Fractional Lindstedt series

The parametric equations of the surfaces on which highly resonant quasi-periodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the perturbation parameter, i.e. they are not analytic functions of the perturbation parameter. However rather generally quasi-periodic motions whose frequencies satisfy only one rational relation ("resonances of order 1") admit formal perturbation expansions in terms of a fractional power of the perturbation parameter, depending on the degeneration of the resonance. We find conditions for this to happen, and in such a case we prove that the formal expansion is convergent after suitable resummation.Comment: 40 pages, 6 figure

Resummation of perturbation series and reducibility for Bryuno skew-product flows

We consider skew-product systems on T^d x SL(2,R) for Bryuno base flows close to constant coefficients, depending on a parameter, in any dimension d, and we prove reducibility for a large measure set of values of the parameter. The proof is based on a resummation procedure of the formal power series for the conjugation, and uses techniques of renormalisation group in quantum field theory.Comment: 30 pages, 12 figure

Control of magnetism in singlet-triplet superconducting heterostructures

We analyze the magnetization at the interface between singlet and triplet superconductors and show that its direction and dependence on the phase difference across the junction are strongly tied to the structure of the triplet order parameter as well as to the pairing interactions. We consider equal spin helical, opposite spin chiral, and mixed symmetry pairing on the triplet side and show that the magnetization vanishes at $\phi=0$ only in the first case, follows approximately a $\cos\phi$ behavior for the second, and shows higher harmonics for the last configuration. We trace the origin of the magnetization to the magnetic structure of the Andreev bound states near the interface, and provide a symmetry-based explanation of the results. Our findings can be used to control the magnetization in superconducting heterostructures and to test symmetries of spin-triplet superconductors.Comment: 5 pages, 3 figure

The use of the McIlwain L-parameter to estimate cosmic ray vertical cutoff rigidities for different epochs of the geomagnetic field

Secular changes in the geomagnetic field between 1955 and 1980 have been large enough to produce significant differences in both the verical cutoff rigidities and in the L-value for a specified position. A useful relationship employing the McIlwain L-parameter to estimate vertical cutoff rigidities has been derived for the twenty-five year period

Periodic solutions for a class of nonlinear partial differential equations in higher dimension

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases where the bifurcation equation is infinite-dimensional, such as the nonlinear Schroedinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.Comment: 34 page

Abdominal nodal localization of Castleman's disease: report of a case.

Abstract Introduction Castleman's disease (CD) is a rare benign disorder that may grow in any area where lymphoid tissue is normally present but the most frequent site is mediastinum (67%); the abdomen is rarely affected by this pathology. In the pathogenesis of CD an important role could be played by HHV-8. Diagnosis is difficult and the diagnostic certainty is obtained only by histological examination. For this disease there is no gold-standard treatment. Case report We report the case of a woman of 33 years of age affected by a rare form of abdominal nodal localization of Castleman's Disease for which the patient underwent surgery. Conclusion CD must be included in the differential diagnosis of retroperitoneal tumors even though the definitive diagnosis can only be achieved by histological and immunohistochemical examination. In the case of single location, the treatment of choice is surgical removal

Estimating the change in asymptotic direction due to secular changes in the geomagnetic field

The concept of geomagnetic optics, as described by the asymptotic directions of approach, is extremely useful in the analysis of cosmic radiation data. However, when changes in cutoff occur as a result of evolution in the geomagnetic field, there are corresponding changes in the asymptotic cones of acceptance. A method is introduced of estimating the change in the asymptotic direction of approach for vertically incident cosmic ray particles from a reference set of directions at a specific epoch by considering the change in the geomagnetic cutoff

Practice Schedule And The Learning Of Motor Skills In Children And Adults: Teaching Implications

Understanding how motor skills are learned influences how one teaches effective motor skill attainment. Educators must ask, “Does repetitive practice of the same task make for better performance or does contextual variability (random practice) offer some benefit when learning motor skills?” Studies on the effects of Contextual Interference may provide some insight. Contextual interference (CI) studies typically use simple tasks involving movements already acquired by adults, which may account for random practice benefits. In contrast, children do not consistently demonstrate CI effects, as tasks usually require acquisition of a new movement pattern. In this experiment, adults and children ((8-10 yrs old) threw a Frisbee to targets for 54 trials under random or blocked conditions. Having had considerable throwing experience with other throwing objects, adults were expected to benefit from random practice. For children, a blocked practice advantage was predicted as it provides for devising and stabilizing a suitable movement pattern. Retention/retraining trials were administered 30 minutes after acquisition and seven days later. Two transfer tests were given after the delayed retention test: (a) same throwing object/different target distances (SODT), which required re-scaling the practiced movement, and (b) different throwing object (ropeball)/same target distances (DOST) which required a new movement pattern. Throwing accuracy was measured by absolute error from the target. Both age groups showed a blocked practice benefit on retention and SODT transfer tests. Findings from this experiment suggest that task variables and stage of learning are important determinants of CI effects and thus should influence how we teach motor skill attainment