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Mikhail Khovanov 《Transactions of the American Mathematical Society》2006,358(1):315-327
We construct a new invariant of tangle cobordisms. The invariant of a tangle is a complex of bimodules over certain rings, well-defined up to chain homotopy equivalence. The invariant of a tangle cobordism is a homomorphism between complexes of bimodules assigned to boundaries of the cobordism.
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S.M. Cosseddu I.A. Khovanov M.P. Allen P.M. Rodger D.G. Luchinsky P.V.E. McClintock 《The European physical journal. Special topics》2013,222(10):2595-2605
The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications. 相似文献
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In this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the groupS
n coincide with the coefficients of the canonical basis innth tensor power of the fundamental representation of the quantum groupU
q
k
. We also use known results about canonical bases forU
q
2 to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds
to Grassmannians), due to Lascoux-Schützenberger and Zelevinsky. 相似文献
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MF Miller IA Franchi AS Sexton CT Pillinger 《Rapid communications in mass spectrometry : RCM》1999,13(13):1211-1217
The use of infrared laser-assisted fluorination to release oxygen from milligram quantities of silicates or other oxide mineral grains is a well-established technique. However, relatively few studies have reported the optimisation of this procedure for oxygen-17 isotope measurements. We describe here details of an analytical system using infrared (10 μm) laser-assisted fluorination, in conjunction with a dual inlet mass spectrometer of high resolving power ( approximately 250) to provide (17)O and (18)O oxygen isotope measurements from 0.5-2 mg of silicates or other oxide mineral grains. Respective precisions (1) of typically 0.08 and 0.04 per thousand are obtained for the complete analytical procedure. Departures from the mass-dependent oxygen isotope fractionation line are quantified by Delta(17)O; our precision (1) of such measurements on individual samples is shown to be +/-0.024 per thousand. In turn, this permits the offset between parallel, mass-dependent fractionation lines to be characterised to substantially greater precision than has been possible hitherto. Application of this system to investigate the (17)O versus (18)O relationship for numerous terrestrial whole-rock and mineral samples, of diverse geological origins and age, indicates that the complete data set may be described by a single, mass-dependent fractionation line of slope 0.5244+/- 0.00038 (standard error). Copyright 1999 John Wiley & Sons, Ltd. 相似文献
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Noise-induced escape from the basin of attraction of a strange attractor (SA) in a periodically excited nonlinear oscillator
is investigated. It is shown by numerical simulation methods that escape occurs in two steps: transfer of the system from
the SA to a close-lying saddle cycle along several optimal trajectories, and a subsequent fluctuation-induced transfer from
the basin of attraction of the SA along a single optimal trajectory. The possibility of using the results of this work to
solve problems of the optimal control of switchings from an attractor and for constructing theoretical estimates of the escape
probability is discussed.
Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 782–787 (10 June 1999) 相似文献
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We consider the derived categories of modules over a certain family () of graded rings, and Floer cohomology of Lagrangian intersections in the symplectic manifolds which are the Milnor fibres of simple singularities of type We show that each of these two rather different objects encodes the topology of curves on an -punctured disc. We prove that the braid group acts faithfully on the derived category of -modules, and that it injects into the symplectic mapping class group of the Milnor fibers. The philosophy behind our results is as follows. Using Floer cohomology, one should be able to associate to the Milnor fibre a triangulated category (its construction has not been carried out in detail yet). This triangulated category should contain a full subcategory which is equivalent, up to a slight difference in the grading, to the derived category of -modules. The full embedding would connect the two occurrences of the braid group, thus explaining the similarity between them.
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Mikhail Khovanov 《Transactions of the American Mathematical Society》1997,349(6):2297-2315
A doodle is a finite number of closed curves without triple intersections on an oriented surface. There is a ``fundamental' group, naturally associated with a doodle. In this paper we study these groups, in particular, we show that fundamental groups of some doodles are automatic and give examples of doodles whose fundamental groups have non-trivial center.
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