Morita equivalences of Ariki–Koike algebras

We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for the Ariki–Koike algebras defined over fields of characteristic zero are now known in principle. Received: 22 March 2000; in final form: 19 September 2001 / Published online: 29 April 2002     

k/N:G冗余表决系统的渐近稳定性

分析了带有修理设备和多重致命及非致命操作故障的k／N(G)冗余表决系统的渐近稳定性．用该系统算子生成的正定C-半群证明了系统非负时间依赖解的存在唯一性．同时通过对系统算子谱点分布的分析，证明了本征值0对应的本征向量恰好是系统的静态解，并且，0是虚轴上系统算子唯一的谱点，从而证明了系统的渐近稳定性．     

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.     

On Hadamard differentiability in k-sample semiparametric models—with applications to the assessment of structural relationships

Semiparametric models to describe the functional relationship between k groups of observations are broadly applied in statistical analysis, ranging from nonparametric ANOVA to proportional hazard (ph) rate models in survival analysis. In this paper we deal with the empirical assessment of the validity of such a model, which will be denoted as a “structural relationship model”. To this end Hadamard differentiability of a suitable goodness-of-fit measure in the k-sample case is proved. This yields asymptotic limit laws which are applied to construct tests for various semiparametric models, including the Cox ph model. Two types of asymptotics are obtained, first when the hypothesis of the semiparametric model under investigation holds true, and second for the case when a fixed alternative is present. The latter result can be used to validate the presence of a semiparametric model instead of simply checking the null hypothesis “the model holds true”. Finally, various bootstrap approximations are numerically investigated and a data example is analyzed.     

The Cohomology of the Universal Steenrod Algebra

The mod 2 universal Steenrod algebra Q is a homogeneous quadratic algebra closely related to the ordinary mod 2 Steenrod algebra and the Lambda algebra introduced in [1]. In this paper we show that Q is Koszul. It follows by [7] that its cohomology, being purely diagonal, is isomorphic to a completion of Q itself with respect to a suitable chain of two-sided ideals.     

关于G-M成果研究的若干新动态Ⅰ——G-M型空间的若干品种

结合自己的工作，对Gowers-Maurey系列成果获Fields奖以来的研究的新动态作一综述。本是上篇，主要讨论含遗传不可分解空间在内的G－M型空间的若干品种。     

Z-scan measurements of photorefractive nonlinearities for a SBN: Ce crystal

 In this paper, we derived the Z-scan formula for a photorefractive crystal sample under an external applied electric field. The far-field diffraction pattern of a Gaussian beam wavefront through a photorefractive crystal is calculated by considering spatial-phase perturbation induced by the space-charge field. The photorefractive drift nonlinearities and correspondingly, the electro-optic coefficients r ₃₃, r ₁₃, (r ₂₃) and the characteristic ratio n ³ _e r ₃₃/n ³ _o r ₁₃ for a cerium-doped Sr_0.61Ba_0.39Nb₂O₆ crystal are determined from the Z-scan experiments. Z-scan with enhanced sensitivity is also realized by measuring the normalized transmittance at the off-axis position in the far field. A deviation between the off-axis Z-scan experimental results and the theoretical prediction is discussed too. Received: 22 July 1996/Revised version: 7 October 1996     

Confined Banach spaces

We discuss smoothness of theWeyl functional calculus and use it to prove that every C*-algebra is a confined Banach space. Received: 17 August 2005     

Logarithmic residues, generalized idempotents, and sums of idempotents in Banach algebras

In a commutative Banach algebraB the set of logarithmic residues (i.e., the elements that can be written as a contour integral of the logarithmic derivative of an analyticB-valued function), the set of generalized idempotents (i.e., the elements that are annihilated by a polynomial with non-negative integer simple zeros), and the set of sums of idempotents are all the same. Also, these (coinciding) sets consist of isolated points only and are closed under the operations of addition and multiplication. Counterexamples show that the commutativity condition onB is essential. The results extend to logarithmic residues of meromorphicB-valued functions.