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...     

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.     

Quantitative aspects of gradient HPLC of copolymers from styrene and ethyl methacrylate

Summary Prerequisite of quantitative evaluation in chromatography is equivalence of sample composition and detector signal. This includes complete retention and proper elution of all sample constituents. In polymer HPLC, complete retention requires a poor starting eluent, a sufficiently active column, and a low ratio of injection volume to column volume. On small pore columns, insufficient retention caused the polymer to elute either in the interstitial volume (sample exclusion), together with the sample solvent, or immediately after the solvent plug.Stat-copoly(styrene/ethyl methacrylate) samples are more difficultly retained thanstat-copoly(styrene/acrylonitrile) specimes. With the former copolymer it could be shown that incomplete retention did not cause sample demixing. In order to gain complete retention, non-exclusion HPLC of polymers should be performed with columns whose solvent volume is at least 50 times as large as the injection volume. This consequence is of practical importance in chromatographic cross-fractionation where rather large volumes of SEC eluate are injected into the apparatus for gradient HPLC.     

Magnetism in hydrogenated YBa2Cu3O7 a comparison of μSR and NMR results

Hydrogenated YBa₂Cu₃O₇ with [H]/cell=2.0 was studied by X-ray diffraction, SR and¹H-NMR. For the first time, the hydride phase (16% larger c-axis) known from thin film experiments was seen in a bulk sample. A comparison of the SR and NMR results shows that the 15 mT site (2 MHz in SR) is the stable position for the proton and muon. The three other muon sites (4 MHz line and two exponentially decaying components) are metastable.