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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Analytic smoothing effect of a class of ultra-parabolic equations
一类超抛物型方程 解析 光滑效应
2023/11/29
We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity results in mapping class groups and homeomorphism groups
映射类群 同胚群 刚性结果
2023/11/13
Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
THE ACTION OF THE MAPPING CLASS GROUP ON REPRESENTATION VARIETIES
MAPPING CLASS GROUP REPRESENTATION VARIETIES
2015/12/17
These notes are based on lectures given at Zhejiang University, July 14–20, 2008. My goal was to present some analytic techniques that can be used to study the action of the mapping class group on the...
THE EXTENDED BLOCH GROUP AND THE CHEEGER-CHERN-SIMONS CLASS
THE EXTENDED BLOCH GROUP CHEEGER-CHERN-SIMONS CLASS
2015/12/17
We present a formula for the full Cheeger-Chern-Simons class of the tautological flat
complex vector bundle of rank 2 over BSL(2, C
δ
). Our formula improves the formula in [DZ], where
the c...
In the famous papers [1] and [2], J Cheeger, S Chern and J Simons define characteristic
classes for flat G–bundles. Each such characteristic class is given by a corresponding
universal c...
PRECONDITIONING A CLASS OF FOURTH ORDER PROBLEMS BY OPERATOR SPLITTING
parabolic problems fourth order problems preconditioning
2015/12/11
We develop preconditioners for systems arising from finite element discretizations of
parabolic problems which are fourth order in space. We consider boundary conditions which yield
a natural ...
A Posteriori Error Analysis for A Class of Integral Equations and Variational Inequalities
Integral Equations Variational Inequalities
2015/12/11
We consider elliptic and parabolic variational equations and inequalities governed by
integro-differential operators of order 2s ∈ (0,2]. Our main motivation is the pricing of European
or Amer...
Optimal order a posteriori error estimates for a class of Runge{Kutta and Galerkin methods
error estimates Galerkin methods
2015/12/11
We derive a posteriori error estimates, which exhibit
optimal global order, for a class of time stepping methods of any
order that include Runge{Kutta Collocation (RK-C) methods and
the continuous ...
Compactons in a Class of Nonlinearly Quintic Equations
Five nonlinear dispersion equation and linear equation the line the numerical simulation
2015/10/8
We introduce a nonlinear dispersive quintic equation. Its travelling waves are governed by a linear equation. We construct a large variety of explicit compact solitary waves with one or many humps. So...
An Extension of Barbashin-Kraso vski-LaSalle Theorem to a Class of Nonautonomous Systems
Barbashin-Kraso vski-LaSalle Theorem Class of Nonautonomous Systems
2015/9/29
An Extension of Barbashin-Kraso vski-LaSalle Theorem to a Class of Nonautonomous Systems.
ERGODICITY OF MAPPING CLASS GROUP ACTIONS ON SU(2)-CHARACTER VAR IET IES
GROUP ACTIONS MAPPING CLASS
2015/9/29
Let be a compact orientable surface with genus g andnboundary components
∂1,..., ∂n. Let b = (b1,...,bn) ∈ [−2,2]
n. Then the mapping class group
Mod() acts on the relative SU(2)-...
THE MAPPING CLASS GROUP ACTS REDUCIBLY ON SU(n)-CHARACTER VARIETIES
CLASS GROUP ACTS REDUCIBLY VARIETIES
2015/9/29
When G is a connected compact Lie group, and π
is a closed surface group, then Hom(π, G)/G contains an open
dense Out(π)-invariant subset which is a smooth symplectic manifold.
Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom
fast diffusion non-convex Hamiltonians two degrees of freedom
2015/9/25
In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees offreedom, and we prove a result of diffusion for an open and dense set of perturbations, ...
EXPLICIT CLASS FIELD THEORY FOR GLOBAL FUNCTION FIELDS
EXPLICIT CLASS FIELD THEORY GLOBAL FUNCTION FIELDS
2015/8/26
Let F be a global function field and let F ab be its maximal abelian extension. Following an approach of D. Hayes, we shall construct a continuous homomorphism ρ: Gal(F ab/F) → CF , where CF is the id...
Multi-class AdaBoost
boosting exponential loss multi-class classification stagewise modeling
2015/8/21
Boosting has been a very successful technique for solving the two-class classification problem. In going from two-class to multi-class classification, most algorithms have been restricted to reducing ...