Existence Results for Evolution Noncoercive Hemivariational Inequalities

This paper is devoted to the existence of solutions for evolution hemivariational inequalities as generalizations of evolution variational inequalities to nonconvex functionals. The operators involved are taken to be multivalued and noncoercive. Using the notion of the generalized gradient of Clarke and the recession method, some existence results of solutions are proved.     

Positive linear operators which preserve x 2

A sequence of positive linear operators which approximate each continuous function on [0,1] while preserving the functione ₂ (x) =x ² is presented. Quantitative estimates are given and are compared with estimates of approximation by Bernstein polynomials. Connections with summability are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections

By suitably extending a Feynman-Kac formula of Simon (Canad. Math. Soc. Conf. Proc. 28 (2000) 317), we study one-parameter semigroups generated by (the negative of) rather general Schrödinger operators, which may be unbounded from below and include a magnetic vector potential. In particular, a common domain of essential self-adjointness for such a semigroup is specified. Moreover, each member of the semigroup is proven to be a maximal Carleman operator with a continuous integral kernel given by a Brownian-bridge expectation. The results are used to show that the spectral projections of the generating Schrödinger operator also act as Carleman operators with continuous integral kernels. Applications to Schrödinger operators with rather general random scalar potentials include a rigorous justification of an integral-kernel representation of their integrated density of states—a relation frequently used in the physics literature on disordered solids.     

算子值加权模式在Banach空间的实现理论

本文处理能在Ｂａｎａｃｈ空间中实现的线性连续时间系统．这里，输入、输出和状态空间都是无穷维Ｂａｎａｃｈ空间．我们证明：加权模式有Ｂａｎａｃｈ空间实现的充要条件是它强连续且为指数阶．对状态算子是解析半群的无穷小生成元的情况，得到了Ｂａｎａｃｈ空间实现的存在性定理．所有定理都是在时间域中给出的．     

各向异性极大算子及它们的应用

本文证明了一类与异性伸缩相关的极大算子在Ｌ＾ｐ（Ｒ＾ｎ）上是有界的，其中１〈ｐ≤∝，ｎ≥２。进一步，作为应用我们建立了算子Ｔｆ（ｘ）＝ｓｕｐε〉０│Ｔεｆ（ｘ）│Ｌ＾ｐ有界性，其中Ｔε是带有变化核的奇异积分。     

BMO与弱核条件下的Calderón-Zygmund算子交换子的有界性

本文证明了BMO与弱核条件下Calderón-Zygmund奇异积分算子的交换子 [B,T]f=BTf-T(Bf)的L2有界性,这里B ∈BMO,T对增生的b1,b2,满足 T(b1)∈BMO,T*(b2)∈BMO,b2Tb1∈WBP．     

On Computing Gröbner Bases in Rings of Differential Operators with Coefficients in a Ring

Following the definition of Gr?bner bases in rings of differential operators given by Insa and Pauer (1998), we discuss some computational properties of Gr?bner bases arising when the coefficient set is a ring. First we give examples to show that the generalization of S-polynomials is necessary for computation of Gr?bner bases. Then we prove that under certain conditions the G-S-polynomials can be reduced to be simpler than the original one. Especially for some simple case it is enough to consider S-polynomials in the computation of Gr?bner bases. The algorithm for computation of Gr?bner bases can thus be simplified. Last we discuss the elimination property of Gr?bner bases in rings of differential operators and give some examples of solving PDE by elimination using Gr?bner bases. This work was supported by the NSFC project 60473019.     

The Canopy Graph and Level Statistics for Random Operators on Trees

For operators with homogeneous disorder, it is generally expected that there is a relation between the spectral characteristics of a random operator in the infinite setup and the distribution of the energy gaps in its finite volume versions, in corresponding energy ranges. Whereas pure point spectrum of the infinite operator goes along with Poisson level statistics, it is expected that purely absolutely continuous spectrum would be associated with gap distributions resembling the corresponding random matrix ensemble. We prove that on regular rooted trees, which exhibit both spectral types, the eigenstate point process has always Poissonian limit. However, we also find that this does not contradict the picture described above if that is carefully interpreted, as the relevant limit of finite trees is not the infinite homogenous tree graph but rather a single-ended ‘canopy graph.’ For this tree graph, the random Schrödinger operator is proven here to have only pure-point spectrum at any strength of the disorder. For more general single-ended trees it is shown that the spectrum is always singular – pure point possibly with singular continuous component which is proven to occur in some cases.     

An algebraic invariant for Jordan automorphisms on В(H): The set of idempotents

Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempo-tents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ {-1,1,2,3,1/2,1/3} and A, B ∈ B(H), A - λB ∈ I(H) (?) Φ(A) - λΦ(B) ∈ I(H), then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT-1 for all A ∈ B(H), or Φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A-iB ∈ I(H) (?) Φ(A) -ιΦ(B) ∈ I(H), here ι is the imaginary unit, then Φ is either an automorphism or an anti-automorphism.     

Generalized OWA Aggregation Operators

We extend the ordered weighted averaging (OWA) operator to a provide a new class of operators called the generalized OWA (GOWA) operators. These operators add to the OWA operator an additional parameter controlling the power to which the argument values are raised. We look at some special cases of these operators. One important case corresponds to the generalized mean and another special case is the ordered weighted geometric operator.