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

Vortex-antivortex annihilation in mesoscopic superconductors with a central pinning center

In this work we solved the time-dependent Ginzburg-Landau equations, TDGL, to simulate two superconducting systems with different lateral sizes and with an antidot inserted in the center. Then, by cycling the external magnetic field, the creation and annihilation dynamics of a vortex-antivortex pair was studied as well as the range of temperatures for which such processes could occur. We verified that in the annihilation process both vortex and antivortex acquire an elongated format while an accelerated motion takes place.Comment: 4 pages, 5 figures, work presented in Vortex VII

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

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

Public Health England's recovery tools: potential teaching resources?

The file attached to this record is the author's final peer reviewed version.Training to combat chemical and radiation accidents, incidents or attacks is critical for health professionals due to recent events involving these hazards or their use as unconventional weapons, such as the use of the nerve agent novichok in Salisbury, UK. Health professionals need to have appropriate knowledge and skills to effectively respond to future events involving any of these substances, which requires a rapid and coordinated response from different professionals to protect the environment and minimise the number of people exposed and reduce morbidity and mortality. However, despite chemical and radiation incidents becoming increasingly prevalent, literature reviews have shown that there is a lack of teaching of appropriate competences to face future crises in Europe, particularly amongst clinicians and other health professionals that would be part of the initial response. Thus, De Montfort University (DMU, UK) in collaboration with different academics from the University of Alcalá (Spain) and researchers from Public Health England (PHE) with comprehensive experience in environmental decontamination and restoration, have created a short training course for providing undergraduate/postgraduate students with basic skills to respond to chemical incidents, basic skills that are based on the major competences recently identified by the European Commission [1]. This novel training has been tested with students from different backgrounds in various European universities, recording high degrees of acquisition of the various basic competences that we developed to initially respond to chemical events [2]. To develop the practical part of this chemical training, we have incorporated the novel guidance and methodology developed by PHE to successfully tailor a protection and recovery response to any incident involving chemical substances, which is available in the “UK Recovery Handbook for Chemical Incidents” [3] and its web-based tools: “Chemical Recovery Navigation Tool” (CRNT, [4]) and “Chemical Recovery Record Form” (CRRF, [5]). These innovative resources aid the user to select effective protection, decontamination and restoration techniques or strategies from a pool of up-to-date options applicable to different environments according to the physicochemical properties of the chemical(s) involved and the area affected. The CRNT is accompanied by the CRRF, which facilitates collection and analysis of the necessary data to inform decisions, and an e-learning resource named “Chemical Recovery: Background” (CRB, [6]), which could facilitate the learning of environmental decontamination and restoration. We are currently developing a short training course to cover minor radiation incidents; this radiation training will follow the same methods used to develop the chemical training, but with the specific PHE recovery tools to tackle such events, specifically the “UK Recovery Handbooks for Radiation Incidents” [7] and its associated web-based tools “Radiation Recovery Navigation Tool” (Rad RNT, [8]), one for each environment: food production systems, inhabited areas and drinking water supplies. This communication will explore the use of the PHE’s Recovery Navigation Tools as potential resources to facilitate the acquisition of basic knowledge to tailor protection and recovery interventions for minor chemical and radiation incidents to protect the public

Communications-Inspired Projection Design with Application to Compressive Sensing

We consider the recovery of an underlying signal x \in C^m based on projection measurements of the form y=Mx+w, where y \in C^l and w is measurement noise; we are interested in the case l < m. It is assumed that the signal model p(x) is known, and w CN(w;0,S_w), for known S_W. The objective is to design a projection matrix M \in C^(l x m) to maximize key information-theoretic quantities with operational significance, including the mutual information between the signal and the projections I(x;y) or the Renyi entropy of the projections h_a(y) (Shannon entropy is a special case). By capitalizing on explicit characterizations of the gradients of the information measures with respect to the projections matrix, where we also partially extend the well-known results of Palomar and Verdu from the mutual information to the Renyi entropy domain, we unveil the key operations carried out by the optimal projections designs: mode exposure and mode alignment. Experiments are considered for the case of compressive sensing (CS) applied to imagery. In this context, we provide a demonstration of the performance improvement possible through the application of the novel projection designs in relation to conventional ones, as well as justification for a fast online projections design method with which state-of-the-art adaptive CS signal recovery is achieved.Comment: 25 pages, 7 figures, parts of material published in IEEE ICASSP 2012, submitted to SIIM