The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

A novel editing technique for F MRI: Molecule-specific imaging

A novel technique is proposed to facilitate the selective imaging of specific molecules from a mixture. The application of the technique presented here demonstrates the ability to selectively produce ¹⁹F MR images of either trifluoroacetic acid or the perfluorocarbon emulsion Oxypherol-ET (perfluorotributylamine), when both molecules are present simultaneously. Selective detection is based on the presence of homonuclear J-modulation in one molecule and differential spin-spin relaxation time (T₂). Perfluorotributylamine, an A₃B₂ system, is subject to homonuclear J-modulation, which produces a null signal from the antiphase components of the triplet (A₃) when an echo time is used in a spin-echo image. At this echo time the second molecule, in this example trifluoroacetic acid, a non-coupled spin system, is selectively imaged. At longer echo times, e.g., TE = 1/J there is substantial recovery of the J-modulated signal, which may be solely observed due to T₂ decay of the trifluoroacetic acid signal. The method is demonstrated both using phantoms and in vivo.     

Reversibly self-assembled pH-responsive PEG-p(CL-g-TMC) polymersomes

Polymersomes have gained much interest within the biomedical field as drug delivery systems due to their ability to transport and protect cargo from the harsh environment inside the body. For an improved drug efficacy, control over cargo release is however also an important factor to take into account. An often employed method is to incorporate pH sensitive groups in the vesicle membrane, which induce disassembly and content release when the particles have reached a target site in the body with the appropriate pH, such as the acidic microenvironment of tumor tissue or the endosome. In this paper, biodegradable poly(ethylene glycol)-poly(caprolactone-gradient-trimethylene carbonate)-based polymeric vesicles have been developed with disassembly features at mild acidic conditions. Modifying the polymer backbone with imidazole moieties results in vesicle disassembly upon protonation due to the lowered pH. Furthermore, upon increasing the pH efficient re-assembly into vesicles is observed due to the switchable amphiphilic nature of the polymer. When this re-assembly process is conducted in presence of cargo, enhanced encapsulation is achieved. Furthermore, the potency of the polymeric system for future biomedical applications such as adjuvant delivery is demonstrated.     

Dynamic metal-ligand coupling in the infrared MCD spectra of the cobalt(II) tetrahalides

The axial single-crystal magnetic circular dichroism spectra of Cs₃ZnCl₅/Co²⁺ and Cs₃ZnBr₅/Co²⁺ have been measured over the 4000–7000 cm^?1 region of the ⁴A₂ → ⁴T₁ (F) transition at ambient and liquid-helium temperature. The B/D and C/D terms obtained give transition moment ratios, 〈t₂∥m∥t₂〉/〈e∥m∥t₂〉, in accord with the value required (?3^{$\text{1}\text{2}$}/2^{$\text{1}\text{2}$}) by a dynamic ligand-polarisation model for d-electron transition probabilities in tetrahedral metal complexes.     

Quinazolines and 1,4-benzodiazepines. XCV. Synthesis of 1,4-benzodiazepines by ring expansion of 2-chloromethylquinazolines with carbanions

1,4-Benzodiazepines bearing a carbon substituent at the 2-position were obtained by reaction of 2-chloromethylquinazoline 3-oxides with stabilized carbanions. The carbanions of alkyl acetates, N,N-disubstituted acetamides, acetonitrile, dimethylsulfone, N,N-dimethyl methanesulfonamide and 2-methylpyridine were successfully applied. The conversion of some of the 2-carbon substituted 1,4-benzodiazepines to imidazo[1,5-a][1,4]benzodiazepines and [1,2,5]oxadiazino[5,4-a][1,4]benzodiazepines is described.     

The Surface Energy of MgO: Multiscale Reconstruction from Thermal Groove Geometry

The surface energy of MgO is determined using experimental data collected from equilibrated thermal grooves circumscribing island grains. Local equilibrium assumptions at each groove require that the Herring equations be satisfied at each data site, thereby yielding a large and overdetermined system of equations involving the surface energy . This inverse problem is then solved using a new technique that is statistical in nature and multiscale in implementation. The resulting discrete solution represents a statistically significant representation of the surface energy of MgO as a function of surface orientation. Comparisons to results derived from a more traditional approach, along with suggested further applications, are discussed.     

Laurent–Padé Approximants to Four Kinds of Chebyshev Polynomial Expansions. Part I. Maehly Type Approximants

Laurent Padé–Chebyshev rational approximants, A _m (z,z ^–1)/B _n (z,z ^–1), whose Laurent series expansions match that of a given function f(z,z ^–1) up to as high a degree in z,z ^–1 as possible, were introduced for first kind Chebyshev polynomials by Clenshaw and Lord [2] and, using Laurent series, by Gragg and Johnson [4]. Further real and complex extensions, based mainly on trigonometric expansions, were discussed by Chisholm and Common [1]. All of these methods require knowledge of Chebyshev coefficients of f up to degree m+n. Earlier, Maehly [5] introduced Padé approximants of the same form, which matched expansions between f(z,z ^–1)B _n (z,z ^–1) and A _m (z,z ^–1). The derivation was relatively simple but required knowledge of Chebyshev coefficients of f up to degree m+2n. In the present paper, Padé–Chebyshev approximants are developed not only to first, but also to second, third and fourth kind Chebyshev polynomial series, based throughout on Laurent series representations of the Maehly type. The procedures for developing the Padé–Chebyshev coefficients are similar to that for a traditional Padé approximant based on power series [8] but with essential modifications. By equating series coefficients and combining equations appropriately, a linear system of equations is successfully developed into two sub-systems, one for determining the denominator coefficients only and one for explicitly defining the numerator coefficients in terms of the denominator coefficients. In all cases, a type (m,n) Padé–Chebyshev approximant, of degree m in the numerator and n in the denominator, is matched to the Chebyshev series up to terms of degree m+n, based on knowledge of the Chebyshev coefficients up to degree m+2n. Numerical tests are carried out on all four Padé–Chebyshev approximants, and results are outstanding, with some formidable improvements being achieved over partial sums of Laurent–Chebyshev series on a variety of functions. In part II of this paper [7] Padé–Chebyshev approximants of Clenshaw–Lord type will be developed for the four kinds of Chebyshev series and compared with those of the Maehly type.     

Histidine and deuterium-labelled histidine by asymmetric catalytic reduction and assignment of the absolute stereochemistry by neutron diffraction

We describe an efficient and convenient route for the preparation of enantiomerically pure d-labelled histidine by asymmetric hydrogenation with a Rh–diphosphine complex in the presence of strong non-coordinating acids. A single-crystal neutron diffraction study of the selectively dideuterated N-benzoyl-histidine methyl ester, tetrafluoroborate salt determined the absolute stereochemistry. This allowed us to clarify the role of H⁺ in the whole reduction process.     

Radical identification by liquid chromatography/thermospray mass spectrometry

Radical adducts of 5,5-dimethyl-1-pyrroline N-oxide (DMPO) with hydroxyl, methanol-derived, and ethanol-derived radicals were detected by a combination of liquid chromatography with either electron paramagnetic resonance or thermospray mass spectrometry (LC/EPR or LC/TSP-MS) in the Fenton system (with methanol or ethanol). One radical adduct was observed in the reaction of DMPO with the hydroxyl radical or the methanol-derived radical, while two adducts were detected in the reaction of DMPO with ethanol-derived radicals. The LC/TSP-MS spectra showed quasi-molecular ions [M + H]+ at m/z 146 and m/z 160 for the methanol-derived and ethanol-derived radical adducts, respectively, and an apparent molecular ion M+ at m/z 130 for the hydroxyl radical adduct. Use of methyl-D3 alcohol (CD3OH) and ethyl-D5 alcohol (CD3CD2OH) indicated that carbon-centered radicals are formed. Experiments with partially deuterated ethanol (CD3CH2OH and CH3CD2OH) indicated that the two adducts observed in the reaction of DMPO with ethanol-derived radicals correspond to the two diastereomeric adducts of DMPO with the alpha-hydroxyethyl free radical.