Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

Comments On The Pseudo-Microfossil Linotolypen

Hollow, black reticulate ‘microfossils’ of unknown affinity found in Ordovician to late Cretaceous sediments from North America, Europe and Australia were given the name Linotolypa by Eisenack in 1962. In 1978, he recognised that they were pseudo-microfossils consisting of asphalt, and noted that their structure resembled that of soap bubbles formed in agitated suspensions. These objects are well known as a component of the particles caught from the air by pollen and spore traps at the present day. They are correctly termed ‘cenospheres’ and are formed from coal and possibly pitch and fuel oil by incomplete combustion. If their presence were to be confirmed in Palaeozoic sediments, this would provide important new evidence for the occurrence of fire in the geological record and of the history of levels of O2 in the atmosphere.

Validation of the detection of Pseudo-nitzschia spp. using specific RNA probes tested in a microarray format: Calibration of signal based on variability of RNA content with environmental conditions.

Harmful algal blooms (HAB) occur worldwide and cause health problems and economic damage to fisheries and tourism. Monitoring for toxic algae is therefore essential but is based primarily on light microscopy, which is time consuming and can be limited by insufficient morphological characters such that more time is needed to examine critical features with electron microscopy. Monitoring with molecular tools is done in only a few places world-wide. EU FP7 MIDTAL (Microarray Detection of Toxic Algae) used SSU and LSU rRNA genes as targets on microarrays to identify toxic species. In order to comply with current monitoring requirements to report cell numbers as the relevant threshold measurement to trigger closure of fisheries, it was necessary to calibrate our microarray to convert the hybridisation signal obtained to cell numbers. Calibration curves for two species of Pseudo-nitzschia for use with the MIDTAL microarray are presented to obtain cell numbers following hybridisation. It complements work presented by Barra et al. (2012b. Environ. Sci. Pollut. Res. doi: 10.1007/s11356-012-1330-1v) for two other Pseudo-nitzschia spp., Dittami and Edvardsen (2012a. J. Phycol. 48, 1050) for Pseudochatonella, Blanco et al. (2013. Harmful Algae 24, 80) for Heterosigma, McCoy et al. (2013. FEMS. doi: 10.1111/1574-6941.12277) for Prymnesium spp., Karlodinium veneficum, and cf. Chatonella spp. and Taylor et al. (2014. Harmful Algae, in press) for Alexandrium.

Role of calcium influx through voltage-operated calcium channels and of calcium mobilization in the physiology of Schistosoma mansoni muscle contractions

We tested the hypothesis that voltage-operated Ca2+ channels mediate an extracellular Ca2+ influx in muscle fibres from the human parasite Schistosoma mansoni and, along with Ca2+ mobilization from the sarcoplasmic reticulum, contribute to Muscle contraction. Indeed, whole-cell voltage clamp revealed voltage-gated inward currents carried by divalent ions with a peak current elicited by steps to + 20 mV (from a holding potential of -70 mV). Depolarization of the fibres by elevated extracellular K+ elicited contractions that were completely dependent on extracellular Ca2+ and inhibited by nicardipine (half inhibition at 4(.)1 mu M). However these contractions were not very sensitive to other classical blockers of voltage-gated Ca2+ channels, indicating that the schistosome Muscle channels have an atypical pharmacology when compared to their mammalian counterparts. Furthermore, the contraction induced by 5 mM caffeine was inhibited after depletion of the sarcoplasmic reticulum either with thapsigargin (10 mu M) or ryanodine (10 mu M). These data suggest that voltage-operated Ca2+ channels docontribute to S. mansoni contraction as does the mobilization of stored Ca2+, despite the small volume of sarcoplasmic reticulum in schistosome smooth muscles.

The effect of simultaneous contractions of ipsilateral muscles on changes in corticospinal excitability induced by paired associative stimulation (PAS)

Consideration was given to means of increasing the reliability and muscle specificity of paired associative stimulation (PAS) by utilising the phenomenon of crossed-facilitation. Eight participants completed three separate sessions: isometric flexor contractions of the left wrist at 20% of maximum voluntary contraction (MVC) simultaneously with PAS (20s intervals; 14 min duration) delivered at the right median nerve and left primary motor cortex (MI); isometric contractions at 20% of MVC: and PAS only ( 14 min). Eight further participants completed two sessions of longer duration PAS (28 min): either alone or in conjunction with flexion contractions of the left wrist. Thirty motor potentials (MEPs) were evoked in the right flexor (rFCR) and extensor (rECR) carpi radialis muscles by magnetic stimulation of left M1 Prior to the interventions, immediately post-intervention, and 10 min post-intervention. Both 14 and 28 min of combined PAS and (left wrist flexion) contractions resulted in reliable increases in rFCR MEP amplitude, which were not present in rECR. In the PAS only conditions, 14 min of stimulation gave rise to unreliable increases in MEP amplitudes in rFCR and rECR, whereas 28 min of PAS induced small (unreliable) changes only for rFCR. These results support the conclusion that changes in the excitability of the corticospinal pathway induced by PAS interact with those associated with contraction of the muscles ipsilateral to the site of cortical stimulation. Furthermore, focal contractions applied by the opposite limb increase the extent and muscle specificity of the induced changes in excitability associated with PAS. (C) 2008 Elsevier Ireland Ltd. All rights reserved.