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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear stability of travelling wave solution of the Navier-Stokes-Poisson system for ions with $\gamma$-law pressure
纳维-斯托克斯-泊松系统 行波解 $γ$定律压力离子 非线性稳定性
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2023/4/17
We consider the existence, uniqueness and nonlinear stability of the travelling wave solution of the Navier-Stokes-Poisson system with density-dependent viscosity for ions. Firstly, we derive a system...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Uniqueness of BV Solution for Compressible Euler Equations
可压缩 欧拉方程 BV解 唯一性
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2023/4/17
Compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general. It is well known that global BV solutions of system of hyperbolic conser...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stokes phenomenon and isomonodromy deformation equations: Explicit solution to the Riemann-Hilbert problem and integrability of the isomonodromy equation
斯托克斯现象 等单向变形方程 黎曼-希尔伯特问题 显式解 单场方程 可积性
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2023/5/6
Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quanti...
Fast Solution of `1-norm Minimization Problems When the Solution May be Sparse
LASSO. LARS Homotopy Methods Basis Pursuit.
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2015/8/21
The minimum `1-norm solution to an underdetermined system of linear equations y = Ax,
is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property
is of interest i...
Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit
compressed sensing decoding error-correcting codes
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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
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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
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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
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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
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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 SOLUTION TO THE L SPACE PROBLEM
SOLUTION L SPACE PROBLEM
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2015/8/17
In [23], Todorcevic gives a survey of basis problems in combinatorial set theory,listing nine theorems and six working conjectures.
Numerical solution of a two-disk problem
Numerical solution control system and feedback compensator Fahrenheit convex programming numerical Fahrenheit programming
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2015/8/12
A multidisk problem in frequency domain control system synthesis is a problem in which the designer wishes to find a feedback compensator that minimizes the H_infty-norm of a certain transfer matrix r...
A sharp bound on the L2 norm of the solution of a random elliptic difference equation
sharp bound L2 norm random elliptic difference equation
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2015/7/14
We consider a stationary solution of the Poisson equation (λ − Lω)φλ(x; ω) = −∂∗b(x; ω), where λ > 0 and Lω is a random, discrete, elliptic operator given by Lωu(x) := ∂&...
Solution of the Inverse Problem of Linear Optimal Control with Positiveness Conditions and Relation to Sensitivity
Linear Optimal Control Positiveness Conditions
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2015/6/23
The property that the feedback control minimizes some performance index (1.3)
with Q ≥ 0 is of considerable interest because of its connection with the ability
of the control to reduce the sensitivi...
广东外语外贸大学运筹学英文课件第三章 Linear Programming-Sensitivity Analysis and Interpretation of Solution
广东外语外贸大学 运筹学 英文课件 第三章 Linear Programming-Sensitivity Analysis and Interpretation of Solution
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2015/6/4
广东外语外贸大学运筹学英文课件第三章 Linear Programming-Sensitivity Analysis and Interpretation of Solution。
Exact solution of some new planar polygon models. Plus aspects of a ”new” SAW model
planar polygon models new SAW model
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2015/3/19
Exact solution of some new planar polygon models. Plus aspects of a ”new” SAW model.