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61.
We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess–Zumino–Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain convex polytopes, and write them explicitly as multiple sums measuring those volumes. We focus on su(2), but discuss higher-point (
) and higher-genus fusion in a general way. The method follows that of our previous work on tensor product multiplicities, and so is based on the concepts of generalised Berenstein–Zelevinsky diagrams, and virtual couplings. As a by-product, we also determine necessary and sufficient conditions for non-vanishing higher-point fusion multiplicities. In the limit of large level, these inequalities reduce to very simple non-vanishing conditions for the corresponding tensor product multiplicities. Finally, we find the minimum level at which the higher-point fusion and tensor product multiplicities coincide. 相似文献
62.
Seth C. Rasmussen Jason C. Pickens James E. Hutchison 《Journal of heterocyclic chemistry》1997,34(1):285-288
A new synthetic route to 4-substituted-2,2′-bithiophenes has been developed utilizing 4-bromo-2,2′-bithiophene ( 1 ). Formation of the bithienyllithium adduct via halogen-metal exchange was found to be problematic and resulted in complex mixtures of products. The Grignard reagent of 1 can be obtained easily via the “entrainment” method, allowing the production of 4-substituted-2,2′-bithiophenes (where sub-stituent = octyl, hydroxyethyl, hydroxymethyl, carboxy, carbomethoxy, acetoxyethyl, and acetoxymethyl). 相似文献
63.
Molten LLDPE and HDPE plates (thickness 2 mm) have been inflated into a circular cylinder (inner radius 31 mm) under isothermal conditions. Low deformation rates allow the plates to be inflated considerably into the cylinder, and at high inflation rates an early burst is observed.Axis-symmetric numerical simulation of the inflations have been performed, using a constitutive equation in the form of a separable memory integral where the strain dependence is described by the Linear Molecular Stress Function (L-MSF) model with dissipative convective constraint release. The material parameters in the constitutive model are obtained using liner viscoelastic (oscillatory shear) and uni-axial elongational measurements.The numerical simulations were performed for inflation of a flat plate and a perturbed plate, where a small circular cone was removed from the centre of the surface of the plate. This was done in order to investigate the stability of the inflations. It is shown that all of the inflations are hydrodynamically unstable, though the effect on the occurrence of the burst is limited. One exception is at slow inflation, where an unexpected burst may appear as a consequence of minute deviations from an ideal flat plate. All of the numerical calculations show quantitative agreement with the experiments for a wide range of experimental conditions. This strongly suggests that the initiation of the burst is a hydrodynamic phenomenon.The critical parameters in the inflation of molten linear polymers have been investigated using the Gel equation as a memory function (M(s)=Ans
–(1+n)) and inflating the plate with a constant velocity for the top of the plate. The hydrodynamic burst in a linear polymer is mainly associated with the linear viscoelastic properties and only slightly with the non-linear strain dependence. Increased (linear) elasticity reduces the inflated volume, at the same inflation velocity, before the burst occurs. Furthermore, the critical parameter for the occurrence of the burst (whether or not the burst occurs) is related to the crossover point (G=G) in linear viscoelasticity. 相似文献
64.
The gauge cell Monte Carlo method is extended to calculations of the incremental chemical potentials and free energies of linear chain molecules. The method was applied to chains of Lennard-Jones beads with stiff harmonic bonds up to 500 monomers in length. We show that the suggested method quantitatively reproduces the modified Widom particle insertion method of Kumar et al. [S. K. Kumar, I. Szleifer, and A. Z. Panagiotopoulos, Phys. Rev. Lett. 66(22), 2935 (1991)], and is by an order of magnitude more efficient for long chains in terms of the computational time required for the same accuracy of chemical potential calculations. The chain increment ansatz, which suggests that the incremental chemical potential is independent of the chain length, was tested at different temperatures. We confirmed that the ansatz holds only for coils above the θ temperature. Special attention is paid to the effects of the magnitude of adsorption potential and temperature on the behavior of single chains in confinements that are comparable in size with the free chain radius of gyration. At sufficiently low temperatures, the dependence of the incremental chemical potential on the chain length in wetting pores is superficially similar to a capillary condensation isotherm, reflecting monolayer formation following by pore volume filling, as the chain length increases. We find that the incremental gauge cell method is an accurate and efficient technique for calculations of the free energies of chain molecules in bulk systems and nanoconfinements alike. The suggested method may find practical applications, such as modeling polymer partitioning on porous substrates and dynamics of chain translocation into nanopores. 相似文献
65.
Harrison S Fraser K Lane G Hughes D Villas-Boas S Rasmussen S 《Analytical and bioanalytical chemistry》2011,401(9):2955-2963
The main water-soluble carbohydrates in temperate forage grasses are polymeric fructans. Fructans consist of fructose chains
of various chain lengths attached to sucrose as a core molecule. In grasses, fructans are a complex mixture of a large number
of isomeric oligomers with a degree of polymerisation ranging from 3 to >100. Accurate monitoring and unambiguous peak identification
requires chromatographic separation coupled to mass spectrometry. The mass range of ion trap mass spectrometers is limited,
and we show here how monitoring selected multiply charged ions can be used for the detection and quantification of individual
isomers and oligomers of high mass, particularly those of high degree of polymerization (DP > 20) in complex plant extracts.
Previously reported methods using linear ion traps with low mass resolution have been shown to be useful for the detection
of fructans with a DP up to 49. Here, we report a method using high-resolution mass spectrometry (MS) using an Exactive Orbitrap
MS which greatly improves the signal-to-noise ratio and allows the detection of fructans up to DP = 100. High-sugar (HS) Lolium perenne cultivars with high concentrations of these fructans have been shown to be of benefit to the pastoral agricultural industry
because they improve rumen nitrogen use efficiency and reduce nitrous oxide emissions from pastures. We demonstrate with our
method that these HS grasses not only contain increased amounts of fructans in leaf blades but also accumulate fructans with
much higher DP compared to cultivars with normal sugar levels. 相似文献
66.
Anne Rasmussen John Wyller Jon Olav Vik 《Nonlinear Analysis: Real World Applications》2011,12(1):304-319
We review and complement the study of the mathematical properties of the predator–prey dynamical system for spruce–budworm interactions studied in Ludwig et al. [D. Ludwig, D. Jones, C.S. Holling, Qualitative analysis of insect outbreak systems: the spruce budworm and forest, Journal of Animal Ecology 47 (1978), 315–332]. We use the singular perturbation method to identify parameter regimes which permit relaxation oscillations. The leading order contribution to the period of these oscillations is computed by means of this method and compared with the outcome of direct numerical simulations. 相似文献
67.
Abstract We wish to report on some hitherto partly unnoticed and unexplained features in the infrared spectra of hydrogen halides of ethylenediamine. We have prepared normal, C-, N-, and perdeuterated ethylenediammonium chlorides and bromides and measured their infrared spectra in the range 4000–10 cm?1. 相似文献
68.
R. A. Broglia T. Døssing M. Matsuo E. Vigezzi P. Bosetti A. Bracco S. Frattini B. Herskind S. Leoni P. Rasmussen 《Zeitschrift für Physik A Hadrons and Nuclei》1987,356(3):259-262
Rotational motion loses its coherence as a function of the nuclear internal excitation energy. The damping process does not proceed in a continuous fashion and scars of discrete rotational bands are found, inbedded in a background of damped rotational states, regardless whether the calculations are carried out using effective or “random” forces. The complexity of the damping mechanism is revealed in the lineshape of the ridges in the γ-γ correlation spectrum. 相似文献
69.
E. F. Jones P. M. Gore S. J. Zhu J. H. Hamilton A. V. Ramayya J. K. Hwang R. Q. Xu L. M. Yang K. Li Z. Jiang Z. Zhang S. D. Xiao X. Q. Zhang W. C. Ma J. D. Cole M. W. Drigert I. Y. Lee J. O. Rasmussen Y. X. Luo M. A. Stoyer 《Physics of Atomic Nuclei》2006,69(7):1198-1203
We have used our analysis of γ-γ-γ data (5.7 × 1011 triples and higher folds) taken with Gammasphere from prompt γ rays emitted in the spontaneous fission of 252Cf to study the collective bands in 104,106,108Mo. The one-phonon and two-phonon γ-vibrational bands and known two-quasiparticle bands in neutron-rich 104,106Mo were extended to higher spins. The one-and two-phonon γ-vibrational bands have remarkably close energies for transitions from the same spin states and identical moments of inertia.
Several new bands are observed and are proposed as quasiparticle bands in 104,106Mo, along with the first β-type vibrational band in 106Mo. The quasiparticle bands have essentially constant moments of inertia near the rigid-body value that indicate blocking
of the pairing interaction. Candidates for chiral doublet bands in 106Mo are strong. These are the first reported chiral vibrational bands in an even-even nucleus.
The text was submitted by the authors in English. 相似文献
70.
This study investigates students' retention of mathematical knowledge and skills in two differential equations classes. Posttests and delayed posttests after 1 year were administered to students in inquiry‐oriented and traditional classes. The results show that students in the inquiry‐oriented class retained conceptual knowledge, as seen by their performance on modeling problems, and retained equal proficiency in procedural problems, when compared with students in the traditionally taught classes. The results of this study add additional support to the claim that teaching for conceptual understanding can lead to longer retention of mathematical knowledge. 相似文献