弱Orlicz鞅空间的弱原子分解及其应用

对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理.     

弱Hardy正规鞅空间与原子分解

本文证明了弱Hardy正规鞅空间wHp和wH^sp上的原子分解定理.利用鞅的原子分解给出了弱Hardy正规鞅空间上的次线性算子有界的一个充分条件.利用这个条件得到了关于正规鞅的一些弱Lp范数不等式和弱（p,p）型不等式.这些结果是经典Hp鞅论中一些重要结果的弱型对应.     

Banach空间值弱Garsia型鞅空间及其原子分解

定义了Banach空间值弱Garsia型鞅空间和三种类型原子,证明了Banach空间值弱Garsia型鞅空间上的四个原子分解定理,并利用这些定理,得到Banach空间值弱Garsia型鞅空间的互相嵌入关系,其结果与Banach空间的凸性和光滑性有密切关系.     

The Structure of Hopf Algebras with a Weak Projection

We analyze the structure of a Hopf algebra H that has a Hopf subalgebra H " and a left H "-module coalgebra projection onto H ". In this situation H H " Q for Q = H / H "⁺ H, and the Hopf algebra structure on H can be recovered from suitable structures on Q, among others an in general nonassociative multiplication. The construction of H from H " and Q generalizes Radford biproduct, double crossproducts, and certain bicrossproducts. Further examples are Hopf algebras with a triangular decomposition, like all quantized enveloping algebras. In an appendix, we improve a standard criterion for a bicrossproduct A B of two Hopf algebras to be a Hopf algebra, and we show that in this case the antipode of the bicrossproduct is bijective if the antipodes of the factors are.     

并素元有限生成格的弱直积分解

本文建立了并素元有限生成格的弱直积分解,并给出一个解决并素元生成的完全Heyting代数的直积分解问题的新方法;作为弱直积分解的应用,证明了并素元有限生成的完全Heyting代数必然同构于有限个既约的完全Heyting代数的直积,证明了并素元有限生成格是Boole代数的充要条件是它同构于某有限集的幂集格.     

Weak Convergence of Topological Measures

Journal of Theoretical Probability - Topological measures and deficient topological measures are defined on open and closed subsets of a topological space, generalize regular Borel measures, and...     

可积鞅测度的弱收敛(英语)

本文引入了可积鞅测度弱收敛的概念,并给出了可积鞅测弱收敛的一系列条件     

B 值复测度拟鞅的原子分解

设P 是一个概率测度,ψ是一个复值可积函数,dμ =ψdP是一个复值测度. 在权函数ψ∈a₁∩b_∝⁺和Banach空间X 具有适当的凸性和光滑性的条件下, 作者证明了关于复测度μ 的X值拟鞅空间D_α(X) 和_pQ_α(X) 上的原子分解定理. 并且利用复测度拟鞅的原子分解定理, 在0<α≤ 1 的情形, 证明了关于X 值复测度拟鞅的两个重要不等式.     

Decision Theory and Weak Statistical Dominance

This note presents an alternative proof of a result on statistical dominance first given by Fishburn. The proof is simpler than the original, and avoids the use of the rather complex Abel's summation identity. A criterion of "weak" dominance is then proposed in order to deal with situations where it is not possible to establish Fishburn's "strict" dominance. It is also shown that "strict" dominance is a special case of the more general concept of "weak" dominance.     

Weak Convergence of Measures in Conservative Systems

Families of probability measures on the phase space of a dynamical system are considered. These measures are obtained as shifts of a given measure by the phase flow. Sufficient conditions for the existence of the weak convergence of the measures as the rate of the shift tends to infinity are suggested. The existence of such a limit leads to a new interpretation of the second law of thermodynamics. Bibliography: 5 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 194–205     

Some Model Theory Over an Exceptional Uniserial Ring and Decompositions of Serial Modules

An example is given of a direct summand of a serial module thatdoes not admit an indecomposable decomposition.     

THEORY OF SPECTRAL DECOMPOSITIONS WITH RESPECT TO THE IDENTITY FOR CLOSED OPERATORS

In this paper,the auther discusses some properties of closed operators acting on aBanach space with the spectral decomposition property with respect to the identity(abbrev.SDI).First,some equivalent conditions are given for a closed operator T to have the SDI.Next,for every hyperinvariant subspace Y of T with the SDI,it is proved that thecoinduced operator=T/Y has the SDI.Finally,properties of maximal nets of hyperinva-riant subspaces are discussed.     

New Identities for Weak KAM Theory

This paper records for the Hamiltonian H =1/2│P│2 + W(x) some old and new identities relevant for the PDE/variational approach to weak KAM theory.     

Weak Barriers in Nonlinear Potential Theory

We characterize regular boundary points for p-harmonic functions using weak barriers. We use this to obtain some consequences on boundary regularity. The results also hold for -harmonic functions under the usual assumptions on , and for Cheeger p-harmonic functions in metric spaces.      

Decompositions of rings

Translated from Matematicheskie Zametki, Vol. 57, No. 1, pp. 137–139, January, 1995.     

Existence of Solutions To Weak Parabolic Equations For Measures

Let A = (a^ij) be a Borel mapping on [0, 1] x R^d with valuesin the space of non-negative operators on R^d and let b = (bⁱ)be a Borel mapping on [0, 1] x R^d with values in R^d. Let Under broad assumptions on A and b, we construct a family µ= (µ_t)_t [0, 1] of probability measures µ_t on R^dwhich solvesthe Cauchy problem L* µ = 0 with initial conditionµ₀ = , where \nu is a probability measure on R^d, in thefollowing weak sense: and Such an equation is satisfied by transition probabilities ofa diffusion process associated with A and b provided such aprocess exists. However, we do not assume the existence of aprocess and allow quite singular coefficients, in particular,b may be locally unbounded or A may be degenerate. An infinite-dimensionalanalogue is discussed as well. Main methods are L^p-analysiswith respect to suitably chosen measures and reduction to theelliptic case (studied previously) by piecewise constant approximationsin time. 2000 Mathematics Subject Classification 35K10, 35K12,60J35, 60J60, 47D07.     

Decompositions of comodules

In this paper we study the relations among the different decomposition theories of comodules.