Optimal radius of convergence of interpolatory iterations for operator equations

The convergence of the class of direct interpolatory iterationsI _n for a simple zero of a non-linear operatorF in a Banach space of finite or infinite dimension is studied.A general convergence result is established and used to show that ifF is entire the radius of convergence goes to infinity withn while ifF is analytic in a ball of radiusR the radius of convergence increases to at leastR/2 withn.The research was supported in part by the National Science Foundation under Grant MCS 75-222-55 and the office of Naval Research under Contract N00014-76-C-0370, NR 044-422.     

Some regularity properties of algorithms and additive functions with respect to them

Summary The paper deals with the behaviour of the so-called algorithms with respect to interval filling sequences A connection is established between the uniquely representable points and the continuity points of the algorithms; also strong continuity properties on monotonic algorithms are proved. Finally the results are applied to additive functions. The theorems extend some former results by the authors, by I. Kátai and by A. Járai.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth     

An Ω(n 4/3) lower bound on the randomized complexity of graph properties

We improve King's (n ^5/4) lower bound on the randomized decision tree complexity of monotone graph properties to (n ^4/3). The proof follows Yao's approach and improves it in a different direction from King's. At the heart of the proof are a duality argument combined with a new packing lemma for bipartite graphs.The paper was written while the author was a graduate student at the University of Chicago and was completed at M.I.T. The work was supported in part by NSF under GRANT number NSF 5-27561, the Air Force under Contract OSR-86-0076 and by DIMACS (Center for Discret Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center-NSF-STC88-09648.     

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

Beta-delayed two-proton decay of39Ti

The beta-delayed two-proton decay of theT _z =–5/2 nuclide³⁹Ti has been observed. The³⁹Sc isobaric analog state has been calculated to lie at 8.82 MeV using the measured two-proton sum energy of 4750±40 keV for its decay to the³⁷K ground state. Combining this excitation energy with a Coulomb displacement energy calculation has lowered the energy available for ground state two-proton emission of³⁹Ti from 760 to 530 keV.This work was supported by Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Depeartment of Energy under Contracts DE-AC03-76SF00098 with Lawrence Berkeley Laboratory, DE-AC02-76CH00016 with Brookhaven National Laboratory and DE-AC06-76RL0 1830 with Pacific Northwest Laboratories.     

Investigation of the fusion reaction27Al+236U→263105 at excitation energies of 57 MeV and 65 MeV

The neutron-deficient isotopes^257,258105 were produced in the reaction²⁷Al+²³⁶u in 6n and 5n evaporation channels, respectively. The evaporation residues emerging from the target were separated in-flight from the projectiles and from products of different nuclear reactions by the electrostatic separator VASSILISSA [1]. The isotopes were then implanted into position-sensitive silicon detectors and identified using the --correlation method. The measured production cross-section is (5n)=(0.45±0.20)nb atE _P =154 MeV and (6n)=(0.075±0.055) nb atE _P =163 MeV. These cross-sections are compared with data measured for the same isotopes in the more symmetrical reaction⁵⁰Ti+²⁰⁹Bi.     

Self-consistent truncation of the BBGKY hierarchy on the two-body level

We present a coupled set of equations for the one-body density matrix and the two-body correlation function consistent with trace relations and conservation laws which provide an extension of correlation dynamics on the two-body level. The additional interaction terms are discussed in the context of time-dependent G-matrix theory and NQCD and studied numerically by one-dimensional calculations for colliding finite fermion systems.Supported by BMFT and GSI Darmstadt     

Preequilibrium versus thermalized light-charged particle emissions in the40Ar (1100MeV)+24Mg reaction. Dynamical calculations

In an attempt to separate preequilibrium and thermalised emissions of light particles in low impact parameter heavy-ion collisions, the⁴⁰Ar+²⁴Mg reaction has been studied at 27.5 MeV/nucleon. Exclusive measurements have permitted us to examine, in some detail, heavy fragments and charged particles (p, d, t,-particle). The fragments recognized as evaporation residues have been selected and, due to inverse kinematic conditions, the related preequilibrium and statistical emissions of light particles resulting from incomplete fusion reaction appear to be distinguishable to a fair extent. This separation is fully supported by Monte Carlo calculations. Some experimental characteristics of the light particles have been examined and compared to the predictions of dynamical calculations. These calculations, associating a preequilibrium (interpreted as prompt emitted particles) model with a statistical-decay model, follow the evolution of the collision from the point of contact between the projectile and the target to the final evaporation-residue formation on an event by event basis. The predictions of these calculations have been compared to experimental data and satisfactory agreement is achieved for fragment-mass distribution, proton-energy spectra, and proton-angular distribution.     

Dynamical and thermal aspects of relativistic heavy-ion collisions

Within a covariant BUU-approach we simulate heavyion collisions at various bombarding energies from 400 MeV/u to 1 GeV/u. We evaluate locally the energymomentum tensorT ^v (x), and extract pressures, energydensities and temperatures. The connection of these thermodynamical quantities to experimental observables and their sensitivity to the equation of state is discussed. Furthermore, we investigate the question of local equilibration and evaluate the entropy produced in these reactions.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday. Work supported by BMFT and GSI Darmstadt     

Large electron polarization of H-like20Ne-ions traversing gd foils at very high velocities

It is shown that transient magnetic fields in Gd-host for²⁰Ne ions at a mean velocity of 12.5v₀(v₀=c/137), considerably beyond the Bohr velocity of 1s electrons of Ne ions (v_1s=10v₀), are dominated by the Fermi contact field of these electrons. The first excited 2⁺-state of²Ne was used as probe. The derived value for the mean degree of polarization p_1s=0.32(13), is surprisingly large, though still consistent with values obtained at lower velocities. Present calculations of spin exchange cross sections severely underestimate the observed polarization at this high velocity.The authors are grateful to the operating staff of the UNILAC for providing excellent beam conditions. They also thank Dr. P. Maier-Komor for preparing the delicate targets. Support by the BMFT is acknowledged.