6 research outputs found
Conspiracy in bacterial genomes
The rank ordered distribution of the codon usage frequencies for 123
bacteriae is best fitted by a three parameters function that is the sum of a
constant, an exponential and a linear term in the rank n. The parameters depend
(two parabolically) from the total GC content. The rank ordered distribution of
the amino acids is fitted by a straight line. The Shannon entropy computed over
all the codons is well fitted by a parabola in the GC content, while the
partial entropies computed over subsets of the codons show peculiar different
behavior, exhibiting therefore a first conspiracy effect. Moreover the sum of
the codon usage frequencies over particular sets, e.g. with C and A
(respectively G and U) as i-th nucleotide, shows a clear linear dependence from
the GC content, exhibiting another conspiracy effect.Comment: revised version: introduction and conclusion enhanced, references
added, figures added, some tables remove
From the Mendeleev periodic table to particle physics and back to the periodic table
We briefly describe in this paper the passage from Mendeleev's chemistry
(1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and
particle physics (from 1953 to 2006). We show how the consideration of
symmetries, largely used in physics since the end of the 1920's, gave rise to a
new format of the periodic table in the 1970's. More specifically, this paper
is concerned with the application of the group SO(4,2)xSU(2) to the periodic
table of chemical elements. It is shown how the Madelung rule of the atomic
shell model can be used for setting up a periodic table that can be further
rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative
results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry
(special issue to commemorate the one hundredth anniversary of the death of
Mendeleev who died in 1907); version 2: 16 pages; some sentences added;
acknowledgment and references added; misprints correcte
On the equivalence of different approaches for generating multisoliton solutions of the KPII equation
The unexpectedly rich structure of the multisoliton solutions of the KPII
equation has been explored by using different approaches, running from dressing
method to twisting transformations and to the tau-function formulation. All
these approaches proved to be useful in order to display different properties
of these solutions and their related Jost solutions. The aim of this paper is
to establish the explicit formulae relating all these approaches. In addition
some hidden invariance properties of these multisoliton solutions are
discussed
Kinematical superalgebras and Lie algebras of order 3
We study and classify kinematical algebras which appear in the framework of Lie superalgebras or Lie algebras of order three. All these algebras are related through generalised InonĂĽ-Wigner contractions from either the orthosymplectic
superalgebra or the de Sitter Lie algebra of order three