The fixed point property in ordered sets of width two

We consider the fixed point property (FPP) in an ordered set of width two (every antichain contains at most two elements). The necessary condition of the FPP and a number of equivalent conditions to the FPP in such sets is established. The product theorem is proved, as well.     

A particle method for first-order symmetric systems

Summary We present and study a conservative particle method of approximation of linear hyperbolic and parabolic systems. This method is based on an extensive use of cut-off functions. We prove its convergence inL ² at the order as soon as the cut-off function belongs toW ^m+1.1.Dedicated to Professor Joachim Nitsche on the occasion of his 60th birthday     

On switching paths polyhedra

A class of integer polyhedra with totally dual integral (tdi) systems is proposed, which generalizes and unifies the “Switching Paths Polyhedra” of Hoffman (introduced in his generalization of Max Flow-Min Cut) and such polyhedra as the convex hull of (the incidence vectors of) all “path-closed sets” of an acyclic digraph, or the convex hull of all sets partitionable intok path-closed sets. As an application, new min-max theorems concerning the mentioned sets are given. A general lemma on when a tdi system of inequalities is box tdi is also given and used.     

On orthogonal linear ℓ1 approximation

Summary The problem is considered of orthogonal ₁ fitting of discrete data. Local best approximations are characterized and the question of the robustness of these solutions is considered. An algorithm for the problem is presented, along with numerical results of its application to some data sets.     

Roots,iterations and logarithms of formal automorphisms

In this paper it is proved that having a logarithm is equivalent to having roots of arbitrary order in the group of automorphisms of a formal power series ring, and in algebraic subgroups too     

Regressions and monotone chains II: The poset of integer intervals

A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x ₁<...ksuch that (x ₁)...(x_k). Let P _nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P _nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x ^t(x,j–1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) < f(K) <t( + _k, k) , where _k 0 as k. Alternatively, the largest k such that every regression on P _nis guaranteed to have a monotone k-chain lies between lg^*(n) and lg^*(n)–2, inclusive, where lg^*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element.     

Classification of integral trees

A finite poset Q is called integral over a field k if there exists an ASL (algebra with straightening laws) domain on Q{–} over k. We classify all trees (rank one connected posets without cycles) which are integral over an infinite field.     

300 Femtosecond pulses at 497 nanometer generated by an excimer laser pumped cascade of distributed feedback dye lasers

The setup is a cascade of 3 lasers: A competing cavity dye laser pumped by a XeCl excimer laser, followed by two distributed feedback dye lasers. The typical durations of the pulses from the lasers are 100 ps, 5 ps, and 300 fs, respectively. The output pulses at 497 nm are amplified up to 500 MW. The shortest pulse duration obtained was 198 fs.     

Theory of travelling-wave amplified spontaneous emission

A rate-equation model for describing the travelling-wave amplified spontaneous emission pulses (TWASE) in a transversally excited travelling wave arrangement is given. 6.35 ps long ASE pulses have been obtained by 12 ps long pump pulses. The effect of pump intensity, pump-pulse duration, molecular parameters of the dyes and pump-sweep velocity on the ASE pulses is studied.     

Steady state photoisomer accumulation in the absorber jet of the passively mode-locked femtosecond dye laser

In continuous were passively mode-locked dye lasers a steady state distribution of two isomers of the saturable absorber dye can be established. We report the first intracavity transmission measurement and estimation of the amount of the photoisomer of DODCI in the femtosecond CPM ring laser. Comparison with a simple model based on rate equations allows to estimate the quantum yield of a photo-back reaction. The obtained dependence of the photoisomer concentration on the laser wavelength and pulse energy can be used in theories describing the generation process for adequate estimation of its part in the modelocking regime.