Stability of equilibrium states in the Zhukovski case of heavy gyrostat using algebraic methods

We study the stability of the equilibrium points of a skew product system. We analyze the possibility to construct a Lyapunov function using a set of conserved quantities and solving an algebraic system. We apply the theoretical results to study the stability of an equilibrium state of a heavy gyrostat in the Zhukovski case

Problemas de proporcionalidad resueltos por campesinos chilenos

Este artículo -relativo a la proporcionalidad- forma parte de un trabajo anterior (Soto, 1992), en el cual se planteaba la interrogante sobre las estrategias y procedimientos de resolución de problemas y de operaciones utilizadas por algunos campesinos de Chile. Al revisar, aun de manera rápida y somera, algunos problemas o situaciones matemáticas -relacionadas generalmente con las matemáticas elementales-, que encontramos a diario en la vida profesional, familiar, política o social, podemos constatar que el concepto de proporcionalidad desempeña un rol fundamental, "sus aplicaciones son innumerables y están presentes en todos los sectores de la actividad humana" (Dupuis y Pluvinage, 1981, p. 167)

Socioeconomic disparities in diet vary according to migration status among adolescents in Belgium

Little information concerning social disparities in adolescent dietary habits is currently available, especially regarding migration status. The aim of the present study was to estimate socioeconomic disparities in dietary habits of school adolescents from different migration backgrounds. In the 2014 cross-sectional Health Behavior in School-Aged Children survey in Belgium, food consumption was estimated using a self-administrated short food frequency questionnaire. In total, 19,172 school adolescents aged 10-19 years were included in analyses. Multilevel multiple binary and multinomial logistic regressions were performed, stratified by migration status (natives, 2nd- and 1st-generation immigrants). Overall, immigrants more frequently consumed both healthy and unhealthy foods. Indeed, 32.4% of 1st-generation immigrants, 26.5% of 2nd-generation immigrants, and 16.7% of natives consumed fish two days a week. Compared to those having a high family affluence scale (FAS), adolescents with a low FAS were more likely to consume chips and fries once a day (vs. <once a day: Natives aRRR = 1.39 (95%CI: 1.12-1.73); NS in immigrants). Immigrants at schools in Flanders were less likely than those in Brussels to consume sugar-sweetened beverages 2-6 days a week (vs. once a week: Natives aRRR = 1.86 (95%CI: 1.32-2.62); 2nd-generation immigrants aRRR = 1.52 (1.11-2.09); NS in 1st-generation immigrants). The migration gradient observed here underlines a process of acculturation. Narrower socioeconomic disparities in immigrant dietary habits compared with natives suggest that such habits are primarily defined by culture of origin. Nutrition interventions should thus include cultural components of dietary habits

Generic stability of dissipative non-relativistic and relativistic fluids

The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium is asymptotically stable in both cases due to purely thermodynamic restrictions; the only requirements are the thermodynamic stability and the nonnegativity of the transport coefficients.Comment: 22 page

An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

Stability analysis of cosmological models through Liapunov's method

We investigate the general asymptotic behaviour of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Liapunov's method. This method provides information not only about the asymptotic stability of a given equilibrium point but also about its basin of attraction. This cannot be obtained by the usual methods found in the literature, such as linear stability analysis or first order perturbation techniques. Moreover, Liapunov's method is also applicable to non-autonomous systems. We use this advantadge to investigate the mechanism of reheating for the inflaton field in FRW models.Comment: Latex file, 8 pages, no figures, accepted for publication in Class. & Quant. Gra

Anaesthesia in a toxic environment: Pressurized IntraPeritoneal Aerosol Chemotherapy. A retrospective analysis

Objective: Pressurised intraperitoneal aerosol chemotherapy (PIPAC) is a new type of intraperitoneal chemotherapy for peritoneal carcinosis via minimally invasive surgery. This technique’s specificity is the remote application of the therapy because of the potential risk of exposure to toxic products. The present paper summarises the important aspects of PIPAC and analyses the anaesthetic outcomes. Methods: This retrospective study included all patients undergoing PIPAC treatment between January 2015 and February 2018. Data on pro- tocol adherence and perioperative anaesthetic complications and postoperative nausea and vomiting (PONV) and pain levels (visual analogue scale 0–10) from recovery room to 72 h were analysed. Results: The overall analysis included 193 PIPAC procedures on 87 patients. Protocol adherence was high as regards the use of propofol (100%), rocuronium (98%), antiemetic prophylaxis (99%) and lidocaine intravenous (i.v.) (87%). No accidental exposure to chemotherapy oc- curred during the study period. Of the 87 patients, 6.3% suffered delayed recovery, 58% due to hypothermia and 42% due to excessive sedation or curarisation. In the recovery room, 16% of patients suffered moderate to severe pain, requiring &gt;8 mg of morphine i.v., with average doses of 13.7 mg. Median postoperative pain scores were 1 and 3 at 12 h and 0 and 0 at 72 h at rest and mobilisation, respectively. PONV was observed in &lt;10% of patients during the first 12 h, but in 40% at 72 h. Conclusion: A dedicated anaesthetic protocol and intraoperative safety checklist facilitates safe, well-tolerated anaesthesia for PIPAC treatments

Island and The Construction of a Maritime Boundary: Pushing The Limits of State Sovereignity

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Fake Superpotential for Large and Small Extremal Black Holes

We consider the fist order, gradient-flow, description of the scalar fields coupled to spherically symmetric, asymptotically flat black holes in extended supergravities. Using the identification of the fake superpotential with Hamilton's characteristic function we clarify some of its general properties, showing in particular (besides reviewing the issue of its duality invariance) that W has the properties of a Liapunov's function, which implies that its extrema (associated with the horizon of extremal black holes) are asymptotically stable equilibrium points of the corresponding first order dynamical system (in the sense of Liapunov). Moreover, we show that the fake superpotential W has, along the entire radial flow, the same flat directions which exist at the attractor point. This allows to study properties of the ADM mass also for small black holes where in fact W has no critical points at finite distance in moduli space. In particular the W function for small non-BPS black holes can always be computed analytically, unlike for the large black-hole case.Comment: 30 pages, LaTeX source. Discussion on the radial evolution of the scalar fields, in relation to the symmetries of the W-function, extended. Table 1 added. Typos correcte