19,426 research outputs found
A unification in the theory of linearization of second order nonlinear ordinary differential equations
In this letter, we introduce a new generalized linearizing transformation
(GLT) for second order nonlinear ordinary differential equations (SNODEs). The
well known invertible point (IPT) and non-point transformations (NPT) can be
derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be
linearized through NPT and IPT can be linearized by this GLT. We also
illustrate how to construct GLTs and to identify the form of the linearizable
equations and propose a procedure to derive the general solution from this GLT
for the SNODEs. We demonstrate the theory with two examples which are of
contemporary interest.Comment: 8 page
The mass and environmental dependence on the secular processes of AGN in terms of morphology, colour, and specific star-formation rate
Galaxy mass and environment play a major role in the evolution of galaxies.
In the transition from star-forming to quenched galaxies, Active galactic
nuclei (AGN) have also a principal action. However, the connections between
these three actors are still uncertain. In this work we investigate the effects
of stellar mass and the large-scale environment (LSS), on the fraction of
optical nuclear activity in a population of isolated galaxies, where AGN would
not be triggered by recent galaxy interactions or mergers. As a continuation of
a previous work, we focus on isolated galaxies to study the effect of stellar
mass and the LSS in terms of morphology (early- and late-type), colour (red and
blue), and specific star formation rate (quenched and star-forming). To explore
where AGN activity is affected by the LSS we fix the stellar mass into low- and
high-mass galaxies. We use the tidal strength parameter to quantify their
effects. We found that AGN is strongly affected by stellar mass in 'active'
galaxies (namely late-type, blue, and star-forming), however it has no
influence for 'quiescent' galaxies (namely early-type, red, and quenched), at
least for masses down to . In relation to the LSS, we
found an increment on the fraction of SFN with denser LSS in low-mass star
forming and red isolated galaxies. Regarding AGN, we find a clear increment of
the fraction of AGN with denser environment in quenched and red isolated
galaxies, independently of the stellar mass. AGN activity would be 'mass
triggered' in 'active' isolated galaxies. This means that AGN is independent of
the intrinsic property of the galaxies, but on its stellar mass. On the other
hand, AGN would be 'environment triggered' in 'quiescent' isolated galaxies,
where the fraction of AGN in terms of sSFR and colour increases from void
regions to denser LSS, independently of its stellar mass.Comment: 14 pages, 9 figures (11 pages and 6 figures without appendix),
accepted for publication in Astronomy & Astrophysic
On the distribution of high-frequency stock market traded volume: a dynamical scenario
This manuscript reports a stochastic dynamical scenario whose associated
stationary probability density function is exactly a previously proposed one to
adjust high-frequency traded volume distributions. This dynamical conjecture,
physically connected to superstatiscs, which is intimately related with the
current nonextensive statistical mechanics framework, is based on the idea of
local fluctuations in the mean traded volume associated to financial markets
agents herding behaviour. The corroboration of this mesoscopic model is done by
modelising NASDAQ 1 and 2 minute stock market traded volume
A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II
We present a semi-decision procedure to tackle first order differential
equations, with Liouvillian functions in the solution (LFOODEs). As in the case
of the Prelle-Singer procedure, this method is based on the knowledge of the
integrating factor structure.Comment: 11 pages, late
Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence
We report a general technique to study a given experimental time series with
superstatistics. Crucial for the applicability of the superstatistics concept
is the existence of a parameter that fluctuates on a large time scale
as compared to the other time scales of the complex system under consideration.
The proposed method extracts the main superstatistical parameters out of a
given data set and examines the validity of the superstatistical model
assumptions. We test the method thoroughly with surrogate data sets. Then the
applicability of the superstatistical approach is illustrated using real
experimental data. We study two examples, velocity time series measured in
turbulent Taylor-Couette flows and time series of log returns of the closing
prices of some stock market indices
Solving 1ODEs with functions
Here we present a new approach to deal with first order ordinary differential
equations (1ODEs), presenting functions. This method is an alternative to the
one we have presented in [1]. In [2], we have establish the theoretical
background to deal, in the extended Prelle-Singer approach context, with
systems of 1ODEs. In this present paper, we will apply these results in order
to produce a method that is more efficient in a great number of cases.
Directly, the solving of 1ODEs is applicable to any problem presenting
parameters to which the rate of change is related to the parameter itself.
Apart from that, the solving of 1ODEs can be a part of larger mathematical
processes vital to dealing with many problems.Comment: 31 page
Clone size distributions in networks of genetic similarity
We build networks of genetic similarity in which the nodes are organisms
sampled from biological populations. The procedure is illustrated by
constructing networks from genetic data of a marine clonal plant. An important
feature in the networks is the presence of clone subgraphs, i.e. sets of
organisms with identical genotype forming clones. As a first step to understand
the dynamics that has shaped these networks, we point up a relationship between
a particular degree distribution and the clone size distribution in the
populations. We construct a dynamical model for the population dynamics,
focussing on the dynamics of the clones, and solve it for the required
distributions. Scale free and exponentially decaying forms are obtained
depending on parameter values, the first type being obtained when clonal growth
is the dominant process. Average distributions are dominated by the power law
behavior presented by the fastest replicating populations.Comment: 17 pages, 4 figures. One figure improved and other minor changes. To
appear in Physica
- …