Onset of chaos in a single-phase power electronic inverter.

Supported by experiments on a power electronic DC/AC converter, this paper considers an unusual transition from the domain of stable periodic dynamics (corresponding to the desired mode of operation) to chaotic dynamics. The behavior of the converter is studied by means of a 1D stroboscopic map derived from a non-autonomous ordinary differential equation with discontinuous right-hand side. By construction, this stroboscopic map has a high number of border points. It is shown that the onset of chaos occurs stepwise, via irregular cascades of different border collisions, some of which lead to bifurcations while others do not.

Chronic hepatitis B in pregnant women: Current trends and approaches.

Chronic hepatitis B (CHB) is a significant public health problem worldwide. The aim of the present review is to summarize the actual trends in the management of CHB in pregnant women. The prevalence of hepatitis B virus (HBV) infection in pregnant women is usually comparable to that in the general population in the corresponding geographic area. All women have to be screened for hepatitis B surface antigen (HBsAg) during pregnancy. Additional examinations of pregnant women with CHB may include maternal hepatitis B e antigen, HBV viral load, alanine aminotransferase level, and HBsAg level. The management of pregnancy depends on the phase of the HBV infection, which has to be determined before pregnancy. In women of childbearing age with CHB, antiviral therapy can pursue two main goals: Treatment of active CHB, and vertical transmission prevention. During pregnancy, tenofovir is the drug of choice in both cases. A combination of hepatitis B immunoglobulin and vaccine against hepatitis B should be administered within the first 12 h to all infants born to mothers with CHB. In such cases, there are no contraindications to breastfeeding.

Nordmark map and the problem of large-amplitude chaos in impact oscillators.

Physical experiments have long revealed that impact oscillators commonly exhibit large-amplitude chaos over a narrow band of parameter values close to grazing bifurcations. This phenomenon is not explained by the square-root singularity of the Nordmark map, which captures the local dynamics to leading order, because this map does not exhibit such dynamics. In this paper, we compare a Poincaré map for a prototypical impact oscillator model with the corresponding Nordmark map. Though the maps agree to leading order, the Poincaré map exhibits a large-amplitude chaotic attractor while the Nordmark map does not because part of the attractor resides in a region of phase space where the two maps differ significantly.

Codimension-three bifurcations: explanation of the complex one-, two-, and three-dimensional bifurcation structures in nonsmooth maps.

Many physical and engineering systems exhibit cascades of periodic attractors arranged in period increment and period adding sequences as a parameter is varied. Such systems have been found to yield piecewise smooth maps, and in some cases the obtained map is discontinuous. By investigating the normal form of such maps, we have detected a type of codimension-three bifurcation which serves as the organizing center of periodic and aperiodic dynamics in the parameter space. The results will help in understanding the occurrence and structure of such cascades observed in many nonsmooth systems in science and engineering.

HBsAg level and hepatitis B viral load correlation with focus on pregnancy.

BACKGROUND: Viral load measurement is necessary to estimate mother-to-child transmission risk for women with chronic hepatitis B (CHB), however, it is expensive. The present study aimed to investigate the relationship between HBsAg and hepatitis B virus (HBV) DNA levels, and to determine potential applications of HBsAg level monitoring for estimating viral load. METHODS: 85 patients with CHB (31 pregnant women, 26 non-pregnant women, 28 men) were included in the study. HBV DNA level was measured by real-time PCR, and HBsAg level by chemiluminescent immunoassay method. Dependency between viral load and HBsAg level was determined by Spearman correlation coefficient ρ. RESULTS: The correlation between HBsAg and HBV DNA levels was significant for all patients [ρ=0.3762 (P<0.0005; n=85)]. In the group of pregnant women, a low (unmeasurable) HBV DNA level led to a decrease in the Spearman coefficient ρ. In almost all cases a low level of the HBsAg corresponded to a low HBV DNA level. Only 2 patients had a low level of HBsAg and a relatively high viral load. By contrast, a high HBsAg level was observed in patients both with high and low viral load. CONCLUSIONS: Correlation between HBsAg and HBV DNA levels is significant. In most cases, a low level of HBsAg indicates a low HBV DNA level, whereas a high HBsAg level does not always correspond to a high viral load. The measurement of HBV DNA level is necessary for pregnant women with a high HBsAg level.

Border-collision period-doubling scenario.

Using a one-dimensional dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, we investigate the border-collision period-doubling bifurcation scenario. In contrast to the classical period-doubling scenario, this scenario is formed by a sequence of pairs of bifurcations, whereby each pair consists of a border-collision bifurcation and a pitchfork bifurcation. The characteristic properties of this scenario, like symmetry-breaking and symmetry-recovering as well as emergence of coexisting attractors and noninvariant attractive sets, are investigated.