GUS-property for Lorentz cone linear complementarity problems on Hilbert spaces

Given a real(finite-dimensional or infinite-dimensional) Hilbert space H with a Jordan product,we consider the Lorentz cone linear complementarity problem,denoted by LCP(T,Ω,q),where T is a continuous linear operator on H,ΩH is a Lorentz cone,and q ∈ H.We investigate some conditions for which the problem concerned has a unique solution for all q ∈ H(i.e.,T has the GUS-property).Several sufficient conditions and several necessary conditions are given.In particular,we provide two suficient and necessary conditions of T having the GUS-property.Our approach is based on properties of the Jordan product and the technique from functional analysis,which is different from the pioneer works given by Gowda and Sznajder(2007) in the case of finite-dimensional spaces.

基为Lorentz锥的管状区域上复Hardy空间H^p(0

设H^p(T_Γ)为n维复区域上的复Hardy空间,其中T_Γ是基为R^n中正则开凸锥Γ的管状区域.当p≥1时,Li利用函数边值的Fourier变换得到了函数在H^p(T_Γ)中的充要条件,把经典的Paley-Wiener定理之一推广到了高维.当0<p≤1时,还得到了Γ为第一卦限时,对应Hardy空间中函数边值在分布意义下的Fourier变换的增长性.进一步考虑了Γ为Lorentz锥的情形,拓展了高维复Hardy空间中函数边值特征的研究.

Feasibility and Structural Feature on Monotone Second-Order Cone Linear Complementarity Problems in Hilbert Space

Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element q?H. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected.

基于洛伦兹锥规划的声矢量阵宽容自适应波束形成

针对矢量阵Capon波束形成对阵列误差尤其敏感这一不足,提出了运用洛伦兹锥规划(LCP,Lorentz Cone Programming)实现导向矢量范数约束来提高波束形成鲁棒性的方法。鉴于矢量水听器声压分量和振速分量对阵列误差敏感程度不同的特点,采用了"双线约束"的策略。将范数约束波束形成转化为LCP形式,通过内点方法求解器SeDuMi求出其数值解。仿真结果表明,该波束形成器的噪声抑制能力要优于常规波束形成器,其宽容性要优于Capon波束形成器。

洛伦兹变换矩阵的对角化及其意义

通过对角化过程,讨论洛伦兹变换矩阵特征矢量、特征值的意义.将洛伦兹变换矩阵对角化,即将一般惯性参考系变换到光锥坐标系.特征矢量是光锥坐标系坐标轴上的矢量.特征值对应参考系变换下,光锥坐标分量的缩放大小.本文可以帮助学生加深对洛伦兹变换及狭义相对论时空特性的理解.

Some ω-unique and ω-ΡProperties for Linear Transformations on Hilbert Spaces

Given a real （finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product, we introduce the concepts of ω-unique and ω-P properties for linear transformations on H, and investigate some interconnections among these concepts. In particular, we discuss the ω-unique and ω-P properties for Lyapunov-like transformations on H. The properties of the Jordan product and the Lorentz cone in the Hilbert space play important roles in our analysis.

基于高温真实气体效应的双锥磁流体流动控制

磁流体流动控制作为一种主动流动控制技术,通过外加磁场影响强激波后的等离子体流场运动,可有效改善高超声速飞行器的气动性能。通过数值模拟方法研究不同磁感应强度、磁体位置对双锥模型绕流流动结构及流场内关键参数分布的影响机理和规律。结果表明偶极子磁场下随磁感应强度增加,逆流向洛伦兹力始终主导流场内的三波点位置、分离区大小及壁面热流和压力的峰值状态,同时洛伦兹力的存在还将改变激波后电子密度分布;磁体位置前移时,洛伦兹力的分量及峰值位置的变化会导致其对分离激波的作用加强,这有利于进一步控制分离区结构及壁面热流和压力的分布。