EM constructions for a class of generalized quantifiers

Summary We consider a class of Lindström extensions of first-order logic which are susceptible to a natural Skolemization procedure. In these logics Ehrenfeucht Mostowski (EM) functors for theories with arbitrarily large models can be obtained under suitable restrictions. Characteristic dependencies between algebraic properties of the quantifiers and the maximal domains of EM functors are investigated.Results are applied to Magidor Malitz logic,L(Q ^<), showing e.g. its Hanf number to be equal to (₁) in the countably compact case. Using results of Baumgartner, the maximal number of isomorphism types of linearly ordered models of regular cardinality is shown to be achieved for theories that admit an EM functor on a typically restricted domain.     

Combings of groups and the grammar of reparameterization

A new construction of combings is used to distinguish between several previously indistinguishable classes of groups associated to the theory of automatic groups and non-positive curvature in group theory. We construct synchronously bounded combings for a class of groups that are neither bicombable nor automatic. The linguistic complexity of these combings is analysed: in many cases the language of words in the combing is an indexed language.     

Codings of graphs with binary edge labels

LetG(V,E) be a graph. A mappingf:E{0,1} ^m is called a (binary) coding ofG, if the induced mapping , assigns different vectors to the vertices. For the Boolean sum,f is called aB-code, and for the mod 2 sum anM-code. Letm _B (G) resp.m _M (G) be the smallest lengthm for whichB-codes resp.M-codes are possible. Trivially,m _B (G),m _M (G) log₂|V|. Improving results of Z. Tuza we showm _B (G)log₂|V| + 1,m _M (G)log₂|V|+4.     

Dynamics of femtosecond laser interactions with dielectrics

Femtosecond laser pulses appear as an emerging and promising tool for processing wide bandgap dielectric materials for a variety of applications. This article aims to provide an overview of recent progress in understanding the fundamental physics of femtosecond laser interactions with dielectrics that may have the potential for innovative materials applications. The focus of the overview is the dynamics of femtosecond laser-excited carriers and the propagation of femtosecond laser pulses inside dielectric materials. PACS 61.80.Ba; 52.38.Mf; 42.65.Jx; 78.47.+p; 71.35.-y     

Waveform-controlled near-single-cycle milli-joule laser pulses generate sub-10 nm extreme ultraviolet continua

We demonstrate the generation of waveform-controlled laser pulses with 1?mJ pulse energy and a full-width-half-maximum duration of ～4 fs, therefore lasting less than two cycles of the electric field oscillating at their carrier frequency. The laser source is carrier-envelope-phase stabilized and used as the backbone of a kHz repetition rate source of high-harmonic continua with unprecedented flux at photon energies between 100 and 200?eV (corresponding to a wavelength range between 12-6?nm respectively). In combination we use these tools for the complete temporal characterization of the laser pulses via attosecond streaking spectroscopy.     

Generation of phase-locked and tunable continuous-wave radiation in the terahertz regime

Broadly tunable phase-stable single-frequency terahertz radiation is generated with an optical heterodyne photomixer. The photomixer is excited by two near-infrared CW diode lasers that are phase locked to the stabilized optical frequency comb of a femtosecond titanium:sapphire laser. The terahertz radiation emitted by the photomixer is downconverted into RF frequencies with a waveguide harmonic mixer and measurement-limited linewidths at the Hertz level are demonstrated.     

Analysis of surface and material modifications caused by laser drilling of AlN ceramics

For the laser drilling of aluminum nitride ceramic the processing results and the effects related to pulsed irradiation were investigated. Images of the drilled surface revealed regular, cylindrically shaped holes of about 100 μm in diameter independently of the laser wavelength (1064/532/355 or 266 nm). The holes were surrounded by circular heat-affected zones of larger diameter. A comparison of the elemental compositions of the original material and the processed one indicated a decrease of the nitrogen concentration in the affected area. The spectral analysis of the ablated material composition revealed the presence of ions and neutrals in dependence on the laser intensity applied. It was found that at intensity values close to the ablation threshold the ejected material consisted mainly of neutrals, while doubling of the intensity resulted in appearance of single-ionized Al species, which were also observed together with Al clusters in the mass spectra of the UV-excited plasma. Their prevailing content was revealed for drilling at higher intensities around 15 GW/cm² at 532 nm. Results of model calculations indicated, in agreement with the experiment, that at the threshold the ceramic decomposes into gaseous nitrogen and solid Al particulates, while at a higher fluence the material particles vaporize and influence the quality of drilling.     

Photon-exchange processes at hadron colliders as a probe of the dynamics of diffraction

The rich structure of photon-exchange processes at hadron colliders is studied. We discuss central vector meson production , W production and production. Each process has distinct, and large, soft pp rescattering effects, which can be directly observed by detecting the outgoing protons. This allows a probe of the optical density of the proton, which plays a crucial role in the evaluation of the rapidity gap survival probabilities in diffractive-like processes at hadron colliders. We note that an alternative mechanism for production is odderon, instead of photon, exchange; and that the ratio of odderon to photon contributions is enhanced (suppressed) for vector meson production. Received: 1 February 2002 / Revised version: 4 April 2002 / Published online: 22 May 2002