7,922 research outputs found
Classification of small matrices
Denote by the set of square matrices of order . The set
, , is partitioned into row/column permutation equivalence classes
enabling derivation of various facts by simple counting. For example, the
number of regular matrices of order 8 is 10160459763342013440. Let
, denote the set of absolute determinant values and Smith normal
forms of matrices from . Denote by the smallest integer not in
. The sets and are obtained; especially,
. The lower bounds for , , (exceeding the known
lower bound , where is th Fibonacci number) are
obtained. Row/permutation equivalence classes of correspond to bipartite
graphs with black and white vertices, and so the other applications of
the classification are possible.Comment: 45 pages. submitted to LA
Low temperature magnetic transition in RuSr2EuCeCu2O10 ruthenocuprate
A new magnetic transition in the ruthenocuprate parent compound
RuSr2EuCeCu2O10 has been observed below 10 K. It shows up only as a kink in the
imaginary part of the ac susceptibility and exhibits a pronounced frequency
dependence. At the same time, the real part of the ac susceptibility and the dc
magnetization study show very little change in the same temperature window
suggesting only a minor fraction of the material to be involved in the
transition. Frequency dependence shows excellent agreement with the predictions
of the Arrhenius law known to describe well the dynamics of the
superparamagnetic particles. The same type of the investigation on the
RuSr2Eu1.1Ce0.9Cu2O10 composition showed no evidence of the similar transition,
which points to a possible intrinsic behavior.Comment: to be published in Physica
Two component butterfly hysteresis in Ru1222 ruthenocuprate
We report detailed studies of the ac susceptibility butterfly hysteresis on
the Ru1222 ruthenocuprate compounds. Two separate contributions to these
hysteresis have been identified and studied. One contribution is
ferromagnetic-like and is characterized by the coercive field maximum. Another
contribution, represented by the so called inverted maximum, is related to the
unusual inverted loops, unique feature of Ru1222 butterfly hysteresis. The
different nature of the two identified magnetic contributions is proved by the
different temperature dependences involved. By lowering the temperature the
inverted peak gradually disappears while the coercive field slowly raises. If
the maximum dc field for the hysteresis is increased, the size of the inverted
part of the butterfly hysteresis monotonously grows while the position of the
peak saturates. In reaching saturation exponential field dependence has been
demonstrated to take place. At T = 78 K the saturation field is 42 Oe.Comment: 5 pages, 5 figure
- …