Solving the Gleason problem on linearly convex domains

Let be a bounded, connected linearly convex set in with boundary. We show that the maximal ideal (both in ) and ) consisting of all functions vanishing at is generated by the coordinate functions . Received: 2 July 2001; in final form: 26 September 2001 / Published online: 28 February 2002     

On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001     

Non-trivial simple poles at negative integers and mass concentration at singularity

Let (X,0) be the germ of a normal space of dimension n+1 and let f be the germ at 0 of a holomorphic function on X. Assume both X and f have an isolated singularity at 0. Denote by J the image of the restriction map , where F is the Milnor fibre of f at 0. We prove that the canonical Hermitian form on , given by poles of order at in the meromorphic extension of , passes to the quotient by J and is non-degenerate on . We show that any non-zero element in J produces a “mass concentration” at the singularity which is related to a simple pole concentrated at for (in a non-na?ve sense). We conclude with an application to the asymptotic expansion of oscillatory integrals , for , when . Received: 28 May 2001 / Published online: 26 April 2002     

Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

Gold nanoparticle-enhanced surface plasmon resonance measurement with a highly sensitive quantification for human tissue inhibitor of metalloproteinases-2

Two different methods for the quantification of human tissue inhibitor of metalloproteinases-2 (TIMP-2) were developed using surface plasmon resonance (SPR) and gold nanoparticles for signal enhancement. The first method, a competitive assay, used TIMP-2 immobilized to the sensor surface and the inactive form of matrix metalloproteinase-2 (proMMP-2) (EC 3.4.24.24) adsorbed to gold nanoparticles. The sensor signals resulting from the interaction of MMP-2-gold nanoparticles with immobilized TIMP-2 were inversely proportional to the amounts of TIMP-2 of the sample. The measuring range for TIMP-2 was about 15–180 pM. The second method, a one-step sandwich assay, used proMMP-2 immobilized to the sensor surface and an anti-TIMP-2 monoclonal antibody coupled to gold nanoparticles. The lower detection limit of this assay format was 0.5 pM of TIMP-2. The binding signals were highly reproducible up to 100 pM of the inhibitor. The improvements obtained in TIMP-2 quantification over already existing tests could contribute to a better understanding and diagnosis of diseases like cancer.     

双水相萃取法分离铍(Ⅱ)、铁(Ⅲ)与铁(Ⅱ)、铬(Ⅲ)、锰(Ⅱ)、铝(Ⅲ)

研究了在聚乙二醇2000(PEG)-硫酸钠(Na2SO4)-邻苯二酚紫(PV)体系中铍(Ⅱ)、铁(Ⅲ)、铁(Ⅱ)、铝(Ⅲ)、铬(Ⅲ)、锰(Ⅱ)的萃取行为。试验结果表明,铍(Ⅱ)在pH 3.5-7.0及铁(Ⅲ)在pH 4.0-7.0范围内可以被PEG相几乎完全萃取,而铝(Ⅲ)、铬(Ⅲ)在pH 1.0-7.0、锰(Ⅱ)在pH 1.0-4.5、铁(Ⅱ)在pH 1.0-4.5则不被萃取。从而实现了将铍(Ⅱ)(pH 3.5)、铁(Ⅲ)(pH 5.0)与铝(Ⅲ)、铬(Ⅲ)、锰(Ⅱ)、铁(Ⅱ)混合离子的定量分离。同时探讨了PEG相的萃取机理。     

Activation of trisacryl gels with chloroformates and their use for affinity chromatography and protein immobilization

In this study we describe the activation with chloroformates of Trisacryl-GF-2000, a new synthetic gel support that is stable, hydrophilic, and contains large amounts of hydroxyl groups available for activation. Of all the reagents tested, the activation withN-hydroxysuccinimide-chloroformate andp-nitrophenylchloroformate in organic solvents provides the best activation yield and subsequent coupling. When Trisacryl was activated in acetone with the chloroformates in the presence of 4-dimethylaminopyridine as base and catalyst, up to 30% of the hydroxyl groups, (i.e., 1/repeating unit) could be activated. Amino-containing ligands and proteins could be coupled to these carriers at pH 8 or higher. For better results in affinitychromatographic applications, spacers of ε-amino caproic acid or diaminohexane were introduced. The efficacy of these columns was demonstrated by purification of enzymes, antibodies, and antigens. The performance of these new columns were compared with that of Sepharose columns activated in various ways. In every case, the properties of the Trisacryl support proved superior with particular reference to the purity of the product obtained.     

The vibrational analysis of methylarsonic acid,trideuteromethylarsonic acid and their anions

Raman and IR spectra of methylarsonic acid, CH₃AsO₃H₂, trideuteromethylarsonic acid, CD₃AsO₃H₂ and their anions in aqueous solution and the solid state are discussed. Some results of a general valence force field and a Urey-Bradley force field are reported.     

Using a process-centered approach to minimize the effort of compliance

 The complexity of different quality standards can, in principle, be covered by different approaches and strategies. In-depth process mapping of quality control (QC) work streams was used by the analytical laboratories of Lonza AG to show up the principle differences in being compliant to different quality systems. The results identified two main drivers for all necessary actions: process-related activities and infrastructure-related activities. In addition, a clear indication of the economic impact of these driving forces was gained, which led the laboratories to decide on a process-oriented approach. This approach has the advantage of being able to reflect the different demands of different quality assurance (QA) regulations within the same QC organizational structure. Following the process helps avoid unnecessary efforts in analytical work and represents a very economical approach, at the same time, providing high flexibility to react to different QA or customer demands. Received: 5 July 2002 Accepted: 12 November 2002 Acknowledgements The process-oriented approach resulted from many, very challenging discussions for which I would like to thank the staff of my organization (Analytics & QC), especially, the QA staff and the LIMS team. Presented at Analytica Conference, 23–26 April 2002, Munich, Germany Correspondence to B. Ciommer     

Convexifactors,generalized convexity and vector optimization

In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors.