Scaling properties of ℤ k- 1 actions on the circle

We derive universal scaling properties for ^k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered.     

Efficient unbiased variance reduction techniques for Monte Carlo simulations of radiative transfer in cloudy atmospheres: The solution

We present five new variance reduction techniques applicable to Monte Carlo simulations of radiative transfer in the atmosphere: detector directional importance sampling, n-tuple local estimate, prediction-based splitting and Russian roulette, and circum-solar virtual importance sampling. With this set of methods it is possible to simulate remote sensing instruments accurately and quickly. In contrast to all other known techniques used to accelerate Monte Carlo simulations in cloudy atmospheres - except for two methods limited to narrow angle lidars - the presented methods do not make any approximations, and hence do not bias the result. Nevertheless, these methods converge as quickly as any of the biasing acceleration techniques, and the probability distribution of the simulation results is almost perfectly normal. The presented variance reduction techniques have been implemented into the Monte Carlo code MYSTIC (“Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) in order to validate the techniques.     

Etude d'impulsions lumineuses breves par interferometrie a deux ondes

We have studied the evolution of the light transmitted through matter in which an optical breakdown is taking place. With a two-waves interferometer made a birefringent plate between polarizers we get informations about the time correlation function of the fields. With an interferometer made of two identical harmonic generating plates separated by a dispersion medium, we learn about the correlation function of the square of the fields. Both systems act as spectral filters with a notch cosine-shaped centered at the incident frequency. We have also observed a transient angular spreading of the beam not previously emphasized which brings a further complication in the picture.     

Possible evidence for a narrow isovectorB=2 resonance below pion production threshold

Some evidence is presented for a narrow peak at 1969±2 MeV (FWHM=9±2 MeV) in the missing mass spectrum of the³He(p, d) reaction, with 3 standard deviations. The nature of this state, the mass of which is below the NN threshold, is discussed in connection with structures found in other experiments.     

The twenty-fourth Fermat number is composite

We have shown by machine proof that is composite. The rigorous Pépin primality test was performed using independently developed programs running simultaneously on two different, physically separated processors. Each program employed a floating-point, FFT-based discrete weighted transform (DWT) to effect multiplication modulo . The final, respective Pépin residues obtained by these two machines were in complete agreement. Using intermediate residues stored periodically during one of the floating-point runs, a separate algorithm for pure-integer negacyclic convolution verified the result in a ``wavefront' paradigm, by running simultaneously on numerous additional machines, to effect piecewise verification of a saturating set of deterministic links for the Pépin chain. We deposited a final Pépin residue for possible use by future investigators in the event that a proper factor of should be discovered; herein we report the more compact, traditional Selfridge-Hurwitz residues. For the sake of completeness, we also generated a Pépin residue for , and via the Suyama test determined that the known cofactor of this number is composite.

     

Rigidity in holomorphic and quasiregular dynamics

We consider rigidity phenomena for holomorphic functions and then more generally for uniformly quasiregular maps.

     

Hypernuclear production in the (K, π) reaction

Cross sections for the production of hypernuclei were measured in the reaction A(K⁻, π⁻) _ΛA. on light and heavy nuclear targets, using a separated K⁻ beam at the CERN Proton Synchrotron. The pions were detected in the forward direction. The results are compared with cross sections calculated under the assumption that the reaction took place on a single neutron. The good agreement between the measured and the calculated cross sections justifies the use of the (K⁻, π⁻) reaction in order to obtain spectroscopic information on hypernuclei.     

On the gap problem for the sequence ∥mβ∥

We discuss the gap problem for the sequence m used in our previous Letter (D. H. Mayer, Lett. Math. Phys. 16, 139–143 (1988)).     

Silicone polymer deposition by CO2 laser induced decomposition of silane in the presence of methyl methacrylate

Infrared multiphoton decomposition of monosilane in the presence of methyl methacrylate results in the formation of gaseous methane, acetylene, butenes and carbon monoxide along with a solid polymer whose chemical mechanism of formation is discussed in line of the poly(dimethylsiloxane) structure inferred from ESCA and IR spectral analysis.