On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups

We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied. Accepted 29 August 2001. Online publication 17 December 2001.     

带有弹性碰撞的离散的凝结方程

带有弹性碰撞的离散的凝结方程是反映粒子增长动力学的数学模型，它刻划了这样一种粒子反应系统；系统中任意两个粒子碰撞后一定的概率或者凝结成为更大的粒子，或者发生弹性碰撞．本文研究了这一系统发生冻肢的可能性，并给出了一个充分条件．     

A note on the complexity and tractability of the heat equation

We wish to solve the heat equation u_t=Δu-qu in I^d×(0,T), where I is the unit interval and T is a maximum time value, subject to homogeneous Dirichlet boundary conditions and to initial conditions u(·,0)=f over I^d. We show that this problem is intractable if f belongs to standard Sobolev spaces, even if we have complete information about q. However, if f and q belong to a reproducing kernel Hilbert space with finite-order weights, we can show that the problem is tractable, and can actually be strongly tractable.     

Coercive boundary value problems for regular degenerate differential-operator equations

This study focuses on nonlocal boundary value problems (BVP) for degenerate elliptic differential-operator equations (DOE), that are defined in Banach-valued function spaces, where boundary conditions contain a degenerate function and a principal part of the equation possess varying coefficients. Several conditions obtained, that guarantee the maximal L_p regularity and Fredholmness. These results are also applied to nonlocal BVP for regular degenerate partial differential equations on cylindrical domain to obtain the algebraic conditions that ensure the same properties.     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

A characterization of an order ideal in Riesz spaces

In this paper we give a characterization of order ideals in Riesz spaces.

     

局部域上的仿交换算子与Schatten类性质

设Tb^s是局部域K上带符号b的仿交换算子，本文证明了当Tb^st定义式中函数A（ξ，η）满足一定的条件时，Tb^st∈Sp的充要条件是b∈Bp^s t 1/p。     

Q-正则Loewner空间中的拟对称映射

本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示.     

The Module Structure Theorem for Sobolev Spaces on Open Manifolds

We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.     

A problem in extremal quasiconformal extensions

A constantK ₀ ^(m) (h) is introduced for every quasisymmetric mappingh of the unit circle and every integerm≥4 which contains the constantK ₀(h) (indicated by the change in module of the quadrilaterals with vertices on the circle) as a special case. A necessary and sufficient condition is established forK ₀ ^(m) (h) =K ₁(h). It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property thatK ₀ ^(m) (h)<K ₁(h), wherek ₁(h) is the maximal dilatation ofh.