Analysis of uniform binary subdivision schemes for curve design

The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form

Generalized reinhardt domains

In this paper we investigate a class of Lie group actions on , the so-calledpolar actions, that naturally generalize the standard actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain containing the origin of we also compute its automorphism group. Supported in part by NSF Grant 8602020     

On the implementation of Sμ U(2) action in the irreducible representations of twisted canonical commutation relations

The natural S U(2) action on the creation and annihilation operators satisfying twisted canonical commutation relations (TCCR) is investigated. It is shown that the Fock representation is the only covariant irreducible representation of TCCR.Partially supported by the program RP.1.10.     

A class of nonmixing dynamical systems with monotonic semigroup property

In order to illustrate the class of conservative dynamical systems for which a Boltzmann entropy can be obtained under finite coarse-graining [2], we consider dynamical systems defined by the shift transformation on K , where K is any finite set of integers. We give a class of non-Markovian invariant measures that verify the Chapman-Kolmogorov equation (equivalent to a Boltzmann entropy) for any positive stochastic matrix and that are ergodic but not weakly mixing.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

High gain amplification of femtosecond pulses with low amplified spontaneous emission in a multipass dye cell

We present a multipass femtosecond amplifier pumped by a Nd-YAG laser where the gain medium is given by a variable length dye cell. This system allows amplification factors up to 5 · 10⁶ and output pulse energies of 150 J, while restricting the contribution of amplified spontaneous emission to 0.5% of the total output energy, without using any saturable absorber stage. A detailed study of the output pulsewidth as a function of the duration of the input chirped pulse is also presented.     

Spectral line competition in a coaxial electron-beam-pumped high pressure Ar/Xe laser

In order to study the kinetic mechanism of the e-beam pumped Ar/Xe laser, the temporal profiles of individual laser lines during multiline oscillation have been measured as a function of power deposition (1–12MW/cm³) and gas laser pressure (2–14 bar) using a short pulse (30 ns) coaxial electron beam as excitation source. It was found that the optimum output energy at each pressure was obtained at the same specific power deposition.Strong line competition has been observed between the 2.65 and 1.73 m transitions. In order to explain our results we suggest that besides electron collision mixing (ECM) between the 5d and 6p levels of Xe, there is also a redistribution between all 6p levels which strongly favours the lower levels at higher pumping densities.     

Laser-induced electron emission from an Au surface irradiated by single picosecond pulses at λ=2.94 μm. The intermediate region between multiphoton and tunneling effects

The photoinduced electron emission from the surface of a solid gold target irradiated by single picosecond pulses of an erbium laser is investigated. The applied laser intensity (5–120 GW/cm²) corresponds to the intermediate interaction region between the pure multiphoton and tunnel effects, where the decisive Keldysh-parameter, , is in the range 1<<12=n ₀. In the light intensity region which is free of surface heating (I _L<80 GW/cm²), the slope of the measured logarithmic intensity dependence of the photocurrent decreases from the n ₀=12 perturbative value down to n 5. Therefore the experiment shows that the Keldysh-type theories, which have recently been proved to describe correctly the ionization of atoms, are also valid to a certain extent in the case of the photoeffect in metals.     

Concentrations and velocity distributions of positive ions in laser ablation of copper

It is shown that the generation of secondary electrons by excited neutrals hitting a surface makes the so-called probe method unsuited for measuring the positive ion fraction in laser ablation plumes. Experiments have been performed in a modified set-up, in which the disturbance by secondary electrons is avoided. For a typical case of Cu irradiated in ultra-high vacuum by nanosecond excimer laser pulses of 3 J cm^–2 the ionized fraction is about 10^–8 at a distance of 60 cm. This number is in fair agreement with Saha-Langmuir predictions based on the assumption of local thermal equilibrium at an estimated temperature of about 3000K. Angular-resolved time-of-flight measurements show that there are three different ion velocity distributions. A slow contribution (kinetic energy 2eV) with an angular distribution peaked along the normal, and two fast, isotropic contributions (kinetic energy 20–50 eV). The fast contributions are attributed to ions involved in a Coulomb explosion.     

On the monotonicity of sequences of quadrature formulae

Summary LetI(f)L(f)= _k=0 ^r ₌₀ ^vk–1 a _k f ⁽⁾(X _k ) be a quadrature formula, and let {S _n (f)} _n=1 be successive approximations of the definite integralI(f)= ₀ ¹ f(x)dx obtained by the composition ofL, i.e.,S _n(f)=L( _n ), where .We prove sufficient conditions for monotonicity of the sequence {S _n (f)} _n=1 . As particular cases the monotonicity of well-known Newton-Cotes and Gauss quadratures is shown. Finally, a recovery theorem based on the monotonicity results is presented