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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Finding solutions to the multi-dimensional compressible Euler equations
多维 可压缩 欧拉方程 解
2023/4/24
This talk will survey some results for the two- or three-space dimensional compressible Euler equations. We shall present non-uniqueness results of weak entropy solutions using convex integration and ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fractal solutions of multi-component systems of dispersive evolution equations
色散演化方程 多分量系统 分形解
2023/4/27
In this talk, we investigate the fractalization phenomena for the multi-component systems of the dispersive evolution equations on a bounded interval subject to the periodic boundary conditions. The e...
THE SYMPLECTIC PROPERTIES OF THE PGL(n; C)-GLUING EQUATIONS
GLUING EQUATIONS SYMPLECTIC PROPERTIES
2015/12/17
In [12] we studied PGL(n; C)-representations of a 3-manifold via a generalization of Thurston's gluing equations. Neumann has proved some symplectic properties of
Thurston's gluing equations that pla...
In [11] we parametrized boundary-unipotent representations of a 3-manifold
group into SL(n; C) using Ptolemy coordinates, which were inspired by A-coordinates on
higher Teichmuller space due to Foc...
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...
Hopf bifurcation formula for first order differential-delay equations
Hopf bifurcation Differential delay equation DDE Retarded functional differential equation RFDE
2015/8/27
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The ...
Periodic motions in DDE (Differential-Delay Equations) are typically 4 created in Hopf bifurcations. In this chapter we examine this process from several 5 points of view. Firstly we use Lindstedt’s p...
The Hodgkin and Huxley equations model action potentials in squid giant axons. Variants of
these equations are used in most models for electrical activity of excitable membranes.
Computational tools...
Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit
compressed sensing decoding error-correcting codes
2015/8/21
Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard
in general. We show here that for systems with ‘typical’/‘random’ Φ, a good approximation to the
sparse...
Sparse Nonnegative Solution of Underdetermined Linear Equations by Linear Programming
Neighborly Polytopes Cyclic Polytopes
2015/8/21
Consider an underdetermined system of linear equations y = Ax with known d×n matrix
A and known y. We seek the sparsest nonnegative solution, i.e. the nonnegative x with fewest
nonzeros satisfying y...
Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations
Centrosymetric Polytopes Centrally-Neighborly Polytopes
2015/8/21
Consider a d × n matrix A, with d < n. The problem of solving for x in y = Ax is
underdetermined, and has many possible solutions (if there are any). In several fields it is
of interest to ...
For Most Large Underdetermined Systems of Equations, the Minimal ` 1 -norm Near-Solution Approximates the Sparsest Near-Solution
Solution of Underdetermined Linear Systems Approximate Sparse Solution of Linear equations
2015/8/21
We consider inexact linear equations y ≈ Φα where y is a given vector in R
n
, Φ is a
given n by m matrix, and we wish to find an α0, which is sparse and gives an approximate
solution, obey...
For Most Large Underdetermined Systems of Linear Equations the Minimal ` 1 -norm Solution is also the Sparsest Solution
Solution of Underdetermined Linear Systems Overcomplete Representations
2015/8/21
We consider linear equations y = Φα where y is a given vector in R
n
, Φ is a given n by m
matrix with n < m ≤ An, and we wish to solve for α ∈ Rm. We suppose that the columns
of Φ are normalized ...
A central question in invariant theory is that of determining the relations among
invariants. Geometric invariant theory quotients come with a natural ample line bundle,
and hence often a natural pr...
Principal Lyapunov Exp onent and Principal Flo quet Bundle of Sto chas tic/Ra ndom Para b olic Equations
Principal Lyapunov Exp onen Principal Flo quet Bundle
2015/4/3
Problem – Extension of Principal Eigenvalue/Principal
Eigenfunction Theory for Time Independent Parabolic
Equations to Random Parabolic Equations
I Principal Eigenvalue/Principal Eigenfunction Theo...
