Solving the eigenvalue problem for sparse matrices

A modification of the Danilewski method is presented, permitting the solution of the eigenvalue problem for a constant sparse matrix of large order to be reduced to the solution of the same problem for a polynomial matrix of lower order. Certain solution algorithms are proposed for a partial eigenvalue problem for the polynomial matrix. Questions of the realization of the algorithms on a model PRORAB computer are examined.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 58, pp. 92–110, 1976.     

Investigation of the dispersion equations of a free,transversally isotropic,elastic layer

To investigate the propagation of normal waves in a free, transversally isotropic, elastic layer it is necessary to determine the roots of the corresponding dispersion equation. It is shown that with increasing wave number the roots move monotonically along the axis of the phase velocity. The initial and final points of the roots are found. Examples of computations of the roots are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 99, pp. 85–103, 1980.     

An investigation of the fractional composition of dioxane lignin of the cotton plant by the PMR method

Analysis of the PMR spectra of six fractions of the dioxane lignins of the cotton plant differing considerably in molecular weight has confirmed their chemical nonidentity. It has been established that the low-molecular-weight fractions are less condensed than the high-molecular-weight fractions. It has been found that aliphatic OH groups are approximately evenly distributed between the - and -C atoms of the lignin side chain.Institute of the Chemistry of Plant Substances, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 116–120, January–February, 1980.     

Study of 19Na at SPIRAL

The excitation function for the elastic-scattering reaction p( ¹⁸Ne, p) ¹⁸Ne was measured with the first radioactive beam from the SPIRAL facility at the GANIL laboratory and with a solid cryogenic hydrogen target. Several broad resonances have been observed, corresponding to new excited states in the unbound nucleus ¹⁹Na. In addition, two-proton emission events have been identified and are discussed.     

Use of electron correlation to make attosecond measurements without attosecond pulses

We describe how correlations between electrons can be used to trace the dynamics of correlated two-electron ionization with attosecond precision, without using attosecond pulses. The approach is illustrated using the example of Auger or Coster-Kronig decay triggered by photoionization with an extreme ultraviolet pulse. It requires correlated measurements of angle-resolved energy spectra of both the photo- and Auger electrons in the presence of a laser pulse. To reconstruct the dynamics, we use not only classical time and energy correlation, but also entanglement between the two electrons.     

Unambiguous identification of three beta-decaying isomers in 70Cu

Using resonant laser ionization, beta-decay studies, and for the first time mass measurements, three beta-decaying states have been unambiguously identified in 70Cu. A mass excess of -62 976.1(1.6) keV and a half-life of 44.5(2) s for the (6-) ground state have been determined. The level energies of the (3-) isomer at 101.1(3) keV with T(1/2)=33(2) s and the 1+ isomer at 242.4(3) keV with T(1/2)=6.6(2) s are confirmed by high-precision mass measurements. The low-lying levels of 70Cu populated in the decay of 70Ni and in transfer reactions compare well with large-scale shell-model calculations, and the wave functions appear to be dominated by one proton-one neutron configurations outside the closed Z=28 shell and N=40 subshell. This does not apply to the 1+ state at 1980 keV which exhibits a particular feeding and deexcitation pattern not reproduced by the shell-model calculations.     

Molecule without electrons: binding bare nuclei with strong laser fields

We show how a carefully chosen combination of strong linearly and circularly polarized laser fields can bind two same-sign charges, not only suppressing their Coulomb repulsion in all three spatial dimensions, but also creating an effective attraction. As an example, we show how a molecule HD2+ stripped of both electrons can be kept bound by the laser fields.