6,896 research outputs found
Analytic Tate spaces and reciprocity laws
We consider a functional analytic variant of the notion of Tate space, namely
the category of those topological vector spaces which have a direct sum
decomposition where one summand is nuclear Frechet space and the other is the
dual of a nuclear Frechet. We show that, both in the complex and in the p-adic
setting, one can use this formalism to define symbols for analytic functions
which satisfy Weil-type reciprocity laws
On a twisted Reidemeister torsion
Given a finite simplicial complex, a unimodular representation of its
fundamental group and a closed twisted cochain of odd degree, we define a
twisted version of the Reidemeister torsion, extending a previous definition of
V. Mathai and S. Wu. The main tool is a complex of piecewise smooth currents,
defined by J. Dupont.Comment: References added, some points clarifie
Shannon information, LMC complexity and Renyi entropies: a straightforward approach
The LMC complexity, an indicator of complexity based on a probabilistic
description, is revisited. A straightforward approach allows us to establish
the time evolution of this indicator in a near-equilibrium situation and gives
us a new insight for interpreting the LMC complexity for a general non
equilibrium system. Its relationship with the Renyi entropies is also
explained. One of the advantages of this indicator is that its calculation does
not require a considerable computational effort in many cases of physical and
biological interest.Comment: 11 pages, 0 figure
An approach to the problem of generating irreducible polynomials over the finite field GF(2) and its relationship with the problem of periodicity on the space of binary sequences
A method for generating irreducible polynomials of degree n over the finite
field GF(2) is proposed. The irreducible polynomials are found by solving a
system of equations that brings the information on the internal properties of
the splitting field GF(2^n) . Also, the choice of a primitive normal basis
allows us to build up a natural representation of GF(2^n) in the space of
n-binary sequences. Illustrative examples are given for the lowest orders.Comment: 22 pages, 6 tables, 0 figure
Complex Systems with Trivial Dynamics
In this communication, complex systems with a near trivial dynamics are
addressed. First, under the hypothesis of equiprobability in the asymptotic
equilibrium, it is shown that the (hyper) planar geometry of an -dimensional
multi-agent economic system implies the exponential (Boltzmann-Gibss) wealth
distribution and that the spherical geometry of a gas of particles implies the
Gaussian (Maxwellian) distribution of velocities. Moreover, two non-linear
models are proposed to explain the decay of these statistical systems from an
out-of-equilibrium situation toward their asymptotic equilibrium states.Comment: 9 gaes, 0 figures; Contributed Talk to ECCS'12 (European Conference
of Complex Systems, Brussels, September, 2012
A motivation for some local cohomologies
We explain how some results of M. Nori (on motives) and F. Ivorra (on
perverse motives) can be used to define "motivic" versions of Lyubeznik
numbers, a set of numerical invariants for local rings. We also discuss on
additional structures that might be put on some local cohomology modules
(besides those of D- or F-module). This note is mainly expository, it is an
expanded version of my talk at the FACARD workshop in Barcelona, on January
2019
Bifurcation Curves of Limit Cycles in some Lienard Systems
Lienard systems of the form , with f(x) an
even continous function, are considered. The bifurcation curves of limit cycles
are calculated exactly in the weak () and in the strongly
() nonlinear regime in some examples. The number of limit
cycles does not increase when increases from zero to infinity in all
the cases analyzed.Comment: 25 pages, 0 figures. Published in Int. Journal of Bifurcation and
Chaos, vol. 10, 971-980 (2001
On exponential sums
Let f be a polinomial with coefficients in a finite field F. Let be a non-trivial additive character. In this paper we give bounds
for the exponential sums in some
cases where the highest degree form of f defines a singular projective
hypersurface X (e.g. when X is an arrangement of lines in P^2). The bound
involves the Milnor numbers of the singularities of X. The proof goes via the
classical cohomological interpretation of this exponential sums through
Grothendieck's trace formula.Comment: Latex 2.09, 15 page
The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime
Li\'enard equations of the form , with
an even function, are considered in the weakly nonlinear regime
(). A perturbative algorithm for obtaining the number, amplitude
and shape of the limit cycles of these systems is given. The validity of this
algorithm is shown and several examples illustrating its application are given.
In particular, an approximation for the amplitude of
the van der Pol limit cycle is explicitly obtained.Comment: 17 text-pages, 1 table, 6 figure
Symmetry induced Dynamics in four-dimensional Models deriving from the van der Pol Equation
Different models of self-excited oscillators which are four-dimensional
extensions of the van der Pol system are reported. Their symmetries are
analyzed. Three of them were introduced to model the release of vortices behind
circular cylinders with a possible transition from a symmetric to an
antisymmetric Benard-von Karman vortex street. The fourth reported self-excited
oscillator is a new model which implements the breaking of the inversion
symmetry. It presents the phenomenon of second harmonic generation in a natural
way. The parallelism with second harmonic generation in nonlinear optics is
discussed. There is also a small region in the parameter space where the
dynamics of this system is quasiperiodic or chaotic.Comment: 14 pages, 0 figure
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