1,706 research outputs found
Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II
We deliver here second new recurrence formula,
were array is appointed by sequence of
functions which in predominantly considered cases where chosen to be
polynomials . Secondly, we supply a review of selected related combinatorial
interpretations of generalized binomial coefficients. We then propose also a
kind of transfer of interpretation of coefficients onto
coefficients interpretations thus bringing us back to
and Donald Ervin Knuth relevant investigation decades
ago.Comment: 57 pages, 8 figure
Arithmetic Dynamics
This survey paper is aimed to describe a relatively new branch of symbolic
dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic
expansions of reals and vectors that have a "dynamical" sense. This means
precisely that they (semi-) conjugate a given continuous (or
measure-preserving) dynamical system and a symbolic one. The classes of
dynamical systems and their codings considered in the paper involve: (1)
Beta-expansions, i.e., the radix expansions in non-integer bases; (2)
"Rotational" expansions which arise in the problem of encoding of irrational
rotations of the circle; (3) Toral expansions which naturally appear in
arithmetic symbolic codings of algebraic toral automorphisms (mostly
hyperbolic).
We study ergodic-theoretic and probabilistic properties of these expansions
and their applications. Besides, in some cases we create "redundant"
representations (those whose space of "digits" is a priori larger than
necessary) and study their combinatorics.Comment: 45 pages in Latex + 3 figures in ep
Disorder and fluctuations in nonlinear excitations in DNA
We study the effects of the sequence on the propagation of nonlinear
excitations in simple models of DNA, and how those effects are modified by
noise. Starting from previous results on soliton dynamics on lattices defined
by aperiodic potentials, [F. Dom\'\i nguez-Adame {\em et al.}, Phys. Rev. E
{\bf 52}, 2183 (1995)], we analyze the behavior of lattices built from real DNA
sequences obtained from human genome data. We confirm the existence of
threshold forces, already found in Fibonacci sequences, and of stop positions
highly dependent on the specific sequence. Another relevant conclusion is that
the effective potential, a collective coordinate formalism introduced by
Salerno and Kivshar [Phys. Lett. A {\bf 193}, 263 (1994)] is a useful tool to
identify key regions that control the behaviour of a larger sequence. We then
study how the fluctuations can assist the propagation process by helping the
excitations to escape the stop positions. Our conclusions point out to
improvements of the model which look promising to describe mechanical
denaturation of DNA. Finally, we also consider how randomly distributed energy
focus on the chain as a function of the sequence.Comment: 14 pages, final version, accepted in Fluctuation and Noise Letters,
scheduled to apper in vol. 4, issue 3 (2004
Quasicrystals, model sets, and automatic sequences
We survey mathematical properties of quasicrystals, first from the point of
view of harmonic analysis, then from the point of view of morphic and automatic
sequences.
Nous proposons un tour d'horizon de propri\'et\'es math\'ematiques des
quasicristaux, d'abord du point de vue de l'analyse harmonique, ensuite du
point de vue des suites morphiques et automatiques
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