31 research outputs found
Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time
Nonlinear dynamics of a bouncing ball moving in gravitational field and
colliding with a moving limiter is considered. Displacement of the limiter is a
quadratic function of time. Several dynamical modes, such as fixed points, 2 -
cycles and chaotic bands are studied analytically and numerically. It is shown
that chaotic bands appear due to homoclinic structures created from unstable 2
- cycles in a corner-type bifurcation.Comment: 11 pages, 6 figure
A description of a class of finite semigroups that are near to being Malcev nilpotent
In this paper we continue the investigations on the algebraic structure of a
finite semigroup that is determined by its associated upper non-nilpotent
graph . The vertices of this graph are the elements of and
two vertices are adjacent if they generate a semigroup that is not nilpotent
(in the sense of Malcev). We introduce a class of semigroups in which the
Mal'cev nilpotent property lifts through ideal chains. We call this the class
of \B\ semigroups. The definition is such that the global information that a
semigroup is not nilpotent induces local information, i.e. some two-generated
subsemigroups are not nilpotent. It turns out that a finite monoid (in
particular, a finite group) is \B\ if and only if it is nilpotent. Our main
result is a description of \B\ finite semigroups in terms of their
associated graph . In particular, has a largest nilpotent
ideal, say , and is a 0-disjoint union of its connected components
(adjoined with a zero) with at least two elements
Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential
The S-wave effective range parameters of the neutron-deuteron (nd) scattering
are derived in the Faddeev formalism, using a nonlocal Gaussian potential based
on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy
eigenphase shift is sufficiently attractive to reproduce predictions by the
AV18 plus Urbana three-nucleon force, yielding the observed value of the
doublet scattering length and the correct differential cross sections below the
deuteron breakup threshold. This conclusion is consistent with the previous
result for the triton binding energy, which is nearly reproduced by fss2
without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy