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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The pseudoeffective cone on projective manifolds
射影流形 赝有效锥 全纯线丛
2023/5/15
We report the work of Boucksom-Demailly-Paun-Peternell, which shows that a holomorphic line bundle on a projective manifold is pseudoeffective iff its degree on any member of a covering family of curv...
Applications of second-order cone programming
Second-order cone programming linear function affine sets linear nonlinear convex problem quadratic program
2015/8/11
In a second-order cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of second-order (quadratic) cones. SOCPs are nonlinear convex problems that ...
Asymptotic cone of semisimple orbits for symmetric pairs
asymptotic cone Richardson orbit nilpotent orbit symmetric pair
2011/2/21
Let G be a reductive algebraic group over C and denote its Lie algebra by g. Let Oh be a closed G-orbit through a semisimple element h ∈ g. By a result of Borho and Kraft [BK79], it is known that the ...
The Barrier Cone of a Convex Set and the Closure of the Cover
convex set barrier cone recession cone cover polar cone
2009/1/22
For an arbitrary non-empty closed convex set $A$ in $\mathbb{R}^n$, we prove that the polar of the difference between the barrier cone $\mathbb{B}(A)$ and its interior $\text{int } \mathbb{B} (A)$ co...