广义神经传播方程的整体吸引子

使用Galerkin方法,结合Sobolev空间理论和不等式技巧,给出了广义神经传播方程解的存在唯一性定理,然后利用吸引子存在性定理,采用半群方法证明了方程整体吸引子的存在性.     

Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).     

Approximate Entropy of Brain Network in the Study of Hemispheric Differences

Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments.     

非单C~*-代数α-比较性的等价刻画

给出非单C~*-代数α-比较性的等价刻画:当每个τ∈QT(■H)均为忠实时,■具有α-比较性,当且仅当对于任意的〈a〉,〈b〉∈Cu(■)且∝,若α·d_τ(a)≤在Cu(■)中成立;一般地,当QT(■H)≠Φ时,■具有α-比较性,当且仅当对于任意的,∈Cu(■),若存在η>0,使得d_τ(α)≤(α~(-1)-η)d_τ(b)(_τ∈QT(■H)),则≤在Cu(■)中成立.     

一类双曲型方程的Hamilton算子半群方法

将一类双曲型方程混合问题转换成一阶抽象Cauchy问题,证明所得Hamilton算子矩阵H在相应空间中生成压缩半群,并借助Fourier变换,采用一致连续半群做逼近的方法,得到H所生成的压缩半群,进而给出了问题的古典解.     

半群OCK_n的理想的极大子半群

设X_n={1,2,…,n}并赋予自然数序,OCK_n是X_n上的具有核连续的保序变换半群.将考虑OCK_n的理想OCK(n,r)={α∈OCK_n:|imα|≤r}(3≤r≤n-1),并得到了OCK(n,r)的极大子半群的完全分类.     

一类核具有连续横截面变换半群的秩

设X_n={1,2,…,n}并赋予自然数序,MCK_n是X_n上核具有连续横截面保序或反序变换所构成的半群.K_n是MCK_n的最大正则子半群.本文将考虑K_n的理想K(n,r)={α∈K_n:|im(α)|≤r}(3≤r≤n-1).证明了K(n,r)的秩为(n-r+1)(n-r+2)(n-r+3)/6.     

On the stability of Timoshenko-type systems with internal frictional dampings and discrete time delays

In this paper, we consider a vibrating system of Timoshenko-type in a bounded one-dimensional domain under Dirichlet–Dirichlet or Dirichlet–Neumann boundary conditions with one or two discrete time delays and one or two internal frictional dampings. First, we show that the system is well posed in the sens of semigroup theory. Second, we prove the exponential stability regardless to the speeds of wave propagation of the system if the weights of the time delays are smaller than the ones of the corresponding dampings, respectively. However, when the weight of one time delay is not smaller than the one of the corresponding damping, we prove the exponential stability in case of equal-speed wave propagation, and the polynomial stability in the opposite case.     

Estimates of densities for Lévy processes with lower intensity of large jumps

We obtain general lower estimates of transition densities of jump Lévy processes. We use them for processes with Lévy measures having bounded support, processes with exponentially decaying Lévy measures for large times and for processes with high intensity of small jumps for small times.     

Contractivity results in ordered spaces. Applications to relative operator bounds and projections with norm one

This paper provides various “contractivity” results for linear operators of the form where C are positive contractions on real ordered Banach spaces X . If A generates a positive contraction semigroup in Lebesgue spaces , we show (M. Pierre's result) that is a “contraction on the positive cone ”, i.e. for all provided that .  We show also that this result is not true for 1 ⩽ . We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone . We deduce from this result that, in such spaces, is a contraction on for any positive projection C with norm 1. We give also a direct proof (by E. Ricard) of this last result if additionally the norm is smooth on the positive cone. For any positive contraction C on base‐norm spaces X (e.g. in real spaces or in preduals of hermitian part of von Neumann algebras), we show that for all where N is the canonical half‐norm in X . For any positive contraction C on order‐unit spaces X (e.g. on the hermitian part of a algebra), we show that is a contraction on . Applications to relative operator bounds, ergodic projections and conditional expectations are given.