2,531 research outputs found

### German FDI in Latin America and Caribbean in the Wake of the Crisis

International Relations/Trade,

### The Linear Meson Model and Chiral Perturbation Theory

We compare the linear meson model and chiral perturbation theory in next to
leading order in the quark mass expansion. In particular, we compute the
couplings L_4--L_8 of chiral perturbation theory as functions of the parameters
of the linear model. They are induced by the exchange of 0^{++} scalar mesons.
We use a phenomenological analysis of the effective vertices of the linear
model in terms of pseudoscalar meson masses and decay constants. Our results
for the L_i agree with previous phenomenological estimates.Comment: 21 pages, LaTe

### Effective linear meson model

The effective action of the linear meson model generates the mesonic n-point
functions with all quantum effects included. Based on chiral symmetry and a
systematic quark mass expansion we derive relations between meson masses and
decay constants. The model ``predicts'' values for f_eta and f_eta' which are
compatible with observation. This involves a large momentum dependent eta-eta'
mixing angle which is different for the on--shell decays of the eta and the
eta'. We also present relations for the masses of the 0^{++} octet. The
parameters of the linear meson model are computed and related to cubic and
quartic couplings among pseudoscalar and scalar mesons. We also discuss
extensions for vector and axialvector fields. In a good approximation the
exchange of these fields is responsible for the important nonminimal kinetic
terms and the eta-eta' mixing encountered in the linear meson model.Comment: 79 pages, including 3 abstracts, 9 tables and 9 postscript figures,
LaTeX, requires epsf.st

### Counting Steiner triple systems with classical parameters and prescribed rank

By a famous result of Doyen, Hubaut and Vandensavel \cite{DHV}, the 2-rank of
a Steiner triple system on $2^n-1$ points is at least $2^n -1 -n$, and equality
holds only for the classical point-line design in the projective geometry
$PG(n-1,2)$. It follows from results of Assmus \cite{A} that, given any integer
$t$ with $1 \leq t \leq n-1$, there is a code $C_{n,t}$ containing
representatives of all isomorphism classes of STS$(2^n-1)$ with 2-rank at most
$2^n -1 -n + t$. Using a mixture of coding theoretic, geometric, design
theoretic and combinatorial arguments, we prove a general formula for the
number of distinct STS$(2^n-1)$ with 2-rank at most $2^n -1 -n + t$ contained
in this code. This generalizes the only previously known cases, $t=1$, proved
by Tonchev \cite{T01} in 2001, $t=2$, proved by V. Zinoviev and D. Zinoviev
\cite{ZZ12} in 2012, and $t=3$ (V. Zinoviev and D. Zinoviev \cite{ZZ13},
\cite{ZZ13a} (2013), D. Zinoviev \cite{Z16} (2016)), while also unifying and
simplifying the proofs. This enumeration result allows us to prove lower and
upper bounds for the number of isomorphism classes of STS$(2^n-1)$ with 2-rank
exactly (or at most) $2^n -1 -n + t$. Finally, using our recent systematic
study of the ternary block codes of Steiner triple systems \cite{JT}, we obtain
analogous results for the ternary case, that is, for STS$(3^n)$ with 3-rank at
most (or exactly) $3^n -1 -n + t$. We note that this work provides the first
two infinite families of 2-designs for which one has non-trivial lower and
upper bounds for the number of non-isomorphic examples with a prescribed
$p$-rank in almost the entire range of possible ranks.Comment: 27 page

### Construction of self-dual normal bases and their complexity

Recent work of Pickett has given a construction of self-dual normal bases for
extensions of finite fields, whenever they exist. In this article we present
these results in an explicit and constructive manner and apply them, through
computer search, to identify the lowest complexity of self-dual normal bases
for extensions of low degree. Comparisons to similar searches amongst normal
bases show that the lowest complexity is often achieved from a self-dual normal
basis

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