A symplectic realization of the Volterra lattice

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page

Multiscale expansion and integrability properties of the lattice potential KdV equation

We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schroedinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007 Conferenc

Multiscale reduction of discrete nonlinear Schroedinger equations

We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability conditions for two well-known discretizations of the nonlinear Schroedinger equation.Comment: 12 page

A discrete linearizability test based on multiscale analysis

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A1, A2 and A3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A3 C-integrability conditions can be linearized by a Möbius transformation

On the Integrability of the Discrete Nonlinear Schroedinger Equation

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a reductive perturbation technique to show an obstruction to its integrability.Comment: 4 pages, accepted in EP

Discrete Multiscale Analysis: A Biatomic Lattice System

We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations. We require that also the reduced equation be discrete. To do so coherently we need to discretize the time variable to be able to get asymptotic discrete waves and carry out a discrete multiscale expansion around them. Our resulting nonlinear equation will be a kind of discrete Nonlinear Schr\"odinger equation. If we make its continuum limit, we obtain the standard Nonlinear Schr\"odinger differential equation

Rapid single step atmospheric pressure plasma jet deposition of a SERS active surface

A helium gas atmospheric pressure plasma jet (APPJ) is used to prepare a silver-based SERS substrate. The Raman enhancement from substrates created using APPJ compares well with two commercially available silver-based SERS substrates and an in-house prepared physical deposition of pre-synthesised silver nanoparticles. An aqueous solution of rudimentary silver salt was required as an ink to deposit zero valent silver in a single step with no post processing. An array of 16 × 16 silver ‘islands’ are printed on borosilicate glass, each island taking 5 seconds to print with a power of < 14 W to sustain the plasma. The SERS response was assessed using 4-mercaptobenzoic acid and rhodamine 6G as model analytes, with a calculated detection limit of 1 × 10−6 M. Also demonstrated is the removal of analyte from the surface after Raman measurement by exposure to helium APPJ doped with oxygen followed by hydrogen to restore zero baseline. This regeneration takes less than 10 seconds and allows for replicate measurements using the same SERS substrate

Correction: Rapid single step atmospheric pressure plasma jet deposition of a SERS active surface

Correction for ‘Rapid single step atmospheric pressure plasma jet deposition of a SERS active surface’ by Oliver S. J. Hagger et al., Mater. Adv., 2023, 4, 3239–3245, https://doi.org/10.1039/D3MA00249G. The authors regret that in the Results and discussion section, the particle sizes for PSNP and PDS particles were given in reversed order. The correct particle sizes should be as follows: On average, through analysis of SEM images, PSNP and PDS particles are 51 ± 24 nm, and 42 ± 12 nm in size, respectively, whereas the commercial substrates OI and SS are 242 ± 58 nm and 133 ± 32 nm in size. The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers

On maximally superintegrable systems

Locally any completely integrable system is maximally superintegrable system such as we have the necessary number of the action-angle variables. The main problem is the construction of the single-valued additional integrals of motion on the whole phase space by using these multi-valued action-angle variables. Some constructions of the additional integrals of motion for the St\"ackel systems and for the integrable systems related with two different quadratic $r$-matrix algebras are discussed. Among these system there are the open Heisenberg magnet and the open Toda lattices associated with the different root systems.Comment: 12 pages, LaTeX with AmsFont

Role of TGF-β1 haplotypes in the occurrence of myocardial infarction in young Italian patients

<p>Abstract</p> <p>Background</p> <p>Transforming growth factor beta 1 (TGF-β1) gene play an important role in the acute myocardial infarction (AMI), however no investigation has been conducted so far in young AMI patients.</p> <p>In this study, we evaluated the influence of TGF-β1 polymorphisms/haplotypes on the onset and progression of AMI in young Italian population.</p> <p>Methods</p> <p>201 cases and 201 controls were genotyped for three TGF-β1 polymorphisms (G-800A, C-509T and Leu10Pro). The main follow-up end-points (mean follow-up, 107 ± 49 months) were death, myocardial infarction or revascularization procedures.</p> <p>Results</p> <p>Significant risk factors were smoking (p < 10^-4), family history for coronary artery disease (p < 10^-4), hypercholesterolemia (p = 0.001) and hypertension (p = 0.002). The C-509T and Leu10Pro polymorphisms showed significant differences (p = 0.026 and p = 0.004) between cases and controls.</p> <p>The most common haplotypes revealed a possible protective effect (GCT, OR 0.75, 95% CI 0.57–0.99, p = 0.042) and an increased risk of AMI (GTC, OR 1.51, 95% CI 1.13–2.02, p = 0.005), respectively.</p> <p>No statistical differences were observed in genotype distribution in the follow-up study between the two groups: 61 patients with subsequent events (13 deaths) and 108 without events.</p> <p>Conclusion</p> <p>Even though our results need to be further confirmed in larger studies, this is the first study reporting on a possible role of TGFβ1 common haplotypes in the onset of AMI in young patients.</p