A Tame Degenerate Hopf-Pitchfork Bifurcation in a Modified van der Pol–Duffing Oscillator

We consider a modified van der Pol–Duffing electronic circuit,focusing on the case where a Hopf-pitchfork bifurcation takes places.The analysis of this bifurcation is a simple way to detect andcharacterize purely three-dimensional behaviour (an oscillatory regimein three variables, quasiperiodic motion, etc.).The normal formanalysis provides the classification of different kinds ofHopf-pitchfork bifurcation, organized according to some degeneratecases. One of these degenerate cases is analyzed, by considering acodimension-three unfolding of a reflectionally symmetric planar vectorfield. Later, the implications for three-dimensional flows arepresented. Unlike another degenerate Hopf-pitchfork bifurcationsexhibited by the system, the one studied here does not involvequasiperiodic behaviour, so that the complexity related to quasiperiodicmotion is not present.     

A homogeneity test for bivariate random variables

In this paper, a test for the homogeneity of two bidimensional populations is proposed. It is based on the L ₂-norm of the difference between the empirical characteristic functions associated with independent random samples from each population. We first approximate this norm and then we give two bootstrap algorithms to consistently estimate the null distribution of the resultant test statistic. A simulation study illustrates the goodness of these two bootstrap estimators and compares the proposed test with others.     

A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits

This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors.     

An Algorithm for Computing Quasi-Homogeneous Formal Normal Forms under Equivalence

This paper presents a recursive algorithm which is useful for computing normal forms of vector fields using smooth orbital equivalence. The case of vector fields with a singularity corresponding to a triple-zero eigenvalue with geometric multiplicity one is considered in detail. The results obtained are applied to the study of a simple electronic device, with only one nonlinearity.     

[4-(N-Carbazolyl)-2,6-dichlorophenyl]bis(2,4,6-trichlorophenyl)methyl radical an efficient red light-emitting paramagnetic molecule

We report the synthesis, luminescent properties, electrochemical behavior and electron paramagnetic resonance of a novel stable radical adduct of the tris(2,4,6-trichlorophenyl)methyl radical and carbazole.     

Nanostructured rough gold electrodes as platforms to enhance the sensitivity of electrochemical genosensors

An electrochemical DNA genosensor constructed by using rough gold as electrode support is reported in this work. The electrode surface nanopatterning was accomplished by repetitive square-wave perturbing potential (RSWPP). A synthetic 25-mer DNA capture probe, modified at the 5′ end with a hexaalkylthiol, able to hybridize with a specific sequence of lacZ gene from the Enterobacteriaceae bacterial family was assembled to the rough gold surface. A 25 bases synthetic sequence fully complementary to the thiolated DNA capture probe and a 326 bases fragment of lacZ containing a fully matched sequence with the capture probe, which was amplified by a specific asymmetric polymerase chain reaction (aPCR), were employed as target sequences. The hybridization event was electrochemically monitored by using two different indicators, hexaammineruthenium (III) chloride showing an electrostatic DNA binding mode, and pentaamineruthenium-[3-(2-phenanthren-9-yl-vinyl)-pyridine] (in brief RuL) which binds to double stranded DNA (dsDNA) following an intercalative mechanism. After optimization of the different variables involved in the hybridization and detection reactions, detection limits of 5.30 pg μL⁻¹ and 10 pg μL⁻¹ were obtained for the 25-mer synthetic target DNA and the aPCR amplicon, respectively. A RSD value of 6% was obtained for measurements carried out with 3 different genosensors prepared in the same manner.     

Single-shot Thomson scattering on argon plasmas created by the Microwave Plasma Torch; evidence for a new plasma class

To determine the fine-structure size of plasmas created by a Microwave Plasma Torch (MPT), single-shot Thomson scattering (TS) measurements were performed. The aim was to find a solution for the long-standing discrepancy between experiments and Global Plasma Models (GPMs). Since these GPMs are based on the assumption that (ambipolar) diffusion is the main loss process for charged particles, the diffusion length and thus the fine-structure size should be known with high precision before an appropriate theory-experiment comparison can be carried out. In order to avoid the effect of blurring, which is created during the accumulation of multi-shot TS signals and which obscures the fine-structures, single-shot measurements are indispensable to determine the diffusion length.     

An experimental study on the asymmetry and the dip form of the Hβ line profiles in microwave produced plasmas at atmospheric pressure

An experimental study on the asymmetry of the Balmer H_β profile in plasmas produced by microwaves at atmospheric pressure is presented. The study is based on the definition of several functions that quantify the asymmetry aspects of the profile. Apart from the asymmetry aspects of the flanks also form-functions are defined that characterize the central part of the profile, the so-called dip or central valley, the combination of the two peaks and the dip in between them. The study shows the experimental dependence of these characteristics on the electron density and control parameters such as the gas flow and the hydrogen admixture ratio. The possible use of these newly introduced profile characteristics to plasma diagnosis is discussed.     

A bifurcation analysis of planar nilpotent reversible systems

In this paper, we present a bifurcation analysis for planar nilpotent reversible systems with an equilibrium point located at the origin. We study candidates for the universal unfoldings of the codimension-one non-degenerate cases, as well as a pair of codimension-two degenerate cases, and a codimension-three degenerate case, where a rich bifurcation scenario is pointed out.     

Interactions of Schiff-base ligands with gold nanoparticles: structural, optical and electrocatalytic studies

A study on optical and electrochemical properties resulting upon interaction of Schiff base ligands with gold nanoparticles is presented. The measurements of the optical absorption and fluorescence properties have provided important information about structure-properties dependence. We show that in function of the isomer structure and its attachment orientation with respect to the metal nanoparticle, their optical properties can be modulated. Nanoparticle assemblies mediated by 3,4-DHS were also obtained based on a control of the interparticle interactions and their electrocatalytic activity toward NADH oxidation was investigated.