Stability criteria for positive linear discrete-time systems

Positivity - We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have...     

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     

Scale functions on $p$-adic Lie groups

Let G be a p-adic Lie group. Then G is a locally compact, totally disconnected group, to which Willis [14] associates its scale function G : G→ℕ. We show that s can be computed on the Lie algebra level. The image of s consists of powers of p. If G is a linear algebraic group over ℚ _p , s(x)=s(h) is determined by the semisimple part h of x∈G. For every finite extension K of ℚ _p , the scale functions of G and H:=G(K) are related by s _H ∣ _G =s _G ^{[ K :ℚ} _p ^]. More generally, we clarify the relations between the scale function of a p-adic Lie group and the scale functions of its closed subgroups and Hausdorff quotients. Received: 20 February 1997; Revised version: 18 May 1998     

Dynamically generated parton distributions for high energy collisions

The parton distributions of the nucleon are evaluated dynamically using the assumption that at some low resolution scale the nucleon consists entirely of valence quarks. A simple parametrization of the resulting gluon distribution is presented, forx? 10^?5 up toQ ²?10⁶ GeV². This gluon distribution is predicted dicted to be much steeper and larger in the very smallx region (x<10^?2) than usually assumed. Applications to deep inelastic scaling violations and heavy quark (c, b, t) contribution are discussed and presented as well as hadronic heavy quark production at SSC/LHC energies. For example, the \(b\bar b\) production rate at 40 TeV is predicted to be about an order of magnitude larger than that estimated with other gluon distributions so far.     

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).