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本文是从群的角度对纽结进行研究，构造出了一种从纽结群到置换群的表示，可以更好的反映纽结的性质。通过把这种方法的推广，计算机为工具，通过遍历算法将某些特殊的纽结群到某些置换群的所有的表示找到。共轭是一种等价关系，本文详细的找到在共轭意义下几个简单纽结基本群的所有表示。这比国外学者的结果好很多。
Quasi-polynomial mixing of the 2D stochastic Ising model with "plus" boundary up to criticality
Ising model Mixing time Phase coexistence Glauber dynamics
2011/1/18
We considerably improve upon the recent result of [34] on the mixing time of Glauber dynamics for the 2d Ising model in a box of side L at low temperature and with random boundary conditions whose dis...
Two-dimensional subwavelength plasmonic lattice solitons
Two-dimensional subwavelength plasmonic lattice solitons
2010/12/28
We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two ...
Two-dimensional dissipative solitons supported by localized gain
Two-dimensional dissipative solitons localized gain
2010/12/28
We show that the balance between localized gain and nonlinear cubic dissipation in the twodimensional nonlinear Schr¨odinger equation allows for existence of stable two-dimensional localized modes whi...
Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations
Stretching folding diagnostics three-dimensional Euler Navier-Stokes equations
2010/12/28
Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vor-ticity (q = ω · ∇) associated with solutions of the...
Transitivity and rotation sets with nonempty interior for homeomorphisms of the 2-Torus
Torus homeomorphisms rotation set transitivity omega limits
2011/1/18
We show that, if f is a homeomorphism of the 2–torus isotopic to the identity, and its lift e f is transitive, or even if it is transitive outside of the lift of the elliptic islands, then (0, 0) is i...
Local structure of the set of steady-state solutions to the 2D incompressible Euler equations
Local structure of the set steady-state solutions 2D incompressible Euler equations
2011/1/21
It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions.
On the Multi-Dimensional Controller and Stopper Games
Controller-stopper games weak dynamic programming principle viscosity solutions
2010/11/30
We consider a zero-sum stochastic differential controller-and-stopper game in which
the state process is a controlled jump-diffusion evolving in a multi-dimensional Euclidean space.
Complex networks derived from cellular automata
complex networks cellular automata scale-free small-world
2010/12/16
We propose a method for deriving networks from one-dimensional binary cellular automata. The derived networks are usually directed and have structural properties corresponding to the dynamical behavio...
Infinitesimal Liouville currents, cross-ratios and intersection numbers
Infinitesimal Liouville currents cross-ratios intersection numbers
2010/12/8
Many classical objects on a surface S can be interpreted as cross-ratio functions on the circle at infinity of the universal covering eS.This includes closed curves considered up to homotopy, metrics ...
Codimension one symplectic foliations and regular Poisson structures
Codimension one symplectic foliations regular Poisson structures
2010/11/30
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds,those equipped with a closed one-form defining the symplectic foliation
and a closed ...
A Renewal Theorem for Strongly Ergodic Markov Chains in Dimension $d\geq3$ and Centered Case
Markov chains renewal theorem spectral method
2010/12/14
In dimension d ≥ 3, we present a general assumption under which the renewal theorem established by Spitzer [23] for i.i.d. sequences of centered nonlattice r.v. holds true. Next we appeal to an operat...
Recurrence in 2D Inviscid Channel Flow
Recurrence inviscid channel flow kinetic energy enstrophy compact embedding
2010/12/1
I will prove a recurrence theorem which says that any Hs (s > 2)solution to the 2D inviscid channel flow returns repeatedly to an arbitrarily small H0 neighborhood. Periodic boundary condition is impo...
Large deviations of the extreme eigenvalues of random deformations of matrices
Random matrices large deviations
2010/11/26
Consider a real diagonal deterministic matrix Xn of size n with spectral measure converging to a compactly supported probability measure. We perturb this matrix by adding a random finite rank matrix, ...
The structure of invariant tori in a 3D galactic potential
Chaos and Dynamical Systems Galactic Dynamics 4D surfaces of section
2010/12/16
We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type.We have used the color and rotation method to investigate the ...