Constructing frames for finite dimensional Hilbert spaces

In this paper, we use the characterization of frames, introduced in [W. Rolli, A characterization of frames for finite dimensional Hilbert spaces, preprint], to construct frames for finite dimensional Hilbert spaces. Furthermore this approach allows for the construction of frames with prescribed properties.     

Generic initial ideals of Artinian ideals having Lefschetz properties or the strong Stanley property

For a standard Artinian k-algebra A=R/I, we give equivalent conditions for A to have the weak (or strong) Lefschetz property or the strong Stanley property in terms of the minimal system of generators of gin(I). Using the equivalent condition for the weak Lefschetz property, we show that some graded Betti numbers of gin(I) are determined just by the Hilbert function of I if A has the weak Lefschetz property. Furthermore, for the case that A is a standard Artinian k-algebra of codimension 3, we show that every graded Betti number of gin(I) is determined by the graded Betti numbers of I if A has the weak Lefschetz property. And if A has the strong Lefschetz (respectively Stanley) property, then we show that the minimal system of generators of gin(I) is determined by the graded Betti numbers (respectively by the Hilbert function) of I.     

Inner invariant means and conjugation operators

It is shown that Paschke's result cannot be generalized to the [IN]-group setting given by Lau and Paterson. This resolves negatively a problem raised by Lau and Paterson.

     

A Generalization of the Hilbert Basis Theorem

A generalization of the Hilbert basis theorem in the geometric setting is proposed. It asserts that, for any well-describable (in a certain sense) family of polynomials, there exists a number C such that if P is an everywhere dense (in a certain sense) subfamily of this family, a is an arbitrary point, and the first C polynomials in any sequence from P vanish at the point a, then all polynomials from P vanish at a.     

The p-chain Spectral Sequence

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras.     

命题逻辑系统L*的有效集

针对命题逻辑系统L*,以及增加一元联结词△后的系统L*△,研究了该逻辑系统有效集的特征,进而以有效集为工具得到公式集F(S)的一类分划,即可将L*与L*△中的公式集F(S)分别分为16和20个等价类;最后给出了L*中对M P规则封闭的有效集的特征。     

一类索赔额服从指数幂尾型分布的风险模型及其破产概率的渐近性质

本文研究了一类风险模型,其个体索赔额服从指数-幂尾型分布,索赔次数过程为一更新过程,其更新时间间隔服从指数族分布；给出了这类模型在有限时间内破产概率的渐近性质；并讨论了在破产发生后的特征．     

1H, 13C, 17O NMR and quantum‐chemical study of the stereochemistry of the sulfoxide and sulfone derivatives of 3‐arylidene‐1‐thioflavan‐4‐one epoxides

The oxidation of the trans,cis‐( 2 ) and trans,trans‐epoxides ( 3 ) of differently substituted (Z)‐3‐arylidene‐1‐thioflavan‐4‐ones ( 1 ) with dimethyldioxirane (DMD) yielded the appropriate sulfoxides ( 4, 5 ) and sulfones ( 6, 7 ). The structures were elucidated by the extensive application of one‐ and two‐dimensional ¹H, ¹³C and ¹⁷O NMR spectroscopy. The conformational analysis was achieved by the application of ³J(C,H) coupling constants, NOESY responses and ab initio calculations. The preferred ground‐state conformers (twisted envelope‐A, twisted envelope‐B for 6 and twisted envelope‐A, envelope‐B for 7 ) were obtained as global minima of the theoretical ab initio MO study and also the examination of the ¹⁷O and ¹³C chemical shifts, calculated for the global minima structures of the sulfone isomers by the GIAO method. Analogous results, obtained for the sulfoxide isomers ( 4, 5 ), not only led to the preferred conformers but also gave evidence for the trans arrangement of the 2‐Ph group and the oxygen atom of the S?O group. Chemical shift differences between the isomers, sulfoxides and sulfones were corroborated by ab initio calculations of the anisotropic effects of the oxirane ring and the S?O and SO₂ groups. Copyright © 2003 John Wiley & Sons, Ltd.     

C~*-代数的迹迹秩

引入C~*-代数迹迹秩的概念,讨论它的基本性质.另外,迹迹秩为零和迹拓扑秩为零的C~*-代数等价,同时讨论这类代数的拟对角扩张性质.设O→I→A→A/I→O是拟对角扩张的短正合列,证明如果TTR(I)≤k且TTR(A/I)=0,则TTR(A)≤k.