Complexity and integrability in 4D bi-rational maps with two invariants

In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most quadratic growth. Cubic growth may reflect the existence of non-elliptic fibrations of invariants, whereas we conjecture that the exponentially growing cases lack the necessary conditions for the applicability of the discrete Liouville theorem.Comment: 16 pages, 2 figure

Effects on haemostasis of hormone replacement therapy with transdermal estradiol and oral sequential medroxyprogesterone acetate: A 1-year, double-blind, placebo-controlled study (Article)

After menopause the haemostatic balance shifts towards a latent hypercoagulable state. To evaluate the effects of two regimens of transdermal estradiol (E2) combined with progestin on the balance between procoagulant factors and inhibitors, 255 women in physiological menopause for 1-5 years were randomly allocated to 1 year of treatment with cyclic transdermal E2 (50 μg/day for 21 days) plus medroxyprogesterone acetate (MPA) (10 mg/day from days 10 to 21), continuous transdermal E2 (50 μg/day for 28 days) plus MPA (10 mg/day from days 14 to 25), or placebo. Fibrinogen, factor VII (FVII), factor VIII:C (FVIII:C), antithrombin m (ATIll); protein C, protein S, heparin cofactor II (HCII) and plasminogen activator inhibitor (PAI-1) levels were measured at baseline and after 6 and 12 cycles. 167 women who took the treatment for at least 6 cycles were evaluable. The continuous treatment group had significantly lower final values of fibrinogen, FVII, ATIII, protein S and HCII than the placebo group; the cyclic treatment reduced fibrinogen in comparison with placebo but the difference was not significant. In conclusion, both regimens produce a clinically relevant decrease of fibrinogen levels; the continuous regimen affects also the levels of FVII and inhibitors suggesting that the haemostatic balance is shifted to a more physiological state

Antiproton stopping power in He in the energy range 1-900 keV and the Barkas effect

The p stopping power in helium from 1 keV kinetic energy is evaluated. Contrary to the effect observed around and below the maximum, Obelix data indicate a p stopping power higher than that for proton, the difference being of the order of 15 ± 5% at ≈ 700 keV. The result contributes to assert the fundamental difference between p stoppings in the simplest gases (He, H2 ) and in solid targets below some MeV