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Markus Bödenler Ludovic de Rochefort P. James Ross Nicolas Chanet Geneviève Guillot Gareth R. Davies 《Molecular physics》2019,117(7-8):832-848
ABSTRACTFast field-cycling (FFC) nuclear magnetic resonance relaxometry is a well-established method to determine the relaxation rates as a function of magnetic field strength. This so-called nuclear magnetic relaxation dispersion gives insight into the underlying molecular dynamics of a wide range of complex systems and has gained interest especially in the characterisation of biological tissues and diseases. The combination of FFC techniques with magnetic resonance imaging (MRI) offers a high potential for new types of image contrast more specific to pathological molecular dynamics. This article reviews the progress in FFC-MRI over the last decade and gives an overview of the hardware systems currently in operation. We discuss limitations and error correction strategies specific to FFC-MRI such as field stability and homogeneity, signal-to-noise ratio, eddy currents and acquisition time. We also report potential applications with impact in biology and medicine. Finally, we discuss the challenges and future applications in transferring the underlying molecular dynamics into novel types of image contrast by exploiting the dispersive properties of biological tissue or MRI contrast agents. 相似文献
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A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ
d
withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections
with statistical mechanics. Of course, polygons on ℤ
d
are defined up to a translation, and the relevant statistic is their perimeter.
A SAP on ℤ
d
is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing
it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher
dimension.
We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's
result, which explains combinatorially the form of the generating function. We then compute the generating function for convex
SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However,
our method suggests that the generating function for convex SAPs on ℤ
d
is always a quotient ofdifferentiably finite power series. 相似文献
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By using a sheaf-theoretical language, we introduce a notion of deformation quantization allowing not only for formal deformation parameters but also for real or complex ones as well. As a model for this approach to deformation quantization, we construct a quantization scheme for cotangent bundles of Riemannian manifolds. Here, we essentially use a complete symbol calculus for pseudodifferential operators on a Riemannian manifold. Depending on a scaling parameter, our quantization scheme corresponds to normally ordered, Weyl or antinormally ordered quantization. Finally, it is shown that our quantization scheme induces a family of pairwise isomorphic strongly closed star products on a cotangent bundle. 相似文献
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Markus Szymik 《Topology and its Applications》2007,154(11):2323-2332
Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner [S. Waner, Equivariant RO(G)-graded bordism theories, Topology and its Applications 17 (1984) 1-26], the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterised in terms of congruences. This is first shown to be a stable problem, and then solved using methods of equivariant stable homotopy theory with respect to a semi-free G-universe. 相似文献
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G.Biju Kumar Hetal.V Patel Amrish C Shah Markus Trenkle Christine J Cardin 《Tetrahedron: Asymmetry》1996,7(12):3391-3396
N-Arylsulfonamides of (R)- and (S)-2-amino-1-butanol, on condensation with aromatic aldehydes produced diastereomerically pure 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines. The absolute configurations of one enantiomeric pair have been determined from two fully refined X-ray structures, supplemented by nmr data. 相似文献