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...     

Up to isometries,a deformation is a continuous function of its metric tensorAux isométries près,une déformation est une fonction continue de son tenseur métrique

If the Riemann–Christoffel tensor associated with a field of class $\text{C}{}^2$ of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset $\text{Ω?}\text{R}{}^3$, then this field is the metric tensor field associated with a deformation of class $\text{C}{}^3$ of the set $\text{Ω}$, uniquely determined up to isometries of $\text{R}{}^3$. We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies. To cite this article: P.G. Ciarlet, F. Laurent, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 489–493.     

Arithmetic functions with linear recurrence sequences

We obtain asymptotic formulas for all the moments of certain arithmetic functions with linear recurrence sequences. We also apply our results to obtain asymptotic formulas for some mean values related to average orders of elements in finite fields.     

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 die Identifizierung von Alkoholen mit 1-Chlormethyl-isatin

Monatshefte für Chemie - Chemical Monthly - Primary, secondary and tertiary aliphatic alcohols quickly react with 1-chloromethyl-isatin (1) to give good yields of alkoxymethylisatines4-novel...