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非光滑半无限多目标优化问题的Lagrange鞍点准则
半无限多目标优化 Lagrange函数 鞍点 (弱)有效解 (Φ ρ)-不变凸性
2019/4/17
本文研究了一类非光滑半无限多目标优化问题，并讨论它的鞍点准则.首先，定义了这类半无限多目标优化问题的标量和向量情形的Lagrange函数和鞍点；其次，分别讨论了标量和向量情形的鞍点准则的必要性；最后，在非光滑（Φ，ρ）-不变凸性假设下给出这两种情形的鞍点准则的充分性.
Performance-based fractal fracture model for complex fracture network simulation
Fractal geometry Fractal fracture model Complex fracture network characterization Contributing reservoir volume Refracturing
2018/4/2
The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar...
摩擦接触问题的比例边界等几何B可微方程组方法
弹性摩擦接触问题 比例边界等几何分析方法 比例边界有限元 B可微方程组 数值模拟
2018/12/29
摩擦接触问题是计算力学领域最具挑战性的问题之一,接触系统的泛函具有非线性、非光滑的特点,导致接触算法的收敛性与精确性难以保证.因此将比例边界等几何分析(scaled boundary isogeometric analysis,SBIGA)与B可微方程组(B dierential equation,BDE)相结合,提出了求解二维摩擦接触问题的比例边界等几何B可微方程组方法.在比例边界等几何坐标变换...
A GIAMBELLI FORMULA FOR EVEN ORTHOGONAL GRASSMANNIANS
ORTHOGONAL GRASSMANNIANS GIAMBELLI FORMULA
2015/12/17
Let X be an orthogonal Grassmannian parametrizing isotropic
subspaces in an even dimensional vector space equipped with a nondegenerate
symmetric form. We prove a Giambelli formula which expresses a...
A GIAMBELLI FORMULA FOR ISOTROPIC GRASSMANNIANS
ISOTROPIC GRASSMANNIANS GIAMBELLI FORMULA
2015/12/17
Let X be a symplectic or odd orthogonal Grassmannian. We prove
a Giambelli formula which expresses an arbitrary Schubert class in H∗
(X, Z)
as a polynomial in certain special Schubert classes...
DOUBLE THETA POLYNOMIALS AND EQUIVARIANT GIAMBELLI FORMULAS
EQUIVARIANT GIAMBELLI FORMULAS DOUBLE THETA POLYNOMIALS
2015/12/17
We use Young’s raising operators to introduce and study double
theta polynomials, which specialize to both the theta polynomials of Buch,
Kresch, and Tamvakis, and to double (or factorial) Schur S-p...
Let E : 0 ! S ! E ! Q ! 0 be a short exact sequence of
hermitian vector bundles with metrics on S and Q induced from that
on E. We compute the Bott-Chern form áe(E ) corresponding to any
characteri...
Let F be the complete °ag variety over SpecZ with the tautological
ˉltration 0 ½ E1 ½ E2 ½ ￠ ￠ ￠ ½ En = E of the trivial bundle E of rank
n over F. The trivial hermitian metric o...
Schubert Calculus on the Arithmetic Grassmannian
Arithmetic Grassmannian Schubert Calculus
2015/12/17
Let G be the arithmetic Grassmannian over SpecZ with the natural invariant KÄahler metric on G(C). We study the combinatorics of
the arithmetic Schubert calculus in the Arakelov Chow ring CH(G)
HEIGHT FORMULAS FOR HOMOGENEOUS VARIETIES
HOMOGENEOUS VARIETIES Differential and integral calculus
2015/12/17
We use classicalSchubert calculus to evaluate the integral formula
of Kaiser and Kohler [KK] for the Faltings height of certain homogeneous
varieties in terms of combinatorial data, and verify thei...
Let X = G=P be a homogeneous space of a complex semisimple
Lie group G equipped with a hermitian metric. We study the action of the
Hodge star operator on the space of harmonic di erential forms on ...
DOUBLE SCHUBERT POLYNOMIALS AND DEGENERACY LOCI FOR THE CLASSICAL GROUPS
DOUBLE SCHUBERT POLYNOMIALS DEGENERACY LOCI
2015/12/17
We propose a theory of double Schubert polynomials Pw(X;Y )
for the Lie types B, C, D which naturally extends the family of Lascoux and
Schutzen Ä berger in type A. These polynomials satisfy po...
ENERGY OF TWISTED HARMONIC MAPS OF RIEMANN SURFACES
Riemann surface fundamental group flat bundle harmonic map energy Teichmuller space convex cocompact hyperbolic manifold
2015/12/17
The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function E ρ on Teichm¨uller space TS which is a qualitative invariant of the ...
This paper contains two main results. The first is the existence of an equivariant WeilPetersson geodesic in Teichm¨ uller space for any choice of pseudo-Anosov mapping class. As a consequence one obt...
We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a
two-step °ag variety. We also give symplectic and orthogonal...