Integrability and Ergodicity of Classical Billiards in a Magnetic Field

We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not trivially integrable can be described by a "bouncing map". We compute a general expression for the Jacobian matrix of this map, which allows to determine stability and bifurcation values of specific periodic orbits. In some cases, the bouncing map is a twist map and admits a generating function which is useful to do perturbative calculations and to classify periodic orbits. We prove that billiards in convex domains with sufficiently smooth boundaries possess invariant tori corresponding to skipping trajectories. Moreover, in strong field we construct adiabatic invariants over exponentially large times. On the other hand, we present evidence that the billiard in a square is ergodic for some large enough values of the magnetic field. A numerical study reveals that the scattering on two circles is essentially chaotic.Comment: Explanations added in Section 5, Section 6 enlarged, small errors corrected; Large figures have been bitmapped; 40 pages LaTeX, 15 figures, uuencoded tar.gz. file. To appear in J. Stat. Phys. 8

Married women's decision making power on modern contraceptive use in urban and rural southern Ethiopia

<p>Abstract</p> <p>Background</p> <p>Women in developing countries are either under collective decision making with their partners or completely rely on the male partner's decision on issues that affect their reproductive live. Identifying the major barriers of married women's decision making power on contraceptive use has significant relevance for planning contextually appropriate family planning interventions. The objective of this study was to determine current modern contraceptive practices and decision making power among married women in Tercha Town and surrounding rural areas of Dawro zone, Southern Ethiopia.</p> <p>Methods</p> <p>Community based comparative cross-sectional design with both quantitative and Qualitative study has been employed in March and April 2010. The respondents were 699 married women of child bearing age from urban and rural parts of Dawro zone. After conducting census, we took the sample using simple random sampling technique.</p> <p>Results</p> <p>Current modern contraceptive use among married women in the urban was 293 (87.5%) and 243 (72.8%) in rural. Married women who reside in urban area were more likely to decide on the use of modern contraceptive method than rural women. Having better knowledge about modern contraceptive methods, gender equitable attitude, better involvement in decisions related to children, socio-cultural and family relations were statistically significant factors for decision making power of women on the use of modern contraceptive methods in the urban setting. Better knowledge, fear of partner's opposition or negligence, involvement in decisions about child and economic affairs were statistically significant factors for better decision making power of women on the use of modern contraceptive methods in the rural part.</p> <p>Conclusions</p> <p>High level of current modern contraceptive practice with reduced urban-rural difference was found as compared to regional and national figures. Urban women had better power to make decisions on modern contraceptive than rural women. Modern family planning interventions in the area should be promoted by considering empowering of women on modern contraceptive use decision making.</p

A 3-year multicentre randomized controlled trial of etonogestrel- and levonorgestrel-releasing contraceptive implants, with non-randomized matched copper-intrauterine device controls

STUDY QUESTION Is there any difference in the clinical performance of the 3-year one-rod etonogestrel (ENG)- and the 5-year two-rod levonorgestrel (LNG)-releasing contraceptive implants during 3 years of insertion, and between implant and intrauterine device (IUD) contraception, in particular complaints possibly related to hormonal contraceptives? SUMMARY ANSWER The cumulative contraceptive effectiveness after 3 years and method continuation through 2.5 years were not significantly different between ENG and LNG implants, but both outcomes were significantly worse in the non-randomized age-matched group of IUD users than in the combined implant group. WHAT IS KNOWN ALREADY ENG- and LNG-releasing implants are safe and highly efficacious contraceptives with pregnancy rates reported to be 0.0-0.5 per 100 women-years (W-Y). No head-to-head comparative study of the two implants has been undertaken, and little information is available on comparisons of complaints of side effects of implant and copper IUD users. STUDY DESIGN, SIZE, DURATION This was an open parallel group RCT with 1:1 allocation ratio of the ENG and the LNG implants with non-randomized control group of women choosing TCu380A IUD to address lack of reliable data on common side effects typically attributed to the use of progestogen-only contraceptives. After device(s) placement, follow-ups were at 2 weeks, 3 and 6 months, and semi-annually thereafter for 3 years or until pregnancy, removal or expulsion of the implant/IUD occurred. PARTICIPANTS, SETTING, METHODS The study took place in family planning clinics in Brazil, Chile, Dominican Republic, Hungary, Thailand, Turkey and Zimbabwe. Women seeking long-term contraception were enlisted after an eligibility check and informed consent, and 2982 women were enrolled: 1003, 1005 and 974 in the ENG-implant, LNG-implant and IUD groups, respectively; 995, 997 and 971, respectively, were included in the per protocol analysis reported here. MAIN RESULTS AND THE ROLE OF CHANCE ENG and LNG implants each had the same 3-year cumulative pregnancy rate of 0.4 per 100 W-Y [95% confidence interval (CI) 0.1-1.4]. A weight of ≥70 kg at admission was unrelated to pregnancy. Method continuation rates for ENG and LNG implants at 2.5 years were 69.8 (95% CI 66.8-72.6) and 71.8 per 100 W-Y (68.8-74.5), and at 3 years 12.1 (95% CI 5.2-22.0) and 52.0 per 100 W-Y (95% CI 41.8-61.2), respectively. Bleeding disturbances, the most frequent reason for method discontinuation, were significantly more common in the ENG group [16.7 (95% CI 14.4-19.3)] than in the LNG group [12.5 (95% CI 10.5-14.9)] (P 0.019). The 3-year cumulative loss to follow-up was lower in the ENG- than in the LNG-implant group, 8.1 (95% CI 6.4-10.2) and 14.4 per 100 W-Y (95% CI 12.1-17.1), respectively. The median duration of implant removal was 50 s shorter among women with ENG than among women with LNG implant (P < 0.0001). In the observational comparison between IUD and implant users, the 3-year relative risk for pregnancy in IUD group compared with the combined implant group was 5.7 per 100 W-Y (95% CI 4.4-7.3) (P = 0.0003). The 3-year expulsion rate of the IUD was 17.8 per 100 W-Y (95% CI 14.5-21.9), while the discontinuation rate for bleeding disturbances was 8.5 (95% CI 6.7-10.9). Frequency of complaints of headache and dizziness was not significantly different between implant and IUD users (P = 0.16 and 0.77, respectively), acne and bleeding irregularities were more frequent among implant users (P < 0.0001), while heavy bleeding and lower abdominal pain occurred more often among IUD than implant users (P < 0.0001). LIMITATIONS, REASONS FOR CAUTION Few women were ≤19 years old or nulligravida, the proportion of implant users ≥70 kg was <20% and <8% were obese. WIDER IMPLICATIONS OF THE FINDINGS Findings of the study can inform policy makers and clinicians about choice of implant, but also about TCu380A IUD in relation to implants. STUDY FUNDING/COMPETING INTEREST(S) UNDP/UNFPA/WHO/UNICEF/World Bank Special Programme of Research, Development and Research Training in Human Reproduction (HRP), Department of Reproductive Health and Research (RHR), World Health Organization (WHO). This report contains the views of an international expert group and does not necessarily represent the decisions or the stated policy of the WHO. TRIAL REGISTRATION ISRCTN33378571 registered on 22 March 2004. The first participant was enrolled on 12 May 200

Non-pharmacological management of osteoporosis: a consensus of the Belgian Bone Club

This consensus article reviews the various aspects of the non-pharmacological management of osteoporosis, including the effects of nutriments, physical exercise, lifestyle, fall prevention, and hip protectors. Vertebroplasty is also briefly reviewed. Non-pharmacological management of osteoporosis is a broad concept. It must be viewed as an essential part of the prevention of fractures from childhood through adulthood and the old age. The topic also includes surgical procedures for the treatment of peripheral and vertebral fractures and the post-fracture rehabilitation. The present document is the result of a consensus, based on a systematic review and a critical appraisal of the literature. Diets deficient in calcium, proteins or vitamin D impair skeletal integrity. The effect of other nutriments is less clear, although an excessive consumption of sodium, caffeine, or fibres exerts negative effects on calcium balance. The deleterious effects of tobacco, excessive alcohol consumption and a low BMI are well accepted. Physical activity is of primary importance to reach optimal peak bone mass but, if numerous studies have shown the beneficial effects of various types of exercise on bone mass, fracture data as an endpoint are scanty. Fall prevention strategies are especially efficient in the community setting, but less evidence is available about their effectiveness in preventing fall-related injuries and fractures. The efficacy of hip protectors remains controversial. This is also true for vertebroplasty and kyphoplasty. Several randomized controlled studies had reported a short-term advantage of vertebroplasty over medical treatment for pain relief, but these findings have been questioned by recent sham-controlled randomized clinical studies

Provider and lay perspectives on intra-uterine contraception: a global review

BACKGROUND: Intra-uterine contraception (IUC) involves the use of an intra-uterine device (IUD), a highly effective, long-acting, reversible contraceptive method. Historically, the popularity of IUC has waxed and waned across different world regions, due to policy choices and shifts in public opinion. However, despite its advantages and cost-effectiveness for programmes, IUC's contribution to contraceptive prevalence is currently negligible in many countries. This paper presents the results of a systematic review of the global literature on provider and lay perspectives on IUC. It aims to shed light on the reasons for low use of IUC and reflect on potential opportunities for the method's promotion. METHODS: A systematic search of the literature was conducted in four peer-reviewed journals and four electronic databases (MEDLINE, EMBASE, POPLINE, and Global Health). Screening resulted in the inclusion of 68 relevant publications. RESULTS: Most included studies were conducted in areas where IUD use is moderate or low. Findings are similar across these areas. Many providers have low or uneven levels of knowledge on IUC and limited training. Many wrongly believe that IUC entails serious side effects such as pelvic inflammatory disease (PID), and are reluctant to provide it to entire eligible categories, such as HIV-positive women. There is particular resistance to providing IUC to teenagers and nulliparae. Provider opinions may be more favourable towards the hormonal IUD. Some health-care providers choose IUC for themselves. Many members of the public have low knowledge and unfounded misconceptions about IUC, such as the fear of infertility. Some are concerned about the insertion and removal processes, and about its effect on menses. However, users of IUC are generally satisfied and report a number of benefits. Peers and providers exert a strong influence on women's attitudes. CONCLUSION: Both providers and lay people have inaccurate knowledge and misconceptions about IUC, which contribute to explaining its low use. However, many reported concerns and fears could be alleviated through correct information. Concerted efforts to train providers, combined with demand creation initiatives, could therefore boost the method's popularity. Further research is needed on provider and lay perspectives on IUDs in low- and middle-income countries