Finite reduction and Morse index estimates for mechanical systems

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Application

η3-Allyl carbonyl complexes of group 6 metals: structural aspects, isomerism, dynamic behaviour and reactivity

Transition metal complexes with π-allylic ligands remain an attractive topic in organometallic chemistry, given the numerousreports of a wide variety of synthetic routes, dynamic behaviour and reactivity, structural (including isomerism),spectroscopic and redox properties, and applications in organic synthesis and catalysis. Surprisingly, despite the considerableinterest in the rich and varied chemistry of this family of organometallic compounds, there is no recent review. This review is focused on π-allylic representatives of low-cost Group-6 metals bearing one or more carbonyl ligand, the coordination sphere being complemented with η5-cyclopentadienyl (Section 2), chelating ligands, including redox-active α-diimines and various complementary diphosphines (Section 3), and novel anionic amidinate or pyrazolate ligands (Section 4). In Section 1, particular attention is paid to rearrangements of the π-allylic ligand, namely exo and endo isomerism, interconversion mechanisms, fluxionality, and agostic interactions. In addition, the application of multinuclear NMR spectroscopy to the elucidation of such isomerism, and the effect of the metal-centre oxidation state on the bonding, dynamic behaviour and reactivity of the π-allylic ligand are described. The detailed mechanistic description of the synthetic routes and dynamic behaviour of selected representatives of α-diimine complexes in Section 2 is followed by a description of the [M(CO)2(η3-allyl-H,R)(α-diimine)]0/+ fragment as a convenient scaffold for diverse monodentate ligands participating in a range of substitution, insertion, intramolecular migration and C–C coupling reactions – frequently involving also the π-allylic ligand, such as allylic alkylation. Special attention is devoted to selected examples of redox and acid-base reactivity of the α-diimine complexes with emphasis on prospects in electrocatalysis. The amidinate (and related pyrazolate) ligands treated in Section 4 may directly replace the π-allylic ligand in some cyclopentadienyl complexes (Section 2) or the α-diimine ligand in some dicarbonyl π-allylic complexes (Section 3). The brief description of their synthetic routes is complemented by intriguing examples of fluxionality and characteristic reactivity encountered for these unusual four-electron donor ligands

Numerical Simulations of Dynamos Generated in Spherical Couette Flows

We numerically investigate the efficiency of a spherical Couette flow at generating a self-sustained magnetic field. No dynamo action occurs for axisymmetric flow while we always found a dynamo when non-axisymmetric hydrodynamical instabilities are excited. Without rotation of the outer sphere, typical critical magnetic Reynolds numbers $Rm_c$ are of the order of a few thousands. They increase as the mechanical forcing imposed by the inner core on the flow increases (Reynolds number $Re$). Namely, no dynamo is found if the magnetic Prandtl number $Pm=Rm/Re$ is less than a critical value $Pm_c\sim 1$. Oscillating quadrupolar dynamos are present in the vicinity of the dynamo onset. Saturated magnetic fields obtained in supercritical regimes (either $Re>2 Re_c$ or $Pm>2Pm_c$) correspond to the equipartition between magnetic and kinetic energies. A global rotation of the system (Ekman numbers $E=10^{-3}, 10^{-4}$) yields to a slight decrease (factor 2) of the critical magnetic Prandtl number, but we find a peculiar regime where dynamo action may be obtained for relatively low magnetic Reynolds numbers ($Rm_c\sim 300$). In this dynamical regime (Rossby number $Ro\sim -1$, spheres in opposite direction) at a moderate Ekman number ($E=10^{-3}$), a enhanced shear layer around the inner core might explain the decrease of the dynamo threshold. For lower $E$ ($E=10^{-4}$) this internal shear layer becomes unstable, leading to small scales fluctuations, and the favorable dynamo regime is lost. We also model the effect of ferromagnetic boundary conditions. Their presence have only a small impact on the dynamo onset but clearly enhance the saturated magnetic field in the ferromagnetic parts. Implications for experimental studies are discussed

Shortening of the Short Refractory Periods in Short QT Syndrome.

BACKGROUND: Diagnosis of short QT syndrome (SQTS) remains difficult in case of borderline QT values as often found in normal populations. Whether some shortening of refractory periods (RP) may help in differentiating SQTS from normal subjects is unknown. METHODS AND RESULTS: Atrial and right ventricular RP at the apex and right ventricular outflow tract as determined during standard electrophysiological study were compared between 16 SQTS patients (QTc 324±24 ms) and 15 controls with similar clinical characteristics (QTc 417±32 ms). Atrial RP were significantly shorter in SQTS compared with controls at 600- and 500-ms basic cycle lengths. Baseline ventricular RP were significantly shorter in SQTS patients than in controls, both at the apex and right ventricular outflow tract and for any cycle length. Differences remained significant for RP of any subsequent extrastimulus at any cycle length and any pacing site. A cut-off value of baseline RP <200 ms at the right ventricular outflow tract either at 600- or 500-ms cycle length had a sensitivity of 86% and a specificity of 100% for the diagnosis of SQTS. CONCLUSIONS: Patients with SQTS have shorter ventricular RP than controls, both at baseline during various cycle lengths and after premature extrastimuli. A cut-off value of 200 ms at the right ventricular outflow tract during 600- and 500-ms basic cycle length may help in detecting true SQTS from normal subjects with borderline QT values

Zonal shear and super-rotation in a magnetized spherical Couette flow experiment

We present measurements performed in a spherical shell filled with liquid sodium, where a 74 mm-radius inner sphere is rotated while a 210 mm-radius outer sphere is at rest. The inner sphere holds a dipolar magnetic field and acts as a magnetic propeller when rotated. In this experimental set-up called DTS, direct measurements of the velocity are performed by ultrasonic Doppler velocimetry. Differences in electric potential and the induced magnetic field are also measured to characterize the magnetohydrodynamic flow. Rotation frequencies of the inner sphere are varied between -30 Hz and +30 Hz, the magnetic Reynolds number based on measured sodium velocities and on the shell radius reaching to about 33. We have investigated the mean axisymmetric part of the flow, which consists of differential rotation. Strong super-rotation of the fluid with respect to the rotating inner sphere is directly measured. It is found that the organization of the mean flow does not change much throughout the entire range of parameters covered by our experiment. The direct measurements of zonal velocity give a nice illustration of Ferraro's law of isorotation in the vicinity of the inner sphere where magnetic forces dominate inertial ones. The transition from a Ferraro regime in the interior to a geostrophic regime, where inertial forces predominate, in the outer regions has been well documented. It takes place where the local Elsasser number is about 1. A quantitative agreement with non-linear numerical simulations is obtained when keeping the same Elsasser number. The experiments also reveal a region that violates Ferraro's law just above the inner sphere.Comment: Phys Rev E, in pres

In Vitro Efficacy of Essential Oils from Melaleuca Alternifolia and Rosmarinus Officinalis, Manuka Honey-based Gel, and Propolis as Antibacterial Agents Against Canine Staphylococcus Pseudintermedius Strains

Abstract: Essential oils (EOs) and honeybee products (e.g., honey and propolis) are natural mixtures of dierent volatile compounds that are frequently used in traditional medicine and for pathogen eradication. The aim of this study was to evaluate the antibacterial properties of tea tree (Melaleuca alternifolia) EO (TTEO), Rosmarinus ocinalis EO (ROEO), manuka-based gel, and propolis against 23 strains of Staphylococcus pseudintermedius (SP) isolated from canine pyoderma. Antimicrobial resistance screening was assessed using a panel of nine antimicrobial agents coupled with a PCR approach. An aromatogram was done for both EOs, using the disk diusion method. The minimum inhibitory concentration (MIC) was determined for all the compounds. Among the 23 SP strains, 14 (60.9%) were multidrug-resistant (MDR), 11 strains (47.8%) were methicillin-resistant (MRSP), and 9 (39.1%) were non-MDR. The mean diameter of the inhibition zone for Melaleuca and Rosmarinus were 24.5 8.8 mm and 15.2 8.9 mm, respectively, resulting as statistically dierent (p = 0.0006). MIC values of TTEO and ROEO were similar (7.6 3.2% and 8.9 2.1%, respectively) and no statistical significances were found. Honeybee products showed lower MIC compared to those of EOs, 0.22 0.1% for Manuka and 0.8 0.5% for propolis. These findings reveal a significant antibacterial eect for all the tested products

Neural Networks Supporting Phoneme Monitoring Are Modulated by Phonology but Not Lexicality or Iconicity: Evidence From British and Swedish Sign Language

Sign languages are natural languages in the visual domain. Because they lack a written form, they provide a sharper tool than spoken languages for investigating lexicality effects which may be confounded by orthographic processing. In a previous study, we showed that the neural networks supporting phoneme monitoring in deaf British Sign Language (BSL) users are modulated by phonology but not lexicality or iconicity. In the present study, we investigated whether this pattern generalizes to deaf Swedish Sign Language (SSL) users. British and SSLs have a largely overlapping phoneme inventory but are mutually unintelligible because lexical overlap is small. This is important because it means that even when signs lexicalized in BSL are unintelligible to users of SSL they are usually still phonologically acceptable. During fMRI scanning, deaf users of the two different sign languages monitored signs that were lexicalized in either one or both of those languages for phonologically contrastive elements. Neural activation patterns relating to different linguistic levels of processing were similar across SLs; in particular, we found no effect of lexicality, supporting the notion that apparent lexicality effects on sublexical processing of speech may be driven by orthographic strategies. As expected, we found an effect of phonology but not iconicity. Further, there was a difference in neural activation between the two groups in a motion-processing region of the left occipital cortex, possibly driven by cultural differences, such as education. Importantly, this difference was not modulated by the linguistic characteristics of the material, underscoring the robustness of the neural activation patterns relating to different linguistic levels of processing