Strong uniform consistency of nonparametric regression function estimates

Let (X, Y) be a ^dx-valued random vector and let r(t)=E(Y/X=t) be the regression function of Y on X that has to be estimated from a sample (X _i, Y_i), i=1,..., n. We establish conditions ensuring that an estimate of the form

Synthesis of N-(tosyl)azetidin-2-imines

A synthetic route for N-(tosyl)azetidin-2-imines $\text{6}$, a novel class of derivatives of β-lactams, has been developed. The procedure is applicable to the synthesis of azetidin-2-imines related to penicillins and cephalosporins.     

Zur Aktivierung partiell silylierter Kohlenhydrate mittels Triphenylphosphan/Azodicarbonsäureester

On the Activation of Partially Silylated Carbohydrates Using Triphenylphosphane/Diethylazodicarboxylate Reaction of methyl α-D-glucopyranoside ( 1 ) with two equivalents of t-butyldimethylchlorosilane yields methyl 2,6-bis[O-(t-butyldimethylsilyl)]-α-D-glucopyranoside ( 1a ) and methyl 3,6-bis[O(t-butyldimethylsilyl)]-α-D-glucopyranoside ( 1b ) in a ratio of 4:1. The anomeric β-pyranoside 2 affords methyl 2,6-bis[O(t-butyldimethylsilyl)]-β-D-glucopyranoside ( 2a ) and methyl 3,6-bis[O(t-butyldimethylsilyl)]-β-D-glucopyranoside ( 2b ) in nearly equal amounts. 2b is isomerized to methyl 4,6-bis[O(t-butyldimethylsilyl)]-β;-D-glucopyranoside ( 2c ) (83%) and 2a (10%) with triphenylphosphane/diethylazodicarboxylate. Structures were assigned by NMR.-analysis and CD.-analysis of the corresponding benzoates 1c , 1d and 2d and of the acetates 2e and 2f . 1a is transformed into methyl 4-azido-2, 6-bis[O(t-butyldimethylsilyl)]-4-deoxy-α-D-galactopyranoside ( 3 ) with triphenylphosphane/diethylazodicarboxylate/HN₃. 2a and 2c yield the 3-azido-allosides 5 and 7 respectively under similar conditions. The activation by triphenylphosphane/diethylazodicarboxylate is high enough to introduce also p-nitrobenzoate groups with inversion of configuration at the reaction center. By this way 1a and 2a give methyl 2, 6-bis[O(t-butyldimethylsilyl)]-4-O-p-nitrobenzoyl-α-D-galactopyranoside ( 4 ) and methyl 2, 6-bis[O-(t-butyldimethylsilyl)]-3-O?ptrobenzoyl-β-D-allopyranoside ( 6 ) respectively. For elucidation of structures the acetate derivatives 3a-7a were prepared.     

Strukturelle Abwandlungen anN-Acetylneuraminsäure, 3

From methyl-5-acetylamino-7,8-anhydro-4,9-O-bis-(t-butyldimethylsilyl)-3,5-dideoxy--D-glycero-D-galacto-2-nonulopyranosidonic acid methylester (1) the derivatives1 a and1 b were obtained by removing the 9-O-(t-butyldimethylsilyl)group withBu ₄NF, followed by acetylation. Treatment of1 b with 80% acetic acid and acetanhydride/pyridine yields the 8-epi-N-acetylneuraminic acid derivative2 a and the 7-epi-N-acetylneuraminic acid derivative3 a in a ratio of 3:1 (Scheme 1). The structure elucidation of2 b was achieved by converting2 b via the 4,9-bis-O-(tBDMSi)-8-O-tosyl-derivative2 d into the epoxide1 (Scheme 2). Using the same sequence the epoxides4 and5 were transformed into theN-acetylneuraminic acid derivative6 a and the 7,8-bis-epi-N-acetylneuraminic acid derivative7 a (Scheme 3). After treatment with sodium hydroxide and 0.025m HCl and Dowex 50 H⁺ the 8-epi-, 7-epi- and 7,8-bis-epi-N-acetylneuraminic acids2,3, and7 were obtained. These three compounds were tested withCMP-N-acetylneuraminic acid synthetase.

Herrn KollegenK. Schlögl mit den besten Wünschen zum 60. Geburtstag.     

Column selection and method development for the separation of nucleoside phosphotriester diastereoisomers, new potential anti-viral drugs. Application to cellular extract analysis

Analytical HPLC methods using derivatized cellulose and amylose chiral stationary phases used in normal and reversed-phase modes were developed for the diastereoisomeric separation of mononucleotide prodrugs (pronucleotides) of 3'-azido-2',3'-dideoxythymidine (AZT). The resolutions were performed with two silica-based celluloses using normal and reversed-phase methodologies: Tris-3,5-dimethylphenylcarbamate (Chiralcel OD-H and Chiracel OD-RH) and Tris-methylbenzoate (Chiralcel OJ and OJ-R). Two amyloses phases, Tris-3,5-dimethylphenylcarbamate (Chiralpak AD) and Tris-(S)-1-phenylethylcarbamate (Chiralpak AS), were used in normal-phase mode. Additionally, we developed separation using two stationary phases with immobilized cyclodextrins in reversed-phase and polar-organic modes. The mobile phase and the chiral stationary phase were varied to achieve the best resolution. Different types and concentration of aliphatic alcohols, acetonitrile or water in the mobile phase were also tested for the different separation modes. An optimal baseline separation (Rs > 1.5) was readily obtained with all silica-based celluloses and amyloses using a normal-phase methodology. The different columns gave complementary results in term of resolution. Limits of detection and quantification were 0.12-0.20 and 0.40-0.67 microm, respectively. This analytical method was applied in a preliminary study for the pronucleotide 2 quantification in cellular extract.     

Spectral and non-spectral interferences in inductively coupled plasma mass-spectrometry

Inductively coupled plasma mass spectrometry of environmental and biological samples is often hampered by spectral and non-spectral interferences. Spectral interferences, caused by the limited resolution of the quadrupole mass spectrometer, can be eliminated in a variety of ways. For their identification inspection of a signal versus carrier gas flowrate is useful. Anion exchange allows the removal of most S and Cl containing compounds, which are at the origin of the majority of spectral interferences. Matrix modification, for example the addition of ethanol and subsequent optimization of the gas flow rates in a number of cases enables the reduction of the interferences to insignificant values. Often a mathematical correction based on isotopic signal ratios can be applied. Non-spectral interferences can be divided in reversible, that is occurring while the sample is being measured, and irreversible matrix effects, that is clogging of the nebulizer and sampling orifices or deposition on the torch or in the ion lens stack. The errors associated with non-spectral interferences can be eliminated by appropriate calibration procedures, adapted sample preparation or limitation of the amount of sample delivered to nebulizer, plasma and sampling devices, for example by the application of flow injection. Applications of all the elimination procedures are described for the analysis of sea-water, estuarine water, soil and sewage extracts, percolate water, urine, serum and wine.     

Synthesis of 27-nor-25-oxocholest-5-en-3β-yl acetate and 27-nor-25-oxocholestanol from pregnenolone

Grignard-reaction of pregnenolone-3β-acetate with pentan-2-one ethylene ketal-5-magnesium bromide and subsequent dehydration yielded 27-nor-25-oxocholesta-5,20 (22)-dien-3β-yl acetate which was hydrogenated to 27-nor-25-oxocholest-5-en-3β-yl acetate and 27-nor-25-oxocholestan-3β-yl acetate.     

Enantioseparation of chiral N-imidazole derivatives by electrokinetic chromatography using highly sulfated cyclodextrins: mechanism of enantioselective recognition

Baseline separation of ten new substituted [1-(imidazo-1-yl)-1-phenylmethyl)] benzothiazolinone and benzoxazolinone derivatives, with one chiral center, was achieved by CD-EKC using highly sulfated CDs (alpha, beta, gamma highly S-CDs) as chiral selectors. The influence of the type and concentration of the chiral selectors on the enantioseparations was investigated. The highly S-CDs exhibit a very high enantioselectivity power since they allow excellent enantiomeric resolutions compared to those obtained with the neutral CDs. The enantiomers were resolved with analysis times inferior to 2.5 min and resolution factors R(s) of 3.73, 3.90, 1.40, and 4.35 for compounds 1, 2, 3, and 5, respectively, using 25 mM phosphate buffer at pH 2.5 containing either highly S-alpha-CD, highly S-beta-CD, and highly S-gamma-CD (3 or 4% w/v) at 298 K, with an applied field of 0.30 kV/cm. The determination of the enantiomer migration order for the various analytes and the study of the analyte structure-enantioseparation relationships display the high contribution of the interactions between the analytes phenyl ring and the CDs to the enantiorecognition process. The thermodynamic study of the analyte-CD affinities permits us to improve our knowledge about the enantioseparation mechanism.     

Chiral capillary electrophoretic determination of the enantiomeric purity of tetrahydronaphthalenic derivatives, melatoninergic ligands, using highly sulfated beta-cyclodextrins

Using cyclodextrin capillary zone electrophoresis (CD-CZE), baseline separation of synthetic tetrahydronaphthalenic derivatives, potential melatoninergic compounds, was achieved. A method for the enantioresolution of these tetralins and determination of their enantiomeric purity was developed using anionic CDs (highly sulfated-CD or highly S-CD) as chiral selectors and capillaries dynamically coated with polyethylene oxide (PEO). Operational parameters such as the nature and concentration of the chiral selectors, buffer pH, organic modifiers, temperature and applied voltage were investigated. The use of charged CDs provides a driving force for our neutral compounds in the running buffer and enantiomeric resolution by inclusion of compounds in the CD cavity. The highly S-beta-CD was found to be the most effective complexing agent, allowing good enantiomeric resolution. The complete resolution of three tetralin compounds was obtained using 25 mM phosphate buffer at pH 2.5 containing 2.5% w/v of highly S-beta-CD at 25 degrees C with an applied field of 0.25 kV/cm. The apparent association constants of the inclusion complexes were calculated. This optimized method was validated in terms of linearity, sensitivity, accuracy and recovery. The enantiomeric purity for the three molecules was determined and the detection limit of enantiomer impurities is about 0.3-0.6%.