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本文主要研究了单位球笛卡尔积作为约束的优化问题，给出了此类问题的最优性条件.同时将求解此问题的一些经典的梯度算法推广到了更加一般的形式，并证明了新算法的收敛性.随机二次规划问题和求解图像变分去噪模型的数值结果表明新算法并不弱于一些经典的算法，特别是在精度要求较高的情形下.
NOTE ON GLOBAL REGULARITY FOR 2D OLDROYD-B FLUIDS WITH DIFFUSIVE STRESS
Oldroyd-B, complex uids Fokker-Planck equations blow up global existence Euler equations Navier-Stokes equations kinetic equations
2014/4/3
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial di usion of the polymeric stresses.
An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations
Inviscid model, singularity explicit solutions 2D Boussinesq equations
2014/4/3
We give an example of a well posed, nite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce nite time sing...
On the Muskat problem: global in time results in 2D and 3D
Porous media incompressible ows uid interface global existence.
2014/4/3
This paper considers the three dimensional Muskat problem in the stable regime.We obtain a conservation law which provides an L2 maximum principle for the uid interface. We also show global in time ex...
Schauder不动点定理在分数阶三点边值问题中的应用
正解 Schauder不动点定理 三点边值问题 分数阶微分方程
2012/11/13
用Schauder不动点定理研究分数阶三点边值问题:〖FC(〗Dα0+u(t)+f(t,u(t))+e(t)=0,0
A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts (extended version)
probabilistic comparison strength of split, triangle quadrilateral cuts
2010/12/13
We consider mixed integer linear programs defined by two equations involving two integer variables and non-negative continuous variables. The non-trivial facet-defining inequalities of such problems c...
On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background
Duffin-Kemmer-Petiau theory nonminimal coupling Klein’s paradox
2010/12/1
The problem of spin-0 and spin-1 bosons in the background of a general mixing of minimal and
nonminimal vector inversely linear potentials is explored in a unified way in the context of the Duffin-Ke...
Coupling solutions of BGG-equations in conformal spin geometry
overdetermined systems conformal spin geometry twistor spinors conformal Killing fields conformal Killing forms
2010/12/1
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and su...
Two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations
Camassa–Holm equation Degasperis–Procesi equation semidirect product geodesic flow
2010/11/26
We use geometric methods to study two natural two-component generalizations of the periodic Camassa–Holm and Degasperis–Procesi equations.