191,289 research outputs found
Relative motion in spacetime
In Minkowski spacetime, we consider an isolated system made of two pointlike
bodies interacting at a distance, in the nonradiative approximation. Our
framework is the covariant and a priori Hamiltonian formalism of "predictive
relativistic mechanics", founded on the equal-time condition. The issue of an
equivalent one-body description is discussed. We distinguish two different
concepts: on the one hand an almost purely kinematic relative particle, on the
other hand an effective particle which involves an explicit dynamical
formulation; several versions of the latter are possible. Relative and
effective particles have the same orbit, but may differ by their schedules.Comment: 26 pages, no figure. Several inadequacies and various misprints
corrected. An example, an Appendix, one reference added; some obscure points
clarifie
Inverse problems of symbolic dynamics
This paper reviews some results regarding symbolic dynamics, correspondence
between languages of dynamical systems and combinatorics. Sturmian sequences
provide a pattern for investigation of one-dimensional systems, in particular
interval exchange transformation. Rauzy graphs language can express many
important combinatorial and some dynamical properties. In this case
combinatorial properties are considered as being generated by substitutional
system, and dynamical properties are considered as criteria of superword being
generated by interval exchange transformation. As a consequence, one can get a
morphic word appearing in interval exchange transformation such that
frequencies of letters are algebraic numbers of an arbitrary degree.
Concerning multydimensional systems, our main result is the following. Let
P(n) be a polynomial, having an irrational coefficient of the highest degree. A
word (w=(w_n), n\in \nit) consists of a sequence of first binary numbers
of i.e. . Denote the number of different subwords
of of length by .
\medskip {\bf Theorem.} {\it There exists a polynomial , depending only
on the power of the polynomial , such that for sufficiently
great .
A topological mechanism of discretization for the electric charge
We present a topological mechanism of discretization, which gives for the
fundamental electric charge a value equal to the square root of the Planck
constant times the velocity of light, which is about 3.3 times the electron
charge. Its basis is the following recently proved property of the standard
linear classical Maxwell equations: they can be obtained by change of variables
from an underlying topological theory, using two complex scalar fields, the
level curves of which coincide with the magnetic and the electric lines,
respectively.Comment: 10 pages, LaTeX fil
Combinatorics of normal sequences of braids
Many natural counting problems arise in connection with the normal form of
braids--and seem to have never been considered so far. Here we solve some of
them by analysing the normality condition in terms of the associated
permutations, their descents and the corresponding partitions. A number of
different induction schemes appear in that framework
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