On a Korteweg–de Vries-like equation with higher degree non-linearity

We deal with a non-linear partial differential equation which has been widely investigated owing to its applications in quantum field theory, as well as plasma and solid-state physics. It is the matter of a third order KdV-like equation with higher degree non-linearity in the coefficient of the transport term; it can be derived from a Lagrangian or an Hamiltonian density. In the current literature specific attention has been devoted to the search for traveling-wave solutions, depending upon a positive parameter v, which assesses the speed of the solitary wave. The velocity v is always assumed to be constant, as its dependence on the wave-amplitude is neglected in the mathematical model. In this context, Coffey [On series expansions giving closed-form solutions of Korteweg–de Vries-like equations, SIAM J. Appl. Math. 50 (6) (1990) 1580–1592] exploits an algebraic recursive technique to obtain these solutions in closed form for particular values of v. The aim of this paper is to extend these results by showing that closed-form solutions are achievable for every value of v: to this purpose we supply a proper mathematical framework for these issues by taking into account a suitable special function, namely an elliptic function in the sense of Weierstraß. Furthermore we obtain two classes of the so-called kink solutions, see [M.W. Coffey, On series expansions giving closed-form solutions of Korteweg–de Vries-like equations, SIAM J. Appl. Math. 50 (6) (1990) 1580–1592; B. Dey, Domain wall solutions of KdV-like equations with higher order non-linearity, J. Phys. A 19 (1) (1986) L9–L12], as well as an exponential development of the general solution, for which we prove the convergence. Eventually we show how to implement the resulting functions by means of a symbolic manipulation program.     

Reflection of bounded acoustic beams on a fluid-solid interface

The reflection of an acoustic beam onto a fluid-solid interface is studied under the assumption that the solid medium is viscoelastic. The incident beam is represented as a superposition of plane monochromatic homogeneous waves and its profile is assumed to be Gaussian shaped. The outcoming wave field at the interface, and away from it in the fluid, is numerically calculated for different values of the frequency and of the beam width.

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Sommario Si studia la riflessione di un fascio di onde acustiche sulla superficie di separazione fra un liquido ed un solido nell'ipotesi che il mezzo solido sia viscoelastico. Il fascio incidente ha un profilo gaussiano e viene rappresentato mediante la sovrapposizione di onde piane monocromatiche omogenee. Si calcola numericamente il profilo del fascio riflesso sia sull'interfaccia, sia lontano da essa nel fluido, per diversi valori della frequenza e della larghezza del fascio.

     

Luminescent Ink Based on Upconversion of NaYF4:Er,Yb@MA Nanoparticles: Environmental Friendly Synthesis and Structural and Spectroscopic Assessment

NaYF₄:Er,Yb upconversion luminescent nanoparticles (UCNPs) were prepared by hydrothermal methods at 180 °C for 24 h. The X-ray diffraction (XRD) and TEM (transmission electron microscopy) images show that the resulting 60 nm UCNPs possess a hexagonal structure. In this work, maleic anhydride (MA) was grafted on the surface of UCNPs to induce hydrophilic properties. The photoluminescence spectra (PL) show upconversion emissions centered around 545 nm and 660 nm under excitation at 980 nm. The luminescent inks, including UCNPs@MA, polyvinyl alcohol (PVA), deionized water (DI), and ethylene glycol (EG), exhibit suitable properties for screen printing, such as high stability, emission intensity, and tunable dynamic viscosity. The printed patterns with a height of 5 mm and a width of 1.5 mm were clearly observed under the irradiation of a 980 nm laser. Our strategy provides a new route for the controlled synthesis of hydrophilic UCNPs, and shows that the UCNPs@MAs have great potential in applications of anti-counterfeiting packing.     

Pulsed amperometric detection at glassy carbon electrodes: A new waveform for sensitive and reproducible determination of electroactive compounds

In this work, the application of a new pulsed amperometric detection (PAD) waveform at a glassy carbon electrode, operating in typical chromatographic mobile phases, is proposed for the sensitive and reproducible determination of arylethanolaminic and phenolic moiety based compounds (e.g. beta-agonists and polyphenols). Preliminary experiments by cyclic voltammetry were carried out to investigate the electrochemical behaviour and to select the detection and cleaning electrode potentials. The proposed potential-time profile was designed to prevent the carbon electrode fouling under repeated analyses, thus ensuring a reproducible and sensitive quantitative determination, without the need of any mechanical or chemical electrode cleaning procedure. The waveform electrochemical parameters, including detection and delay times, were optimized in terms of sensitivity, limit of detection and response stability. The optimized waveform allowed the sensitive and stable detection of model compounds, such as clenbuterol and caffeic acid, that showed detection limits of 0.1 μg L⁻¹ and 14 μg L⁻¹, quantification limits of 0.4 μg L⁻¹ and 46 μg L⁻¹, and linearity up to 100 μg L⁻¹ (r = 0.9993) and 10 mg L⁻¹ (r = 0.9998), respectively. Similar results were obtained for other compounds of the same classes, with precision values under repeatability conditions ranging from 3.0 to 5.9%. The proposed method can be then considered as an excellent alternative to the post-column detection of beta-agonists, phenols and polyphenols.     

Symmetry and Short Interval Mean-Squares

The weighted Selberg integral is a discrete mean-square that generalizes the classical Selberg integral of primes to an arithmetic function f, whose values in a short interval are suitably attached to a weight function. We give conditions on f and select a particular class of weights in order to investigate non-trivial bounds of weighted Selberg integrals of both f and f * μ. In particular, we discuss the cases of the symmetry integral and the modified Selberg integral, the latter involving the Cesaro weight. We also prove some side results when f is a divisor function.     

Effect of bioclimatic area on the composition and bioactivity of Tunisian Rosmarinus officinalis essential oils

The chemical composition of eight Tunisian Rosmarinus officinalis L. populations (A–H) from different bioclimatic areas has been examined by gas chromatography (GC) and GC-mass spectrometry. The essential oils are characterised by high amounts of oxygenated monoterpenes (58.2–71.7%) followed by monoterpene hydrocabons (15.1–26.7%). 1,8-Cineole, camphor, α-pinene and borneol are the main representative components. The antioxidant activity was investigated by 2,2-diphenyl-1-picrylhydrazyl radical (DPPH), ferric reducing ability power assay and β-carotene bleaching test. Samples showed antiradical activity by inhibiting DPPH radical with IC₅₀ values ranging from 375.3 to 592.8 μg mL^? 1 for samples F and A, respectively. Sample A also showed the most promising activity in β-carotene bleaching test (IC₅₀ of 31.9 μg mL^? 1). The essential oils were also screened for acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) inhibitory activity. Sample G showed the highest activity against AChE (IC₅₀ of 64.7 μg mL^? 1) while sample D (IC₅₀ of 29.5 μg mL^? 1) exhibited the most potent activity against BChE.     

Modeling cell dynamics under mobile phone radiation

Perturbations by pulse-modulated microwave radiation from GSM mobile phones on neuron cell membrane gating and calcium oscillations have been suggested as a possible mechanism underlying activation of brain states and electroencephalographic epiphenomena. As the employ of UMTS phones seems to reveal other symptoms, a unified phenomenological framework is needed. In order to explain possible effects of mobile phone radiation on cell oscillations, GSM and UMTS low-frequency envelopes have been detected, recorded and used as input in cell models. Dynamical systems endowed with contiguous regular and chaotic regimes suitable to produce stochastic resonance can both account for the perturbation of the neuro-electrical activity and even for the low intensity of the signal perceived by high sensitive subjects. Neuron models of this kind can be employed as a reductionist hint for the mentioned phenomenology. The Hindmarsh-Rose model exhibits frequency enhancement and regularization phenomena induced by weak GSM and UMTS. More realistic simulations of cell membrane gating and calcium oscillations have been performed with the help of an adaptation of the Chay-Keizer dynamical system. This scheme can explain the suspected subjective sensitivity to mobile phone signals under the thermal threshold, in terms of cell calcium regularity mechanisms. Concerning the two kinds of emission, the stronger occupation of the ELF band of last generation UMTS phones is compensated by lower power emitted.     

Structural determination of a short-lived excited iron(II) complex by picosecond x-ray absorption spectroscopy

Structural changes of the iron(II)-tris-bipyridine ([Fe(II)(bpy)(3)](2+)) complex induced by ultrashort pulse excitation and population of its short-lived (< or =0.6 ns) quintet high spin state have been detected by picosecond x-ray absorption spectroscopy. The structural relaxation from the high spin to the low spin state was followed over the entire lifetime of the excited state. A combined analysis of the x-ray-absorption near-edge structure and extended x-ray-absorption fine structure spectroscopy features delivers an Fe-N bond elongation of 0.2 A in the quintet state compared to the singlet ground state.     

Cardiac resynchronization therapy and phase resetting of the sinoatrial node: a conjecture

Congestive heart failure is a severe chronic disease often associated with disorders that alter the mechanisms of excitation-contraction coupling that may result in an asynchronous left ventricular motion which may further impair the ability of the failing heart to eject blood. In recent years a therapeutic approach to resynchronize the ventricles (cardiac resynchronization therapy, CRT) has been performed through the use of a pacemaker device able to provide atrial-based biventricular stimulation. Atrial lead senses the spontaneous occurrence of cells depolarization and sends the information to the generator which, in turn, after a settled delay [atrioventricular (AV) delay], sends electrical impulses to both ventricles to stimulate their synchronous contraction. Recent studies performed on heart rate behavior of chronically implanted patients at different epochs after implantation have shown that CRT can lead to sustained overall improvement of heart function with a reduction in morbidity and mortality. At this moment, however, there are no studies about CRT effects on spontaneous heart activity of chronically implanted patients. We performed an experimental study in which the electrocardiographic signal of five subjects under chronic CRT was recorded during the activity of the pacemaker programmed at different AV delays and under spontaneous cardiac activity after pacemaker deactivation. The different behavior of heart rate variability during pacemaker activity and after pacemaker deactivation suggested the hypothesis of a phase resetting mechanism induced by the pacemaker stimulus on the sinoatrial (SA) node, a phenomenon already known in literature for aggregate of cardiac cells, but still unexplored in vivo. The constraints imposed by the nature of our study (in vivo tests) made it impossible to plan an experiment to prove our hypothesis directly. We therefore considered the best attainable result would be to prove the accordance of our data to the conjecture through the use of models and physical considerations. We first used the data of literature on far-field effects of cardiac defibrillators to prove that the pacemaker impulses delivered to the two ventricles were able to induce modifications in membrane voltage at the level of the SA node. To simulate a phase resetting mechanism of the SA node, we used a Van der Pol modified model to allow the possibility of changing the refractory period and the firing frequency of the cells separately. With appropriate parameters of the model we reproduced phase response curves that can account for our experimental data. Furthermore, the simulated curves closely resemble the functional form proposed in literature for perturbed aggregate of cardiac cells. Despite the small sample of subjects investigated and the limited number of ECG recordings at different AV delays, we think we have proved the plausibility of the proposed conjecture.     

Reversible microwave-assisted cycloaddition of aziridines to carbon nanotubes

We report a new approach that uses microwaves to rapidly functionalize carbon nanotubes by using 1,3-dipolar cycloaddition of aziridines, well-known precursors to azomethine ylides, in solvent-free conditions. The efficiency of our microwave-mediated protocol is confirmed by comparison to a similar protocol in classical conditions for the azomethine ylides in DMF. Under these latter conditions, the reaction proceeds in 5 days (against 1 h under microwave irradiation), and the functionalization degree is much lower, as confirmed by thermogravimetric analysis and Raman spectroscopy. With our procedure, we easily scale-up the reaction up to 250 mg of functionalized MWNT in 1 h. We also provide an indirect proof of the covalent sidewall functionalization of the tubes.