Asymmetry Coefficients as Indicators of Chaos

The aim of this paper is to present a new simple indicator of chaos derived from the dynamics of the motion. For this purpose statistical methods are used. A function describing the motion of the analyzed system (in the example under consideration, the time dependence of the angle of a damped driven pendulum, ω(t)) is recorded in time intervals t∊〈 $T_{s}$, $T_{f_{k}}$〉, k = 1, 2,...K, with $T_{f_{k}}$ > $T_{f_{k-1}}$. Each of the recorded functions is considered as a statistical distribution. The asymmetry coefficients of the set of distributions form a series and their behavior in periodic and chaotic regions is compared. It is shown that the behavior of this series in the chaotic and in the periodic regimes is entirely different. The changes of the asymmetry coefficients for the periodic cases are very regular and for the chaotic ones - random. In periodic cases, the coefficients converge to zero when the length of the distribution increases

Asymmetry Coefficients as Indicators of Chaos: Hyperchaotic Qi System

Statistical properties of the hyperchaotic Qi system are studied. The theory, recently formulated and applied for the damped driven pendulum, is used in this investigation. Asymmetry coefficients, related to the statistical moments of distributions composed from the time-series, are shown to behave in a different way for periodic, chaotic and hyperchaotic solutions and are proposed as indicators of chaos and hyperchaos

Asymmetry Coefficients as Indicators of Chaos

The aim of this paper is to present a new simple indicator of chaos derived from the dynamics of the motion. For this purpose statistical methods are used. A function describing the motion of the analyzed system (in the example under consideration, the time dependence of the angle of a damped driven pendulum, ω(t)) is recorded in time intervals t∊〈 $T_{s}$, $T_{f_{k}}$〉, k = 1, 2,...K, with $T_{f_{k}}$ > $T_{f_{k-1}}$. Each of the recorded functions is considered as a statistical distribution. The asymmetry coefficients of the set of distributions form a series and their behavior in periodic and chaotic regions is compared. It is shown that the behavior of this series in the chaotic and in the periodic regimes is entirely different. The changes of the asymmetry coefficients for the periodic cases are very regular and for the chaotic ones - random. In periodic cases, the coefficients converge to zero when the length of the distribution increases

Normal Terms of Hamiltonian Systems

All the transformation matrices for a Hamiltonian with two and three degrees of freedom are found. They are calculated using algorithms for the linear normalization of Hamiltonian systems near the equilibrium point

Analytical theory of the motion of Phobos: A comparison with numerical integration

A new theory of the motion of Phobos – a moon of Mars – has been presented. The theory is based on the problem of two fixed gravitational centers. The analytical functions appearing in this model are expressed as a series of the third order with respect to the J2 and $\frac{J_3}{J_2}$ zonal harmonics of Mars. The interaction between Phobos and Mars is described by a potential consisting of very many elements. The zonal harmonics of order ≤12 and tesseral harmonics of order ≤6 are taken into account. Interactions of Phobos with the Sun, Jupiter, Deimos – another moon of Mars, and the tidal potential of the Sun are also taken into account

Periodic Motion of Rigid Body in Circular Orbit

The periodic rotations of a symmetric rigid body close to the flat motions are analytically determined. Their orbital stability is investigated. Calculations are done up to the second order terms of a small parameter

Higher diversity in fungal species discriminates children with type 1 diabetes mellitus from healthy control

Beata Kowalewska,1 Katarzyna Zorena,2 Małgorzata Szmigiero-Kawko,3 Piotr Wąż,4 Małgorzata Myśliwiec3 1Department of Tropical Medicine and Epidemiology, Institute of Maritime and Tropical Medicine, 2Department of Immunology and Environmental Microbiology, 3Clinic of Paediatrics, Diabetology and Endocrinology, 4Department of Nuclear Medicine, Medical University of Gdańsk, Gdańsk, Poland Objective: To conduct qualitative and quantitative assessment of yeast-like fungi in the feces of children and adolescents with type 1 diabetes mellitus (T1DM) with respect to their metabolic control and duration of the disease.Materials and methods: The studied materials included samples of fresh feces collected from 53 children and adolescents with T1DM. Control group included 30 age- and sex-matched healthy individuals. Medical history was taken and physical examination was conducted in the two study arms. Prevalence of the yeast-like fungi in the feces was determined as well as their amounts, species diversity, drug susceptibility, and enzymatic activity.Results: The yeast-like fungi were found in the samples of feces from 75.4% of T1DM patients and 70% controls. In the group of T1DM patients, no correlation was found between age (Rs=0.253, P=0.068), duration of diabetes (Rs=−0.038, P=0.787), or body mass index (Rs=0.150, P=0.432) and the amount of the yeast-like fungi isolated in the feces. Moreover, no correlation was seen between the amount of the yeast-like fungi and glycated hemoglobin (Rs=0.0324, P=0.823), systolic blood pressure (Rs=0.102, P=0.483), or diastolic blood pressure (Rs=0.271, P=0.345).Conclusion: Our research has shown that children and adolescents with T1DM show higher species diversity of the yeast-like fungi, with Candida albicans being significantly less prevalent versus control subjects. Moreover, fungal species in patients with T1DM turn out to be more resistant to antifungal treatment. Keywords: children, diabetes mellitus type 1, yeast-like fungi, drug susceptibility, metabolic control, duration of the diseas