Ducks on the torus: existence and uniqueness

We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually occur in two-parametric families. Here we treat systems with a convex slow curve. In this case there is a set of parameter values accumulating to zero for which the system has exactly one attracting and one repelling canard cycle. The basin of the attracting cycle is almost the whole torus.Comment: To appear in Journal of Dynamical and Control Systems, presumably Vol. 16 (2010), No. 2; The final publication is available at www.springerlink.co

Inactive power detection in AC network

Using the examples of wave and vector diagrams, we study the conditions for the appearance of components of inactive power in an AC network, which are known as reactive power and distortion power. It is shown that the components of the active, reactive power and distortion power are mutually orthogonal and form a power balance, which can be violated mainly due to methodological errors in calculating these components under conditions of non-stationary mode parameters. It is established that the interaction of reactive power and distortion power occurs at the instantaneous power level, and changing their phase shifts allows you to adjust the shape of the resulting power without involving additional active power in the AC network. The results obtained will allow not only to correctly determine the proportion and nature of the components of inactive capacities, which is valuable for solving the problems of optimizing modes in AC networks, but also to create effective technical means of compensating for the identified inactive capacities in the future

Differential effects of prenatal and postnatal expressions of mutant human DISC1 on neurobehavioral phenotypes in transgenic mice: evidence for neurodevelopmental origin of major psychiatric disorders

Strong genetic evidence implicates mutations and polymorphisms in the gene Disrupted-In-Schizophrenia-1 (DISC1) as risk factors for both schizophrenia and mood disorders. Recent studies have shown that DISC1 has important functions in both brain development and adult brain function. We have described earlier a transgenic mouse model of inducible expression of mutant human DISC1 (hDISC1) that acts in a dominant-negative manner to induce the marked neurobehavioral abnormalities. To gain insight into the roles of DISC1 at various stages of neurodevelopment, we examined the effects of mutant hDISC1 expressed during (1) only prenatal period, (2) only postnatal period, or (3) both periods. All periods of expression similarly led to decreased levels of cortical dopamine (DA) and fewer parvalbumin-positive neurons in the cortex. Combined prenatal and postnatal expression produced increased aggression and enhanced response to psychostimulants in male mice along with increased linear density of dendritic spines on neurons of the dentate gyrus of the hippocampus, and lower levels of endogenous DISC1 and LIS1. Prenatal expression only resulted in smaller brain volume, whereas selective postnatal expression gave rise to decreased social behavior in male mice and depression-like responses in female mice as well as enlarged lateral ventricles and decreased DA content in the hippocampus of female mice, and decreased level of endogenous DISC1. Our data show that mutant hDISC1 exerts differential effects on neurobehavioral phenotypes, depending on the stage of development at which the protein is expressed. The multiple and diverse abnormalities detected in mutant DISC1 mice are reminiscent of findings in major mental diseases

Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene

12 pages, 10 figuresInternational audienceWe study tunneling of charge carriers in single- and bilayer graphene. We propose an explanation for non-zero "magic angles" with 100% transmission for the case of symmetric potential barrier, as well as for their almost-survival for slightly asymmetric barrier in the bilayer graphene known previously from numerical simulations. Most importantly, we demonstrate that these magic angles are not protected in the case of bilayer and give an explicit example of a barrier with very small electron transmission probability for any angles. This means that one can lock charge carriers by a p-n-p (or n-p-n) junction without opening energy gap. This creates new opportunities for the construction of graphene transistors

Patterned drug-eluting coatings for tracheal stents based on pla, plga, and pcl for the granulation formation reduction: In vivo studies

Expandable metallic stent placement is often the only way to treat airway obstructions. Such treatment with an uncoated stent causes granulation proliferation and subsequent restenosis, resulting in the procedure’s adverse complications. Systemic administration of steroids drugs in high dosages slows down granulation tissue overgrowth but leads to long-term side effects. Drug-eluting coatings have been used widely in cardiology for many years to suppress local granulation and reduce the organism’s systemic load. Still, so far, there are no available analogs for the trachea. Here, we demonstrate that PLA-, PCL-and PLGA-based films with arrays of microchambers to accommodate therapeutic substances can be used as a drug-eluting coating through securely fixing on the surface of an expandable nitinol stent. PCL and PLA were most resistant to mechanical damage associated with packing in delivery devices and making it possible to keep high-molecular-weight cargo. Low-molecular-weight methylprednisolone sodium succinate is poorly retained in PCL-and PLGA-based microchambers after immersion in deionized water (only 9.5% and 15.7% are left, respectively). In comparison, PLA-based microchambers retain 96.3% after the same procedure. In vivo studies on rabbits have shown that effective granulation tissue suppression is achieved when PLA and PLGA are used for coatings. PLGA-based microchamber coating almost completely degrades in 10 days in the trachea, while PLA-based microchamber films partially preserve their structure. The PCL-based film coating is most stable over time, which probably causes blocking the outflow of fluid from the tracheal mucosa and the aggravation of the inflammatory process against the background of low drug concentration. Combination and variability of polymers in the fabrication of films with microchambers to retain therapeutic compounds are suggested as a novel type of drug-eluting coating. © 2021 by the authors. Licensee MDPI, Basel, Switzerland