Limit cycles near hyperbolas in quadratic systems

In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.     

Periodic Solutions of a Class of Duffing Differential Equations

In this work we study the existence of new periodic solutions for the well knwon class of Duffing differential equation of the form $x^{\prime\prime}+ c x^{\prime}+ a(t) x +b(t) x^3 = h(t)$, where $c$ is a real parameter, $a(t)$, $b(t)$ and $h(t)$ are continuous $T$--periodic functions. Our results are proved using three different results on the averaging theory of first order.     

Towards the detection of single polychlorotriphenylmethyl radical derivatives by means of Electron Spin Noise STM

The Electron Spin Noise Scanning Tunnelling Microscopy (ESN-STM) technique is one of the most promising techniques detecting one single spin, combining the spatial resolution of the STM with the ability of spectral resolution and spin manipulation of Electron Spin Resonance. After its first observation, the effectiveness of this technique has been tested by different groups to study the properties of small aggregates or single organic radical molecules.We report on the ongoing ESN-STM study on nano-aggregates of tris(2,4,6-thrichlorophenyl)methyl radical (TTM) derivatives, whose possibility to be used as wires, switches and memory devices has already been investigated in bulk. After deposition on Au(111), TTM radicals preserved their magnetism. To treat the collected noise data we followed a statistical approach; some peculiar characteristics of this analysis will be addressed.     

New central configurations for the planar 7-body problem

In this paper we study numerically the existence of families of planar central configurations for the 7-body problem with the following properties: five bodies are on the vertices of a regular pentagon and the other two bodies are symmetrically positioned in the interior of the pentagon.     

Telegraphic Transport Processes and Their Fractional Generalization: A Review and Some Extensions

We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations.     

Identification of phototransformation products of sildenafil (Viagra) and its N-demethylated human metabolite under simulated sunlight

Recent publications on pharmaceutical monitoring are increasingly covering the field of illicit drugs and lately the forensic evaluation of designing illegal analogs of lifestyle drugs like the phosphodiesterase type 5 (PDE-5) inhibitors Viagra (sildenafil), Levitra (vardenafil) and Cialis (tadalafil). Recently, the presence of all three erectile dysfunction treatment drugs has been reported in wastewaters at very low concentrations. In the environment, contaminants undergo various physical or chemical processes classified into abiotic (photolysis, hydrolysis) and biotic (biodegradation) reactions. Thus, changes in the chemical structure lead to the formation of new transformation products, which may persist in the environment or be further degraded. This study describes the photolysis of sildenafil (SDF) and its human metabolite N-demethylsildenafil (DM-SDF) under simulated solar radiation (Xenon lamp). Following chromatographic separation of the irradiated samples, eight photoproducts in the SDF samples and six photoproducts for DM-SDF were detected and characterized. The combination of ultra performance liquid chromatography-electrospray ionization-quadrupole time-of-flight-mass spectrometry (UPLC-ESI-QToF-MS), liquid chromatography-atmospheric pressure chemical ionization-triple quadrupole mass spectrometry (LC-APCI-QqQ-MS) and hydrogen/deuterium-exchange experiments allowed to propose plausible chemical structures for the photoproducts, taking into account the characteristic fragmentation patterns and the accurate mass measurements. These mass spectral data provided sound evidence for the susceptibility of the piperazine ring toward photodegradation. A gradual breakdown of this heterocyclic structure gave rise to a series of products, which in part were identical for SDF and DM-SDF. The sulfonic acid, as the formal product of sulfonamide hydrolysis, was identified as key intermediate in the photolysis pathway. In both drug/metabolite molecules, phototransformation processes taking place beyond the sulfonamide group were deemed to be of minor relevance.