A Singular Quasilinear Anisotropic Elliptic Boundary Value Problem. II

Let with . We consider the equations

with and . We show that if is a convex bounded region in , there exists at least one classical solution to this boundary value problem. If the region is not convex, we show the existence of a weak solution. Partial results for the existence of classical solutions for non-convex domains in are also given.

     

Volumetric intensity dependence on the formation of molecular and atomic ions within a high intensity laser focus

The mechanism of atomic and molecular ionization in intense, ultra-short laser fields is a subject which continues to receive considerable attention. An inherent difficulty with techniques involving the tight focus of a laser beam is the continuous distribution of intensities contained within the focus, which can vary over several orders of magnitude. The present study adopts time of flight mass spectrometry coupled with a high intensity (8 x 10(15) Wcm(-2)), ultra-short (20 fs) pulse laser in order to investigate the ionization and dissociation of the aromatic molecule benzene-d1 (C(6)H(5)D) as a function of intensity within a focused laser beam, by scanning the laser focus in the direction of propagation, while detecting ions produced only in a "thin" slice (400 and 800 microm) of the focus. The resultant TOF mass spectra varies significantly, highlighting the dependence on the range of specific intensities accessed and their volumetric weightings on the ionization/dissociation pathways accessed.     

C-F Bond activation at Ni(0) and simple reactions of square planar Ni(II) fluoride complexes

The reaction of Ni(COD)(2)(COD = 1,5-cyclooctadiene) with triethylphosphine and pentafluoropyridine in hexane has been shown previously to yield trans-[NiF(2-C(5)NF(4))(PEt(3))(2)](1a) with a preference for reaction at the 2-position of the heteroaromatic. The corresponding reaction with 2,3,5,6-tetrafluoropyridine was shown to yield trans-[NiF(2-C(5)NF(3)H)(PEt(3))(2)](1b). In this paper, we show that reaction of Ni(COD)(2) with triethylphosphine and pentafluoropyridine in THF yields a mixture of 1a and 1b. Competition reactions of Ni(COD)(2) with triethylphosphine in the presence of mixtures of heteroaromatics in hexane reveal a kinetic preference of k(pentafluoropyridine):k(2,3,5,6-tetrafluoropyridine)= 5.4:1. Treatment of 1a and 1b with Me(3)SiN(3) affords trans-[Ni(N(3))(2-C(5)NF(4))(PEt(3))(2)](2a) and trans-[Ni(N(3))(2-C(5)NHF(3))(PEt(3))(2)](2b), respectively. The complex trans-[Ni(NCO)(2-C(5)NHF(3))(PEt(3))(2)](3b) is obtained on reaction of with Me(3)SiNCO and by photolysis of under CO, while trans-[Ni(eta(1)-C [triple bond CPh)(2-C(5)NF(4))(PEt(3))(2)](4a) is obtained by reaction of phenylacetylene with 1a. Addition of KCN, KI and NaOAc to complex 1a affords trans-[Ni(X)(2-C(5)NF(4))(PEt(3))(2)](5a X = CN, 6a X = I, 7a X = OAc), respectively. The PEt(3) groups of complex are readily replaced by addition of 1,2-bis(dicyclohexylphosphino)ethane (dcpe) to produce [NiF(2-C(5)F(4)N)(dcpe)](8a). Addition of dcpe to trans-[Ni(OTf)(2-C(5)F(4)N)(PEt(3))(2)](10a), however, yields the salt [Ni(2-C(5)F(4)N)(dcpe)(PEt(3))](OTf)(9a) by substitution of only one PEt(3) and displacement of the triflate ligand. The structures of 2b, 4a, 7a and 8a were determined by X-ray crystallography. The influence of different ancillary ligands on the bond lengths and angles of square-planar nickel structures with polyfluoropyridyl ligands is analysed.     

Calorimetric glass transition temperature and absolute heat capacity of polystyrene ultrathin films

The absolute heat capacity and glass transition temperature (T_g) of unsupported ultrathin films were measured with differential scanning calorimetry with the step-scan method in an effort to further examine the thermodynamic behavior of glass-forming materials on the nanoscale. Films were stacked in layers with multiple preparation methods. The absolute heat capacity in both the glass and liquid states decreased with decreasing film thickness, and T_g also decreased with decreasing film thickness. The magnitude of the T_g depression was closer to that observed for films supported on rigid substrates than that observed for freely standing films. The stacked thin films regained bulk behavior after the application of pressure at a high temperature. The effects of various preparation methods were examined, including the use of polyisobutylene as an interleaving layer between the polystyrene films. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3518–3527, 2006     

Multiple periodic solutions for a nonlinear suspension bridge equation

We investigate nonlinear oscillations in a fourth-order partialdifferential equation which models a suspension bridge. Previouswork establishes multiple periodic solutions when a parameterexceeds a certain eigenvalue. In this paper, we use Leray-Schauderdegree theory to prove that if the parameter is increased further,beyond a second eigenvalue, then additional solutions are created.     

Routine analysis by high precision gas chromatography/mass selective detector/isotope ratio mass spectrometry to 0.1 parts per mil

Stable isotope methods are potentially quite useful for validating natural or enhanced mineral degradation of contaminants. For this reason, a continuous flow gas chromatograph (GC), isotope ratio mass spectrometer (IRMS) has been coupled with a quadrupole mass selective detector (MSD) to allow simultaneous mass spectral and stable carbon isotope ratio data to be obtained from a single chromatographic analysis. This allows the target contaminant and any extra-cellular degradation intermediates to be both qualified and quantified. Previously acceptable limits of precision (0.3 parts per mil) are undesirable given the small fractionation observed during aerobic degradation. To further understand the fate of organic contaminants and to gain information about the metabolic degradative pathway employed by a microorganism, routine isotopic analyses on a range of analytes have been performed. Quantities of sample producing mass-44 ion beam signal (I(44)) of 2 x 10(-10) to 1 x 10(-8) A were analysed. When the IRMS was tuned for high sensitivity, ion source nonlinearities were overcome by peak height correction from an algorithm that was produced using known isotopic standards of varying concentrations. This led to sample accuracy of <0.01 per thousand and sample precision of 0.1 per thousand. Copyright 1999 John Wiley & Sons, Ltd.     

Investigation of the quantitative properties of the quadrupole orthogonal acceleration time-of-flight mass spectrometer with electrospray ionisation using 3,4-methylenedioxymethamphetamine

This paper describes the investigation of the potential of a quadrupole orthogonal acceleration time-of-flight mass spectrometer (Q-TOF) equipped with an atmospheric pressure ionisation interface for quantitative measurements of small molecules separated by reversed phase liquid chromatography. To this end, the detection limits and linear dynamic range in particular were studied in an LC/MS/MS experiment using 3,4-methylenedioxymethamphetamine standards and 3,4-methylenedioxyethylamphetamine for internal standardisation. In a second phase, the experiment was repeated with real biological extracts (whole blood, serum, and vitreous humour). A calibration for 3,4-methylenedioxymethamphetamine and its metabolite 3,4-methylenedioxyamphetamine was prepared in each of these matrices again using 3,4-methylenedioxyethylamphetamine as internal standard. The resulting quantitative data were compared with those obtained by liquid chromatography with fluorescence detection for the same extracts. The Q-TOF results revealed excellent sensitivity and a linear dynamic range of nearly four decades (2-10 000 pg on-column, r(2) = 0.9998, 1/x weighting). Furthermore, all the calibration curves prepared in biological material were superimposable, LC/MS/MS and LC-fluorescence, and the quantitative results for actual samples compared very favourably. It was concluded that the Q-TOF achieves a linear dynamic range for quantitative LC/MS/MS work exceeding that of fluorescence detection and at much better absolute sensitivity. Copyright 1999 John Wiley & Sons, Ltd.     

Deprotection of heteroaromatic carbamates via a base-catalyzed methanolysis

A simple and mild method for the deprotection of heteroaromatic carbamates via methanolysis using a catalytic amount of base such as sodium methoxide, DBU, or Verkade’s base (proazaphosphatranes) is presented. Carbamate protecting group of an aliphatic amine is not affected under these conditions.