Congruence triples on regular semigroups and their generalizations

In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by using the equivalences on S/ℒ, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.     

Harnack and HWI inequalities on infinite-dimensional spaces

In this paper, the dimensional-free Harnack inequalities are established on infinite-dimensional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy “H”, Wasserstein distance “W”, and Fisher information “I”.     

Global optimization of a class of nonconvex quadratically constrained quadratic programming problems

In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.     

LMI优化问题的择一性定理与对偶

考虑目标函数是线性函数约束条件为线性矩阵不等式的LMI优化问题,讨论了LMI优化问题中的四个择一性定理.每种类型的择一性定理包含两个线性不等式和(或)等式系统,一个原始系统和一个对偶系统.弱择一性定理说明两系统中至多只有其一有解;基于凸集分离理论得到的强择一性定理说明两系统有且仅有其一有解.并在此基础上推导了LMI优化...     

强极值原理中辅助函数的构造

通过分析极值原理在强极值原理证明中的作用,研究如何构造其证明中的辅助函数.     

带恰当断面的拟-型$\delta$半群

In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enrich Saito＇s results on quasi-orthodox semigroups with an inverse transversal.     

强阻尼非线性热弹耦合杆系统的全局吸引子

本文主要以算子半群理论为依据,证明了一类强阻尼非线性热弹耦合杆方程组在初边值条件下,全局吸引子的存在性,并且对吸引子维数做了估计. 关键词： 热弹耦合杆系统 强阻尼 非线性 全局吸引子     

原子在红外激光场中产生高次谐波及阿秒脉冲随波长的变化规律

利用强场近似理论,研究了在长波红外激光场(波长800—2000 nm)驱动下氢原子产生的高次谐波,分析了在截止位置附近高次谐波的转换效率随激光波长的变化规律.发现在截止位置附近原子发射高次谐波的转换效率比平台区域的转换效率低,但获得的阿秒脉冲的宽度会随波长的增大而缩短. 关键词： 强场近似 高次谐波 阿秒脉冲     

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