacts with the motion of the free-surface at highest-order.

     

Polynomial Convexity of Teichmuller Spaces

It is well known that finite-dimensional Teichmüller spacesare holomorphically convex, that is, they are domains of holomorphy.Moreover, the holomorphic convexity is fulfilled for all Teichmüllerspaces in a stronger form: they are complex hyperconvex. In this note we establish that, in fact, finite-dimensionalTeichmüller spaces possess a much stronger convexity property,namely, they are polynomially convex; in other words, they areRunge domains. Additionally, some geometric properties of Teichmüllerspaces are established.     

Synthesis and molecular structure of [Al(CH3)2]2[C10H22N4] [Al(CH3)3]2: Condensation product of trimethylaluminum and a multidentate open-chain amine

The crystalline condensation product [Al(CH₃)₂]₂[C₁₀H₂₂N₄][Al(CH₃)₃]₂ is prepared from reaction of the multidentate open-chain amine 1,4-bis(3-aminopropyl)piperazine with trimethylaluminum in methylene chloride. The compound crystallized in the monoclinic space groupC2/c with unit cell parametersa=25.166(12),b=7.268(4),c=17.316(4) Å,=115.3(4)°, andD _c =1.06 g cm^–3 forZ=4. Least-squares refinement based on 1054 observed reflections with intensitiesI 3(I) in the range 2<2<45° led to a finalR factor of 0.053 (R _w =0.064). The title compound resides on a crystallographic center of symmetry with independent Al-N distances of 1.889(5), 2.058(5), and 2.030(5) Å.     

A sharp exponential inequality for Lorentz-Sobolev spaces on bounded domains

This paper generalizes an inequality of Moser from the case that is in the Lebesgue space to certain subspaces, namely the Lorentz spaces , where . The conclusion is that is integrable, where . This is a higher degree of integrability than in the Moser inequality when . A formula for is given and it is also shown that no larger value of works.

     

A simple method for methylmercury,inorganic mercury and ethylmercury determination in plasma samples by high performance liquid chromatography–cold-vapor-inductively coupled plasma mass spectrometry

A simple and sensitive method with a fast sample preparation procedure is proposed for the determination of mercury species in plasma/serum. The method combines online high-performance liquid chromatography separation, Hg cold-vapor formation and inductively coupled plasma mass spectrometry detection. Prior to analysis, plasma (250 μL) was accurately pipetted into 15 mL conical tubes. Then, an extractant solution containing mercaptoethanol, L-cysteine and HCl was added to the samples following sonication for 10 min. Quantitative mercury extraction was achieved with the proposed procedure. Separation of mercury species was accomplished in less than 8 min on a C8 reverse phase column with a mobile phase containing 3% v/v methanol + 97% v/v (0.5% v/v 2-mercaptoethanol + 0.05% v/v formic acid). The method detection limits were found to be 12 ng L⁻¹, 5 ng L⁻¹ and 4 ng L⁻¹ for inorganic mercury, ethylmercury and methylmercury, respectively. Method accuracy is traceable to Standard Reference Material (SRM) 966 Toxic Metals in Bovine Blood from NIST. Additional validation was provided by the analysis of a secondary reference serum sample from the INSQ-Canada. Finally, the method was successfully applied for the speciation of mercury in plasma samples collected from volunteers exposed to methylmercury through fish consumption. For the first time to our knowledge, levels of different species of Hg in plasma samples from riverside populations exposed to MeHg were determined.     

Chain-configurational properties of novolac phenol–formaldehyde resins

Rotational isomeric-state chain-configurational calculations have been applied to the novolac phenol–formaldehyde structure. Steric interference allows the chain to be considered with a twofold potential energy barrier model. Computations that fit the observed dipole-moment data over a range of molecular weights indicate that the conformational angle is near ±80°, with the g^±g⁼ states on the average being 155 cal/mole below the g^±g^± states. The limiting dipole-moment ratio is computed to be 1.47, compared to the experimental value of 1.48. A negative temperature coefficient agrees in sign with the experimental value, and the characteristic ratio of the end-to-end molecular dimensions is calculated to be 3.27, as compared to the experimental value of 4.76.     

Fluorenyl dendrimer porphyrins: synthesis and photophysical properties

New symmetrical dendrimeric type super-porphyrin bearing sixteen fluorenyl donor groups sixteen fluorenylporphyrin SOFP (1) have been synthesized and characterized. Preliminary photophysical properties are reported; in comparison to the references first generation dendrimer tetrafluorenylporphyrin TOFP (2) bearing four peripheral fluorenyl and second generation dendrimer octafluorenylporphyrin OOFP (3) bearing eight peripheral fluorenyl, the luminescence properties are slightly improved. It is found that the excitation energy transfer occurs from the sixteen fluorenyl units to the porphyrin core, following what the porphyrin emits intense red light.     

Intermolecular coupling of alkenes to heterocycles via C-H bond activation

The intermolecular coupling of unactivated alkenes to a range of heterocycles using a Rh(I) catalyst was investigated. A variety of functional groups were incorporated into the alkene, including esters, nitriles, acetals, and phthalimide. Furthermore, the heterocycle tolerated substitution with both electron-rich and electron-deficient groups. The intermolecular coupling became possible after it was discovered that weak acids dramatically increase the rate of both the inter- and intramolecular reactions. An extensive optimization of additives was performed, and HCl.PCy(3) (Cy = cyclohexyl) and HCl.P-t-Bu(2)Et were in general found to be the best additives for the reaction.     

A family of fluorenyl dendrons for porphyrin dendrimers synthesis

A series of dendrons bearing various number of fluorenyl donor groups have been synthesized. First, the reference compound 2-(bromomethyl)-9H-fluorene (8) with one fluorenyl unit, then dendron 10, with two fluorenyl arms, and finally new generation dendrons, 11 and 12, bearing four peripheral fluorenyl arms were synthesized and characterized. A series of different generations of porphyrin dendrimers, obtained from these dendrons are also presented. Preliminary results on higher generation dendrimers are reported as well. Under mild basic conditions, surprisingly, a new compound 1 incorporating a fluorenyl unit in the cycle and three pendant fluorenyl arms was obtained by an intramolecular reaction of brominated tetrapod dendron 12.