Factorized-Sparse-Approximate-Inverse Preconditionings of Linear Systems with Unsymmetric Matrices

The paper considers the application of factorized-sparse-approximate-inverse (FSAI) preconditionings to linear algebraic systems with nonsingular unsymmetric coefficient matrices. Special attention is paid to methods for optimizing the sparsity pattern of such preconditioners. It is numerically demonstrated that the efficiency of FSAI preconditionings can be substantially improved by applying the so-called postfiltering and prefiltering in order to sparsify preconditioning matrices. Bibliography: 20 titles.     

Prefiltration technique via aggregation for constructing low‐density high‐quality factorized sparse approximate inverse preconditionings

This paper considers a new approach to a priori sparsification of the sparsity pattern of the factorized approximate inverses (FSAI) preconditioner using the so‐called vector aggregation technique. The suggested approach consists in construction of the FSAI preconditioner to the aggregated matrix with a prescribed sparsity pattern. Then small entries of the computed ‘aggregated’ FSAI preconditioning matrix are dropped, and the resulting pointwise sparsity pattern is used to construct the low‐density block sparsity pattern of the FSAI preconditioning matrix to the original matrix. This approach allows to minimize (sometimes significantly) the construction costs of low‐density high‐quality FSAI preconditioners. Numerical results with sample matrices from structural mechanics and thin shell problems are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

An Automatic Procedure for Updating the Block Size in the Block Conjugate Gradient Method for Solving Linear Systems

The paper considers the problem of constructing an efficient automatic procedure for reducing the block size in the block conjugate gradient method insuring that the resulting rate of convergence is comparable with that of the block conjugate gradient method with constant block size. The numerical results provided show that, independently of the type of distribution of the smallest eigenvalues of the preconditioned matrix, the procedure suggested always leads to a decrease of the arithmetic costs with respect to those of the block method with constant block size. Bibliography: 8 titles.     

An algorithm for the single-input partial pole assignment problem

An algorithm for translating unstable eigenvalues of single-input partial pole assignment problems based on rank-one transformations is suggested. Special attention is paid to the practical case where translations are constructed using inexact spectral information provided by the Arnoldi procedure. Estimates of the resulting perturbations of stable and translated poles are derived. These estimates depend on the accuracy of spectral information about the unstable poles. The algorithm proposed is illustrated with numerical examples. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 229, 1995, pp. 5–28. Translated by A. Yu. Yeremin.     

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.     

Regularities of formation and survival probability of compound nuclei in the region of <Emphasis Type="Italic">Z</Emphasis> ≥ 82: Study of complete-fusion reactions with heavy ions using the kinematic separator VASSILISSA

In the last 15 years, the electrostatic separator VASSILISSA has been used for studying evaporation residues produced in the complete-fusion reactions induced by heavy ions. The decay properties and the cross sections for the formation of isotopes of elements with atomic numbers Z ≥ 82 have been studied experimentally. The obtained results, together with data from other recoil separators, were used for studying the formation regularities and the survival probabilities of excited compound nuclei.     

Second experiment at VASSILISSA separator on the synthesis of the element 112

The upgraded separator VASSILISSA was used to confirm results of previous experiments on the synthesis of the heavy isotopes of the element 112 obtained in complete-fusion reactions of ⁴⁸Ca and ²³⁸U. An additional reason was the non-observation of any events in the same reaction studied with the BGS separator at Berkeley. Limits of for the atomic mass number of the observed spontaneously fissioning isotope were measured. The obtained results on the decay mode, half-life and production cross-section are in agreement with those obtained in our first experiment.Received: 10 June 2003, Revised: 29 July 2003, Published online: 2 December 2003PACS: 23.60. + e decay - 25.70.-z Low and intermediate energy heavy-ion reactions - 25.85.Ca Spontaneous fission - 27.90. + b      

Interaction of elemental mercury with selenium surfaces: model experiments for investigations of superheavy elements copernicium and flerovium

The adsorption behavior of ¹⁹⁷Hg and ^183–185Hg on red amorphous selenium (red a-Se) and trigonal selenium (t-Se) was investigated experimentally by off-line and on-line gas chromatographic methods, in preparation of a sensitive chemical separation and characterization of the transactinides copernicium (Cn, Z = 112) and flerovium (Fl, Z = 114). Monte-Carlo simulations of a diffusion controlled deposition were in good agreement with the experimental results, assuming as interaction limits ?ΔH _ads ^red a-Se (Hg) > 85 kJ/mol, and ?ΔH _ads ^t-Se (Hg) < 60 kJ/mol. Both Se allotropes can be used as stationary surfaces in comparative gas-chromatographic chemical investigations of Cn and Fl.     

New results on elements 111 and 112

Experiments on the synthesis and identification of the nuclei ²⁷²111 and ²⁷⁷112 were performed in order to confirm previous results. Three additional decay chains were measured in the reaction ⁶⁴Ni + ²⁰⁹Bi →²⁷³111^*. The study revealed considerably improved data on the decay chain originating from ²⁷²111. One additional chain was measured in the reaction ⁷⁰Zn + ²⁰⁸Pb →²⁷⁸112^*. The decay properties of the chain starting at ²⁷⁷112 are in excellent agreement with the second chain of the first experiment down to ²⁶⁵Sg, where the new chain ends by a previously unknown spontaneous-fission branch. A re-analysis of all the data on elements 110, 111, and 112 measured at GSI since 1994 (a total of 34 decay chains was investigated) revealed that for 2 chains (the second chain of ²⁶⁹110 measured in 1994 and the first chain of ²⁷⁷112 measured in 1996) the results of the new analysis differed from the previous one. In all other cases the earlier data are exactly reproduced. Received: 21 December 2001 / Accepted: 15 January 2002     

GABRIELA setup for nuclear spectroscopy of the transfermium element isotopes at the VASSILISSA separator

The JINR (Dubna)-IN2P3 (France) Collaboration project aimed at the α, β γ, spectroscopy of the transfermium element isotopes using heavy-ion beams of the U-400 cyclotron and the modernized recoil separator VASSILISSA was launched at Dubna. During the first full-scale experiment in September–October 2004, nobelium and lawrencium isotopes produced in the ⁴⁸Ca + ^207,208Pb → ^255,256No* and ⁴⁸Ca + ²⁰⁹Bi → ²⁵⁷Lr* reactions were studied. The text was submitted by the authors in English.