A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice

It is shown that some special reduction of infinite 1D Toda lattice gives differential constraints compatible with the Kaup -- Broer system. A family of the travelling wave solutions of the Kaup -- Broer system and its higher version is constructed.Comment: LaTeX, uses IOP styl

Dissipative Boussinesq System of Equations in the B\'enard-Marangoni Phenomenon

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a B\'enard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussinesq system is obtained. Finnaly, some speculations are made on the nature of the physical phenomena described by this system of equations.Comment: 15 Pages, REVTEX (Version 3.0), no figure

Bifurcation curves of subharmonic solutions

We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order -- i.e. when the subharmonic Melnikov function vanishes identically. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalisations to higher orders of the subharmonic Melnikov function are also identically zero. In general the bifurcation curves are not analytic, and even when they are smooth they can form cusps at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The technique we use is completely different from that of Chow and Hale, and it is essentially based on rigorous perturbation theory.Comment: 29 pages, 2 figure

Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges.Comment: Talk given at the Workshop "Nonlinear Physics: Theory and Experiment. V", Gallipoli (Lecce, Italy), 12-21 June, 200

Clinical and self-reported markers of reproductive function in female survivors of childhood Hodgkin lymphoma

Purpose: To evaluate the impact of treatment for Hodgkin lymphoma (HL) on clinical reproductive markers and pregnancy outcomes.Methods: This study was embedded within the DCOG LATER-VEVO study; a Dutch, multicenter, retrospective cohort study between 2004 and 2014. Serum anti-Müllerian hormone (AMH), follicle stimulating hormone (FSH), inhibin B, antral follicle count (AFC), and self-reported (first) pregnancy outcomes were evaluated in female childhood HL survivors and controls.Results: 84 HL survivors and 798 controls were included, aged 29.6 and 32.7 years old at time of assessment. Median age at HL diagnosis was 13.4 years. Cyclophosphamide equivalent dose (CED-score) exceeded 6000 mg/m2 in 56 women and 14 survivors received pelvic irradiation.All clinical markers were significantly deteriorated in survivors (odds-ratio for low AMH (&lt; p10) 10.1 [95% CI 4.9; 20.6]; low AFC (&lt; p10) 4.6 [95% CI 2.1; 9.9]; elevated FSH (&gt; 10 IU/l) 15.3 [95% CI 5.7; 41.1], low Inhibin B (&lt; 20 ng/l) 3.6 [95% CI 1.7; 7.7], p &lt; 0.001). Pregnancy outcomes were comparable between survivors and controls (± 80% live birth, ± 20% miscarriage). However, survivors were significantly younger at first pregnancy (27.0 years vs 29.0 years, P = 0.04). Adjusted odds-ratio for time to pregnancy &gt; 12 months was 2.5 [95% CI 1.1; 5.6] in survivors, p = 0.031. Adverse outcomes were specifically present after treatment with procarbazine and higher CED-score.Conclusion: HL survivors appear to have an impaired ovarian reserve. However, chance to achieve pregnancy seems reassuring at a young age. Additional follow-up studies are needed to assess fertile life span and reproductive potential of HL survivors, in particular for current HL treatments that are hypothesized to be less gonadotoxic.</p

Structure and photophysics of indigoids for singlet fission: Cibalackrot

We report an investigation of structure and photophysics of thin layers of cibalackrot, a sturdy dye derived from indigo by double annulation at the central double bond. Evaporated layers contain up to three phases, two crystalline and one amorphous. Relative amounts of all three have been determined by a combination of X-ray diffraction and FT-IR reflectance spectroscopy. Initially, excited singlet state rapidly produces a high yield of a transient intermediate whose spectral properties are compatible with charge-transfer nature. This intermediate more slowly converts to a significant yield of triplet, which, however, does not exceed 100% and may well be produced by intersystem crossing rather than singlet fission. The yields were determined by transient absorption spectroscopy and corrected for effects of partial sample alignment by a simple generally applicable procedure. Formation of excimers was also observed. In order to obtain guidance for improving molecular packing by a minor structural modification, calculations by a simplified frontier orbital method were used to find all local maxima of singlet fission rate as a function of geometry of a molecular pair. The method was tested at 48 maxima by comparison with the ab initio Frenkel-Davydov exciton model. Published under license by AIP Publishing

Panorganismal metabolic response modeling of an experimental Echinostoma caproni infection in the mouse.

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