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.     

Über verallgemeinerte Momente additiver Funktionen

In this paper we give characterizations of additive functionsf, for which $$\mathop {\lim \sup }\limits_{x \to \infty } x^{ - 1} \sum\limits_{n \leqslant x} {\varphi (|f(n)|)}$$ is bounded, where φ: ?⁺ → ?⁺ is monotone and or $$\begin{array}{*{20}c} {\varphi (x) = c^x } & {(x \in \mathbb{R}).} \\ \end{array}$$ A typical example is φ (x)=x ^a (a>0) forx≥0.     

Use of solid-phase microextraction-capillary-gas chromatography (SPME-CGC) for the varietal characterization of wines by means of chemometrical methods

The extraction of wine aroma compounds was studied by direct-SPME (DI/SPME), headspace-SPME (HS/SPME) and multiple-headspace-extraction-SPME (MHE/SPME). The aromagrams obtained by HS/SPME-CGC were evaluated with chemometrical methods for the varietal classification of wines. Received: 25 July 1997 / Revised: 24 September 1997 / Accepted: 7 October 1997     

Über die bei hohen Ansäuerungsgraden auftretenden Polymolybdat-Typen,insbesondere zur Frage der „Dekamolybdate”︁ und „Phase C”︁-Polymolybdate

On the Polymolybdate Types Occurring at High Degrees of Acidification, with Particular Reference to the “Decamolybdates” and “Phase C” Polymolybdates It is shown that in the range of high acidification (> 1.6H⁺/MoO₄^2?) of aqueous molybdate solutions only two types of solid polymolybdates occur, namely the 36-molybdate and the “decamolybdate” types. These types can be most conveniently identified by their Raman spectra and also by some other characteristics. All the other polymolybdate types proposed in the literature for this range of acidification (“hexamolybdates”, “octamolybdates”, “dodecamolybdates”, “16-molybdates”, a 19-molybdate, the large group of polymolybdates characterized by a wide range of b in the general formula M₂O · bMoO₃ · cH₂O, “phase C” polymolybdates, a “hexagonal hydrate of molybdenum trioxide”, a “reactive molybdic acid”, “NH₃(MoO₃)₃”, and others) can be assigned to one of these two types. The most important reason for the erroneous assignments in the literature is the isomorphous exchange of varying quantities of the alkali or alkaline earth metal cations by H₃O⁺ in the crystal structure, occurring in the highly acidic solutions, particularly with the small cations. This cannot be recognized by the presently available methods of investigation and, hence, leads to the creation of new polymolybdate types. Another reason causing some of the confusion is the assignment of virtually identical X-ray diffraction data to two different types of lattices, a hexagonal and cubic lattice.     

Diverse redox-active molecules bearing O-, S-, or Se-terminated tethers for attachment to silicon in studies of molecular information storage

A molecular approach to information storage employs redox-active molecules tethered to an electroactive surface. Attachment of the molecules to electroactive surfaces requires control over the nature of the tether (linker and surface attachment group). We have synthesized a collection of redox-active molecules bearing different linkers and surface anchor groups in free or protected form (hydroxy, mercapto, S-acetylthio, and Se-acetylseleno) for attachment to surfaces such as silicon, germanium, and gold. The molecules exhibit a number of cationic oxidation states, including one (ferrocene), two [zinc(II)porphyrin], three [cobalt(II)porphyrin], or four (lanthanide triple-decker sandwich compound). Electrochemical studies of monolayers of a variety of the redox-active molecules attached to Si(100) electrodes indicate that molecules exhibit a regular mode of attachment (via a Si-X bond, X = O, S, or Se), relatively homogeneous surface organization, and robust reversible electrochemical behavior. The acetyl protecting group undergoes cleavage during the surface deposition process, enabling attachment to silicon via thio or seleno groups without handling free thiols or selenols.