Counterexamples in optimal quadrature

It is widely believed that order of exactness is a good measure of the quality of an algorithm for numerical quadrature. We show that this is not the case, by exhibiting a situation in which the optimal algorithm does not even integrate constants exactly. We also show that there are situations in which the penalty for using equidistant nodes is unbounded. Finally, we show that the complexity of obtaining an -approximation can be an arbitrary function of , i.e., there is no hardest quadrature problem.     

Theoretical study of hydrogen-bonded formaldehyde complexes

The hydrogen-bonded complexes involving formaldehyde and a series of proton donors of varying strengths, have been investigated at different levels of ab initio MO theory. The structures of the studied complexes were SCF optimized at the 6-31G basis set level. The binding energy was estimated employing basis set superposition correction, zero-point vibrations and MP2 correlation contribution at the different basis set: STO-3G; 6-31G; MP2/6-31G; 6-31G**; MP2/6-31G**; 6-311G(2d, 2p) and MP2/6-311G(2d, 2p). Linear relationships were found of the calculated binding energy with: the calculated shift in the carbonyl stretching frequency, the changes in carbonyl bond length and the optimum value of hydrogen-bond distance; furthermore the calculations confirm a parallel trend between the proton-donor ability and the strength of the hydrogen bond.     

Quantum field theoretical methods in chemically bonded systems II

Summary Many-body perturbation theory is derived for chemical bonds. Paired quasiparticles represent the bonds. Products of the paired quasiparticles define a model Bardeen-Cooper-Schrieffer function. The pairing force is added as a model interaction to the self-consistent problem. The starting model is based on valency and adiabatic symmetry correlation. Symmetries are enforced by the model Hamiltonian. Perturbative corrections are expressed as ordinary Feynman diagrams. The number of diagrams needed is the same as for particle-hole theory.This work was supported in part by the U.S. Department of the Navy, Space and Naval Warfare Systems Command under Contract N00039-89-C-0001, and in part by NATO Research Grant 1861. It was presented, in part, at the A.C. Wahl Memorial Session, Molecular Spectroscopy Symposium, Columbus, Ohio, 1984; and Midwest Theoretical Chemistry Conference, Milwaukee, Wisconsin, 1985.     

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.