An Analytic Zariski Structure Over a Field

Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms.     

The continuity of superposition operators on some sequence spaces defined by moduli

Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x _k ): (ϕk(|x _k |)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψ_k), we characterize the continuity of the superposition operators P _f from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type. This research was supported by Estonian Science Foundation Grant 5376.     

Interpolation of positive operators

We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces L ₁, L _∞ associated with weights and traces on von Neumann algebras.     

加权Herz—type Triebel—Lizorkin空间的特征及应用

当s∈ R,0,〈q, p〈∈∞,0,〈β≤∞且 max{-n/q,-nδ2/qδ1}〈a时，定义了加权Herz—type　Triebel-Lizorkin空间kq^q,pF^s β（R^n,ω1，ω2）和Kq^a,pF^sβ（R^n，ω1，ω2），并给出这些空间的一些特征及在这些空间上的Hard—Littlewood极大算子不等式．     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure

In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions.     

What Is a Quantum Stochastic Differential Equation from the Point of View of Functional Analysis?

We prove that a quantum stochastic differential equation is the interaction representation of the Cauchy problem for the Schrödinger equation with Hamiltonian given by a certain operator restricted by a boundary condition. If the deficiency index of the boundary-value problem is trivial, then the corresponding quantum stochastic differential equation has a unique unitary solution. Therefore, by the deficiency index of a quantum stochastic differential equation we mean the deficiency index of the related symmetric boundary-value problem.In this paper, conditions sufficient for the essential self-adjointness of the symmetric boundary-value problem are obtained. These conditions are closely related to nonexplosion conditions for the pair of master Markov equations that we canonically assign to the quantum stochastic differential equation.     

关于多线性振荡奇异积分在加权Hardy-型空间上的一致估计

本文对一类具有光滑位相函数的多线性振荡奇异积分算子建立了一致的加权（H^1(R^n),L^1(R^n))估计及一致的加权（HKp(R^n),Kp(R^n)估计。     

全固态多波长飞秒脉冲激光系统

利用棱镜对引进频谱空间啁啾来补偿飞秒脉冲激光二次谐波产生中的相位失配,提高了倍频效率建立了一套全固态、多波长(1065nm, 532nm,823.1nm, 402nm)飞秒脉冲激光系统自制的Nd:YVO4激光器输出532nm绿光激光,最高平均功率可达5.6W当用2.5W绿光激光泵浦时,从自制的钛宝石激光器及经BBO倍频可分别输出中心波长为823.1nm和402nm,平均功率300mW和73mW,谱宽32.3nm和5.1nm,脉宽22fs和33.3fs、重复率108MHz的近红外和蓝光激光整个系统具有结构紧凑、倍频效率高、运行稳定的特点.