Fredholm Operators and Riesz Theory for Polynomially Compact Operators

In this article, we give a characterization of a class of bounded Fredholm operators on a Banach space which is developed to present some general existence results of the operators equation of the second kind. The obtained results are used to describe the Riesz–Schauder theory of compact operators in the more general setting of polynomially compact operators.     

医用重离子回旋加速器引出系统设计

紧凑型回旋加速器作为重离子医学专用装置同步加速器的注入器,其引出系统设计所用的磁场为TOSCA模型计算磁场。通过单粒子轨道计算确定引出系统的元件类型及基本参数;通过多粒子跟踪确定最终的元件参数和束流参数。为了提高引出效率,改善引出束流品质,在引出位置磁场梯度较大的位置,安放了一块C型磁铁,以改善此处的磁场梯度。同时,为了消除此C型磁铁对主磁场的影响,在此区域安放了一对线圈。计算结果表明引出系统的设计能够保证引出束流的强度和品质符合同步加速器的要求。     

关于微分包含的周期解及其应用

研究了一类发展包含的周期问题,其结果应用于建立一类半线性微分包含周期解的存在性定理．给出了半线性微分包含端点解的存在性定理和强松驰定理,并且应用于周期反馈控制系统．     

A proof of W. T. Gowers' theorem

W. T. Gowers' theorem asserts that for every Lipschitz function and 0$">, there exists an infinite-dimensional subspace of such that the oscillation of on is at most . The proof of this theorem has been reduced by W. T. Gowers to the proof of a new Ramsey type theorem. Our aim is to present a proof of the last result.

     

Compact elements in the lattice of radicals

Summary A radical R, in the sense of Kurosh--Amitsur, is said to be compact if, given any collection of radicals X such that R ≤;VX, we have R ≤;VX' for some finite subcollection X' of X. A ring A is said to be radical compact if the lower radical on the singleton {A} is compact. This paper explores the relationship between radical compact rings and rings satisfying certain finiteness conditions. Closure properties of the class of all radical compact rings are also investigated.     

Classes of abelian groups related to sequential convergence

We study classes of abelian groups related to sequential com¬pactness and its generalizations (completeness, coarseness and sequential pre-compactness) in convergence groups. In particular, we describe the algebraic structure of the abelian groups on which every coarse convergence is complete and we prove that: i) every abelian group admits a sequentially precompact convergence; ii) every algebraically compact abelian group admits a sequen¬tially compact convergence.     

Similarity orbits in the Calkin algebra

Let B(H) be the algebra of all bounded linear operators on a complex separable infinite dimensional Hilbert space H.Denote by π the quotient map of B(H) onto the Calkin algebra A(H).In 1984,Apostol et al.raised the following conjecture:If an operator T on H is not similar to a compact perturbation of a Jordan operator,then the similarity orbit of π(T) in A(H) coincides with the π-image of the similarity orbit of T.In this paper,we investigate the structure of similarity orbits in the Calkin algebra and give...     

拓扑空间关于子基的紧致性

覆盖方法的应用在粗糙集理论研究中越来越受到重视,其中拓扑空间的子集关于子基的内部和闭包两个概念尤为重要.在由它们导入的关于子基的开集,闭集的基础上,给出了拓扑空间关于子基的紧致性概念,并研究它的性质,得到一般拓扑空间中紧致性的一种推广.     

On Performance of Methods with Third- and Fifth-Order Compact Upwind Differencing

The difference schemes for fluid dynamics type of equations based on third- and fifth-order Compact Upwind Differencing (CUD) are considered. To validate their properties following from a linear analysis, calculations were carried out using the inviscid and viscous Burgers' equation as well as the compressible Navier–Stokes equation written in the conservative form for curvilinear coordinates. In the latter case, transonic cascade flow was chosen as a representative example. The performance of the CUD methods was estimated by investigating mesh convergence of the solutions and comparing with the results of second-order schemes. It is demonstrated that the oscillation-free steep gradients solutions obtained without using smoothing techniques can provide considerable increase of accuracy even when exploiting coarse meshes.