An extension of a convexity theorem of the generalized numerical range associated with

For any , let be the following subset of :

We show that if , then is always convex. When , it is an ellipsoid, probably degenerate. The convexity result is best possible in the sense that if we have defined similarly, then there are examples which fail to be convex when and .

The set is also symmetric about the origin for all , and contains the origin when . Equivalent statements of this result are given. The convexity result for is similar to Au-Yeung and Tsing's extension of Westwick's convexity result for .

     

Proof of the Mixing Theorem for Statistical Systems in Classical Physics

In a general measure-theoretic context, it is proved that the action of a stochastic map on a pair of probability distributions can be characterized by the criterion of decreasing mixing distance.     

On Harmonic Majorization of the Martin Function at Infinity in a Cone

This paper shows that some characterizations of the harmonic majorization of the Martin function for domains having smooth boundaries also hold for cones.     

关于几何凸函数的Hadamard型不等式

建立了一个关于几何凸函数的 Hadamard型不等式 .     

An extension of the polytope of doubly stochastic matrices

We consider a class of matrices whose row and column sum vectors are majorized by given vectors b and c, and whose entries lie in the interval [0,?1]. This class generalizes the class of doubly stochastic matrices. We investigate the corresponding polytope Ω(b|c) of such matrices. Main results include a generalization of the Birkhoff–von Neumann theorem and a characterization of the faces, including edges, of Ω(b|c).     

Weierstrass不等式的新推广

利用控制不等式理论将 Weierstrass不等式 ∏ni=1( 1± xi) >1± ∑ni=1xi推广到一般初等对称函数上 ,并且给出一个上界估计 .     

反向Chrystal不等式

利用控制不等式理论建立了三个反向Chrysta l不等式,并给出了若干应用.     

Muirhead-Rado inequality for compact groups

Muirhead’s majorization inequality was extended by Rado to the case of arbitrary permutation groups. We further generalize this inequality to compact groups and their linear representations over the reals. We characterize saturation of the inequality, and describe the saturation condition in detail for the case of actions on Hermitian operators. Supported in part by the National Science Foundation and the Center for the Mathematics of Information.     

一个有理分式不等式的加细

利用控制不等式理论给出了一个有理分式不等式的两种加细,并比较了二者的优劣.