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 $\rm 10^{10}\,[M_\odot]$. 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 $\beta$ 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