A computation of the Witt index for rational quadratic forms

Summary This paper adds the finishing touches to an algorithmic treatment of quadratic forms over the rational numbers. The Witt index of a rational quadratic form is explicitly computed. When combined with a recent adjustment in the Haase invariants, this gives a complete set of invariants for rational quadratic forms, a set which can be computed and which respects all of the standard natural operations (including the tensor product) for quadratic forms. The overall approach does not use (at least explicitly) anyp-adic methods, but it does give the Witt ring of thep-adics as well as the Witt ring of the rationals.     

Shubnikov-de Haas effects in Bi2Se3 with high carrier concentrations

Shubnikov-de Haas frequencies were measured in highly degenerate n-type Bi₂Se₃ having a higher carrier density (～9 × 10²⁵m^-3) than previously reported. The Fermi surface was found to be elongated along the trigonal axis, fitting a spheroidal model with an axial ratio of 5.0 for angles up to θ = 45°. Comparison of the number of carriers obtained from Hall measurements with that obtained from the Shubnikov-de Haas measurement supports the contention that the lowest conduction band minimum is a single surface located in the center of the Brillouin zone. The higher effective mass (0.25 m₀) found for these carrier concentrations indicates that the band is non-parabolic.     

Water suppression without signal loss in HR-MAS 1H NMR of cells and tissues

In cell and tissue samples, water is normally three orders of magnitude more abundant than other metabolites. Thus, water suppression is required in the acquisition of NMR spectra to overcome the dynamic range problem and to recover metabolites that overlap with the broad baseline of the strong water resonance. However, the heterogeneous cellular environment often complicates water suppression and the strong coupling of water to membrane lipids interferes with the NMR detection of membrane associated lipid components. The widely used water suppression techniques including presaturation and double pulsed field gradient selective echo result in more than a 70% reduction in membrane associated lipid components in proton spectra of cells and tissues compared to proton spectra acquired in the absence of water suppression. A water suppression technique based on the combination of selective excitation pulses and pulsed field gradients is proposed to use in the acquisition of high resolution MAS NMR spectra of tissue specimens and cell samples. This pulse sequence methodology enables efficient water suppression for intact cells and tissue samples and eliminates signal loss from cellular metabolites.     

Search for Resonant WW and WZ Production in pp collisions at √s=1.96 TeV

We search for resonant WW or WZ production by using up to 5.4 fb(-1) of integrated luminosity collected by the D0 experiment in run II of the Fermilab Tevatron Collider. The data are consistent with the standard model background expectation, and we set limits on a resonance mass by using the sequential standard model W' boson and the Randall-Sundrum model graviton G as benchmarks. We exclude a sequential standard model W' boson in the mass range 180-690 GeV and a Randall-Sundrum graviton in the range 300-754 GeV at 95% C.L.     

Nonlinear behavior of model equations which are linearly ill-posed

We discuss two model equations of nonlinear evolution which demonstrate that linearly ill-posed problems may be well-posed in a mild sense. For the nonlocal equation (1.4), smooth solutions exist for all time, are unique, and depend continuously on the initial data in low norms. For the partial differential equation (1.1), solutions always exist; we do not know whether they are unique, but if they are, they also have continuous dependence on data. The large-time behavior of solutions and other qualitative properties are discussed     

A finite volume method for numerical grid generation

A novel method to generate body‐fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables ξ, η and ζ is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re‐zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid‐correction procedure. The scalar variables are re‐mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet–Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local‐boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point‐by‐point and whole‐field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright © 1999 National Research Council of Canada.     

Spectral baseline ripple in hot-electron bolometer mixers due to local oscillator phase and amplitude instabilities

High resolution millimetre and submillimetre wave astronomical spectrometers using hot-electron bolometer mixers as detectors often show marked standing wave patterns in the spectral baseline. LO phase noise contributes through two mechanisms: the phase noise side-bands may be converted to amplitude noise in the source because of the power-frequency characteristic of the source, or they can be converted to in-band amplitude noise through the action of the quasi-optical discriminator formed by the mixer, beam-splitter and telescope structure. The baseline ripple components due to each of these mechanisms have different characteristic periods, and under some circumstances can dominate the spectrometer baseline. The ripple levels estimated using the theory agree well with those observed in practice. It is shown that with careful design systematic effects due to this cause can be reduced to a negligible level.     

Biosynthetic Studies on Antibiotics

The intricacies of the synthetic chemistry executed by living cells in the assembly of complex organic natural products can be probed in great detail by stable-isotope labeling in conjunction with sophisticated 2D and multiple-quantum NMR methods of analysis. Mechanistic details are revealed by unraveling the “cryptic” stereochemistry of biosynthetic reactions with the aid of stereospecific isotope labeling. Analysis of blocked mutants and cloning of biosynthetic genes provides new tools for the study of biosynthetic pathways and for the exploitation of the chemical capabilities of living organisms.     

Microfabricated bioreactor chips for immobilised enzyme assays

A microfabricated device is reported that has been designed to permit the in situ packing of a section of channel with enzyme immobilised onto controlled pore glass (CPG). It is fabricated from glass and polydimethylsiloxane and to prevent dead volumes, has dedicated channels for packing the reactor. The device has the advantage of being simple in design, the flow through enzyme reactor channel being simply a widened section of the analyte channel. The system is suitable for both hydrodynamic and electro-osmotic pumping, and is designed such that when the packing is exhausted it can be repacked. Controlled pore glass provides a reproducible none swelling, high porosity medium onto which the enzyme could be immobilised. The large particle size meant that it was vital to optimise the immobilisation procedure in order to achieve acceptable enzyme activity. The microfabricated device was developed with two enzymes of different molecular masses; alkaline phosphatase and xanthine oxidase. The pore size of the CPG was found to be very important for xanthine oxidase, where the 697 Å pore size (120-200 mesh) CPG was found to give the highest activity (18-20% activity retained after immobilisation). The microfabricated device was used for the assay of p-nitrophenyl phosphate and hypoxanthine with spectrophotometric detection at 405 and 470 nm, respectively. The limits of detection were 5 and 8 μM, respectively.     

Photochemical Reactions in the Synthesis of Protein–Drug Conjugates

The ability to modify biologically active molecules such as antibodies with drug molecules, fluorophores or radionuclides is crucial in drug discovery and target identification. Classic chemistry used for protein functionalisation relies almost exclusively on thermochemically mediated reactions. Our recent experiments have begun to explore the use of photochemistry to effect rapid and efficient protein functionalisation. This article introduces some of the principles and objectives of using photochemically activated reagents for protein ligation. The concept of simultaneous photoradiosynthesis of radiolabelled antibodies for use in molecular imaging is introduced as a working example. Notably, the goal of producing functionalised proteins in the absence of pre-association (non-covalent ligand-protein binding) introduces requirements that are distinct from the more regular use of photoactive groups in photoaffinity labelling. With this in mind, the chemistry of thirteen different classes of photoactivatable reagents that react through the formation of intermediate carbenes, electrophiles, dienes, or radicals, is assessed.