Domination of uniformly continuous semigroups

We prove that a bounded operator on a Banach lattice, satisfying a growth condition, is regular. Also, we prove that the generator of a C ₀-semigroup on such a lattice for which such an operator exists is bounded.     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

Cationic poly(methacryl oxyethyl trimethylammonium) and its poly(ethylene glycol)‐grafted analogue as capillary coating materials in electrophoresis

Cationic polyelectrolytes were synthesized and used as semipermanent coating materials for capillaries in electrophoresis. The polyelectrolytes used were a homopolymer of poly(methacryl oxyethyl trimethylammonium chloride) (PMOTAC) and its poly(ethylene glycol) (PEG)‐grafted analogue. Two PMOTAC polyelectrolytes, with molar masses of 85,000 and 300,000 g/mol, and PEG‐grafted PMOTAC with a molar mass of 280,000 g/mol were synthesized and then characterized by size exclusion chromatography (SEC) and nuclear magnetic resonance (NMR) spectroscopy. Attachment of the polyelectrolytes to the wall of the fused silica capillary for electrophoresis caused the electroosmotic flow (EOF) to reverse. The polyelectrolyte coatings were tested over the pH range 2–11 at different buffer ionic strengths, and the most stable and strongest anodic EOFs were obtained at acidic pH values with low ionic strength buffers. Between runs the capillary is merely rinsed for 2 or 3 min with the background electrolyte solution. With the PMOTAC coatings at pH values ≤5, the RSDs of the EOFs were less than 2.9% after 60 injections. The effects of the molar mass of the polycation and of PEGylation of PMOTAC on the interactions between the polycations and basic proteins were studied at acidic pH values. The differences in the effective electrophoretic mobilities, resolution values, and plate numbers of the proteins with the different coatings were due to the EOF, as demonstrated through calculations of reduced mobilities, relative resolution values, and relative plate numbers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2655–2663, 2007     

Enantio- and Diastereoselective Aldol-Reaction of 2,6-Dimethylphenyl Propionate Using Titanium-Carbohydrate Complexes

Chloro(cyclopentadienyl)bis(1,2:5,6-di-O-isopropylidene-α-D -glucofuranos-3-O-yl)titanium ( 1 ) is used for the transmetallation of Li-enolates obtained from propionyl derivatives. While such Ti-enolates of ketones and hydrazones appear to be unreactive, the (E)enolate 13 of 2,6-dimethylphenyl propionate ( 11 ) adds to the re-side of aldehydes, affording various syn-aldols 14 with high dia- and enantioselectivity (92–97% ds, 91–97% ee, cf. Scheme 2 and Table 1). Racemic syn-aldols (±)- 14 are obtained analogously from the achiral bis(2-propyloxy)-Ti-enolate 15 (Scheme 2 and Table 2). In contrast to the unstable Li-enolate 10 , the Ti-enolates 13 and 15 isomerize at ?30°, presumably to the thermodynamically more stable (Z)-enolates (Scheme 4), While the diastereoselectivity of the achiral enolate 15 is lost upon this equilibration, the chiral (Z)-enolate 27 quite unexpectedly affords anti-aldols 12 of high optical purity (94–98% ec) and, in most cases, with acceptable-to-good diastereoselectivity (82–90% ds). Notable exceptions are branched unsaturated and aromatic aldehydes which form a greater proportion of synepimers of moderate optical purity (Scheme 5 and Table 3). Consistent with these findings, re-facial-and ami -selective aldol-addition is also exhibited by the (Z)-configurated Ti-enolate 22 of N-propionyl-oxazolidi-none 19 (Scheme 3).     

One-Bond 13C, 13C-Spin Coupling in η4-, η3- and η2-Olefin Transition Metal Complexes

One-bond ¹³C, ¹³C-spin-coupling constants have been measured, with natural isotope abundance, in η⁴-diene, η³-allyl and η²-ene transition-metal carbonyl complexes. Typical values of ¹J(C,C) are given for Fe-, Ru- and Os-complexes with the three types of olefinic ligands. The effects of substituents and the structural significance of the C,C-coupling constants are discussed.