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1 Introduction From its first introduction in [14], the Jones polynomial has played a decisive role in knot theory. This invariant κ → V κ associates to an oriented link κ ⊂ S 3 a Laurent polynomial in t 1/2. It is completely characterised by V unknot = 1 and a relation obtained from the Kauffman bracket calculus, which allows one to successively reduce the(More)
Sixty-four samples from six grade 4 astrocytomas were investigated ex vivo by 1H MRS at 360 MHz and subsequently by histopathology to obtain percentages of viable and necrotic tumour and grey and white matter. MR-visible lipids were detected in 87% of tumour samples. Necrotic foci were < 3 x 3 x 6 mm3. The means of the intensities/unit weight tissue of the(More)
The main metabolic pathways in Methanospirillum hungatei GP1 were followed by using 13C nuclear magnetic resonance, with 13C-labeled acetate and CO2 as carbon sources. The labeling patterns found in carbohydrates, amino acids, lipids, and nucleosides were consistent with the formation of pyruvate from acetate and CO2 as the first step in biosynthesis.(More)
The application of 13-C nuclear magnetic resonance to the analysis of some sialic acid-containing meningococcal polysaccharide antigens is described. Complete assignments of the spectra of both the native serogroup B and the de-O-acetylated serogroup C polysaccharides have been made. These assignments were based on the corresponding data for some related(More)
Isolinoleic acid (18:2 delta 6,9) deuterated at 10 different positions was esterified to form 1-palmitoyl-2-isolinoleoyl-sn-glycero-3-phosphocholine (PiLPC), and the average structural and motional properties of the diunsaturated chain, in aqueous dispersions of PiLPC, were examined by 2H NMR spectroscopy. For each sample, 2H spectra were acquired over a(More)
Oleic acid specifically deuterated at fifteen different positions along the chain, including the double bond, was biosynthetically incorporated into the membrane lipids of the microorganism Acholeplasma laidlawii B. A detailed study of the dynamic conformation of these chains was carried out using deuterium nuclear magnetic resonance. The deuterium spectra(More)
Some biological characteristics of cancer cells and solid tumors are identifiable by the high resolution NMR relaxation behavior of their nonaqueous components. Chemical analysis and two-dimensional scalar correlated (COSY) NMR spectroscopy show these resonances arise from neutral lipid in the plasma membrane. Triglyceride is shown to be the main plasma(More)
We present a new proof of a result due to Taubes: if (X, ω) is a closed symplectic four-manifold with b+(X) > 1 + b1(X) and λ[ω] ∈ H 2 (X; Q) for some λ ∈ R + , then the Poincaré dual of KX may be represented by an embedded symplectic submanifold. The result builds on the existence of Lefschetz pencils on symplectic four-manifolds. We approach the(More)