G(F4′)条件与加强形式的停止定理

首次提出了Ｇ（Ｆ４′）条件，给出了Ｇ（Ｆ４′）条件的两个等价关系，得到了加强形式的停止定理和强鞅的一个等价关系．     

扩散过程的生存时间及其对条件扩散的应用

设τＤ是扩散过程在Ｒｄ中区域Ｄ上的生存时间．本文给出τＤ指数阶矩有限的一个充分条件．这里的区域与扩散算子都是一般的．作为应用，改进了Ｇａｏ（１９９５）关于条件扩散的主要结果．     

满足右零化子特殊升链条件的环

本文讨论了满足右零化子特殊升链条件的环的性质以及与左、右完备环，ＱＦ－环的关系；给出了满足右零化子特殊升链条件的环中素理想是完全素理想的条件，从而给出了Ｇｏｌｄｉｅ定理的一个应用．     

非齐次马尔可夫链的Gesaro—极限定理

本提出了新的非齐次马尔可夫链的遍历条件，并在此条件下，首次证明了非齐次马尔可夫链转移概率的Ｇｅｓａｒｏ－极限定理。另外，本还给出了一个例子，用它表明本的条件确实比Ｄｏｅｂｌｉｎ条件要弱。     

具有一类新压缩条件下自映射的不动点

本推广了[6]中的压缩条件，并给出了度量空间中在该压缩条件下自映射的不动点存在唯一性定理。     

条件Brown运动生命时的一个渐近估计

设Ｄ为Ｒｄ中的有界规则区域．本文绘出了一个Ｄ内条件Ｂｒｏｗｎ运动生命时的渐近估计其中Ｇ为Ｒｄ内满足的开集，为主持征值（关于Ｄｉｒｉｃｈｌｅｔ边值条件），μ是属于广义Ｋａｔｏ类的符号Ｒａｄｏｎ测度，Ａｔ是与μ相联系的Ｂｒｏｗｎ运动（Ｘｔ）ｔ≥０的有界变差连续的可加泛函，ｈ是关Ｄ内的正解。     

反馈法应用的条件

反馈法应用的条件ＰｅｔｅｒＷ．Ｇｌｙｎｎ．ＤｏｎａｌｄＬ．Ｉｇｌｅｈａｒｔ著王伟译估计静态参数的反馈法是模拟输出分析的基本方法之一。这个方法取决于反馈过程的中心极限定理和出现在中心极限定理中的方差常数的弱相容估计。对于中心极限定理和相容估计给定了一个...     

imaNon-Lipschitz条件的随机微分方程的逼近定理(英文)

本文给出了Non Lipschitz条件下的随机微分方程的一个逼近定理 .     

偶数维空间上广义Beltrami方程组及高维空间的Beltrami方程组

本文在ｎ＝２ｌ维偶数空间上得到广义Ｂｅｌｔｒａｍｉ方程组Ｄｔｆ（ｘ）Ｈ（ｘ）Ｄｆ（ｘ）＝Ｊ（ｘ，ｆ）２／ｎＧ（ｘ）的伸张公式，并在Ｈ（ｘ）为对角阵的条件下，给出广义Ｂｅｌｔｒａｍｉ方程组的正则性定理，Ｃａｃｉｏｐｏｌｉ型不等式和可去性定理．此外，还将所有维数的Ｂｅｌｔｒａｍｉ方程组Ｄｔｆ（ｘ）Ｄｆ（ｘ）＝Ｊ（ｘ，ｆ）２／ｎＧ（ｘ）化为一个“Ｂｅｌｔｒａｍｉ方程”     

一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。     

Gauge and conditional gauge on negatively curved graphs

In this paper we study certain edge-weighted random walks on infinite graphs with bounded vertex degree for which the second smallest eigenvalue of the Laplacian is negative.We find analogues of the Feynman-Kac functional and give several conditions equivalent to the boundeness of the corresponding gauge function.From this result we derive a new formula for the second smallest eigenvalue of the Laplacian and we apply this formula to the theory of graph coverings.An analogue of the conditional gauge theorem is shown to hold for certain Schrödinger operators.     

Gaugeability and conditional gaugeability

New Kato classes are introduced for general transient Borel right processes, for which gauge and conditional gauge theorems hold. These new classes are the genuine extensions of the Green-tight measures in the classical Brownian motion case. However, the main focus of this paper is on establishing various equivalent conditions and consequences of gaugeability and conditional gaugeability. We show that gaugeability, conditional gaugeability and the subcriticality for the associated Schrödinger operators are equivalent for transient Borel right processes with strong duals. Analytic characterizations of gaugeability and conditional gaugeability are given for general symmetric Markov processes. These analytic characterizations are very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases. Connections with the positivity of the spectral radii of the associated Schrödinger operators are also established.

     

Conditional gauge theorem for non-local Feynman-Kac transforms

Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L ² -infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.     

Conditioned Brownian motion in planar domains

Summary We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains.Supported in part by NSF grant DMS-9100244 and an AMS Centennial Fellowship     

Homotopy of gauge groups over non-simply-connected five-dimensional manifolds

Both the gauge groups and 5-manifolds are important in physics and mathematics. In this paper,we combine them to study the homotopy aspects of gauge groups over 5-manifolds. For principal bundles over non-simply connected oriented closed 5-manifolds of a certain type, we prove various homotopy decompositions of their gauge groups according to different geometric structures on the manifolds, and give the partial solution to the classification of the gauge groups. As applications, we estimate the homotopy exponents of their gauge groups, and show periodicity results of the homotopy groups of gauge groups analogous to the Bott periodicity.Our treatments here are also very effective for rational gauge groups in the general context, and applicable for higher dimensional manifolds.     

下模(上模)不可加测度的条件期望(英文)

本文研究了下模(上模)不可加测度的条件期望.利用下模不可加测度μ的Choquet积分的最大可加表示定理定义了下模(上模)不可加测度的条件期望, 并且证明了这种条件期望的相关性质.     

Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts

In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a conditional gauge theorem for these diffusions in bounded Lipschitz domains.Informally the Schrödinger-type operators we consider are of the form L+μ⋅∇+ν where L is a uniformly elliptic second order differential operator, μ is a vector-valued signed measure belonging to Kd,1 and ν is a signed measure belonging to Kd,2. In this paper, we establish two-sided estimates for the heat kernels of Schrödinger-type operators in bounded C1,1-domains and a scale invariant boundary Harnack principle for the positive harmonic functions with respect to Schrödinger-type operators in bounded Lipschitz domains.     

Finite-Energy Global Well-Posedness of the Maxwell–Klein–Gordon System in Lorenz Gauge

It is known that the Maxwell–Klein–Gordon system (M–K–G), when written relative to the Coulomb gauge, is globally well-posed for finite-energy initial data. This result, due to Klainerman and Machedon, relies crucially on the null structure of the main bilinear terms of M–K–G in Coulomb gauge. It appears to have been believed that such a structure is not present in Lorenz gauge, but we prove here that it is, and we use this fact to prove finite-energy global well-posedness in Lorenz gauge. The latter has the advantage, compared to Coulomb gauge, of being Lorentz invariant, hence M–K–G in Lorenz gauge is a system of nonlinear wave equations, whereas in Coulomb gauge the system has a less symmetric form, as it contains also an elliptic equation.     

条件期望作为初等算子在冯-代数上的描述

定义并研究了冯-代数.条件期望基于冯-代数的描述,即作为初等算子的良好性质,会较之一般代数简洁许多.这是因为冯-代数包含一些特殊的子代数.给出了此类代数上置信的初等条件期望的描述及其最小存在的充要条件.并且定义了指标冯-有限条件期望.作为以上结果的推论,得出了条件期望指标有限的充分必要条件和一个重要不等式.     

基于条件事件代数系统的条件证据组合与条件信任组合

讨论基于条件事件代数系统上的条件证据与条件信任问题,给出了条件证据的组合方法,由此可作出在条件下对目标支持的判断,我们还给出了综合各条件证据的无条件目标语据组合,它可看作是从全局角度对目标支持的判断,最后我们给出了基于多值映射的条件信任的组合。