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Michael Ruzhansky Ville Turunen Jens Wirth 《Journal of Fourier Analysis and Applications》2014,20(3):476-499
In this paper we give several global characterisations of the Hörmander class \(\Psi ^m(G)\) of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols. 相似文献
13.
We demonstrate experimentally the feasibility of a certain coherence-theoretic algorithm for determining the relative modal weights of a laser beam that consists of multiple Hermite-Gaussian transverse modes. A computer-controlled Young's two-pinhole interferometer with a linear CCD array is used for the coherence measurements. The required scaling parameter (beam width) is obtained iteratively by library routines. Numerical simulations on the stability of the algorithm in the presence of experimental noise are also presented. 相似文献
14.
The relative thermodynamic stabilities of four isomeric vinyl ethers obtained by acid-catalyzed cleavage of MeOH from the dimethyl acetals of both 2-acetyltetrahydrofuran and 2-isobutyryltetrahydrofuran have been determined by chemical equilibration in cyclohexane solution. In addition, the structures and relative energies of many of these compounds have also been studied theoretically by DFT calculations. In each series of compounds, the endocyclic isomers, 5-(1-methoxyethyl)-2,3-dihydrofuran and 5-(1-methoxy-2-methylpropyl)-2,3-dihydrofuran, respectively, show the highest thermodynamic stabilities. This is particularly prominent for the vinyl ethers derived from 2-isobutyryltetrahydrofuran in which the equilibrium mixture consists of 90% of the endocyclic isomer at room temperature. The geometrical (exocyclic) isomers of the latter series of compounds show unexpected relative thermodynamic stabilities, but on the basis of the geometry-optimized structures provided by the DFT calculations, a reasonable explanation can be found. 相似文献
15.
The constitutive models for the viscoelasticity of polymers are presented for determining molecular weight distributions (MWDs) from viscosity measurements. The inversion of this model derived from control theory and melt calibration procedure connects the relaxation modulus, viscosity, and other flow properties of a polymer. The linear principle enables simultaneous and accurate modelling of the relaxation modulus and of viscosity flow curves over a wide range. Starting from viscosity measurements, the new model is used to determine the MWD, linear viscoelastic relaxation moduli, and the relaxation spectra of polyethylene of different grades. In addition, two benchmark analyses of bimodal polystyrene are reported, and the capability of the model is proven by the two-box test of Malkin. The error of the modelled viscosity is smaller than that for previously reported models. One of the main features of this work is that no relaxation time or spectrum procedures were used to generate and model linear viscoelasticity. 相似文献
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Ryan J. Weiss Philip L. S. M. Gordts Dzung Le Ding Xu Jeffrey D. Esko Yitzhak Tor 《Chemical science》2015,6(10):5984-5993
Surfen, bis-2-methyl-4-amino-quinolyl-6-carbamide, was previously reported as a small molecule antagonist of heparan sulfate (HS), a key cell-surface glycosaminoglycan found on all mammalian cells. To generate structure–activity relationships, a series of rationally designed surfen analogs was synthesized, where its dimeric structure, exocyclic amines, and urea linker region were modified to probe the role of each moiety in recognizing HS. An in vitro assay monitoring inhibition of fibroblast growth factor 2 binding to wild-type CHO cells was utilized to quantify interactions with cell surface HS. The dimeric molecular structure of surfen and its aminoquinoline ring systems was essential for its interaction with HS, and certain dimeric analogs displayed higher inhibitory potency than surfen and were also shown to block downstream FGF signaling in mouse embryonic fibroblast cells. These molecules were also able to antagonize other HS–protein interactions including the binding of soluble RAGE to HS. Importantly, selected molecules were shown to neutralize heparin and other heparinoids, including the synthetic pentasaccharide fondaparinux, in a factor Xa chromogenic assay and in vivo in mice. These results suggest that small molecule antagonists of heparan sulfate and heparin can be of therapeutic potential for the treatment of disorders involving glycosaminoglycan–protein interactions. 相似文献
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Esko Taskinen 《Journal of Physical Organic Chemistry》2010,23(2):105-114
A computational study of the stable conformations and gas‐phase enthalpies of formation at 25 °C of the title compounds has been carried out by G3(MP2)//B3LYP calculations. The work stems from our early observations on the thermodynamic and NMR spectroscopic properties of 2‐methylenetetrahydropyran and related compounds suggesting a dominating chair conformation, with poor p–π overlap in the ? O? C?C moiety, for these compounds. Besides computational verification of the chair conformation of 2‐methylenetetrahydropyran, the work was extended to find out the stable conformations of a number of other related compounds and to evaluate the relative stabilities of the various conformers. Another important goal of the work was the estimation of the gas‐phase enthalpies of formation of the present compounds, for which such literature data are scarce. A significant error in the literature value of the enthalpy of formation of methylenecyclohexane was found. Finally, the relative enthalpy levels of the isomeric compounds of this work are discussed. The high thermodynamic stability of the compounds containing an ester functional group, ? O? C?O, relative to the stability of isomeric compounds with an ? O? C?C moiety in place of the ester function, is demonstrated. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
20.
Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, 1994) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains both semimartingales and non-semimartingales. The motivation comes partially from the recent work by Bender et al. (Finance Stoch, 12:441–468, 2008), where it is shown that the quadratic variation of the log-returns determines the hedging strategy. 相似文献