Integrable and superintegrable systems associated with multi-sums of products

We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.Comment: 26 pages, submitted to Proceedings of the royal society

Conservation agriculture/farmers mechanization: Africa RISING science, innovations and technologies with scaling potential from the Ethiopian Highlands

United States Agency for International Developmen

Allograft and Xenograft Acceptance under FK‐506 and Other Immunosuppressant Treatment

We will focus on two issues, both involving, but not confined to FK-506: first, the meaning of the graft acceptance, which is, after all, the objective of immunosuppression for the transplant surgeon; and second, how to take the next great step of xenotransplantation

On integrability of Hirota-Kimura type discretizations

We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.Comment: 47 pages, some minor change

A comparison of methods to adjust for continuous covariates in the analysis of randomised trials

BACKGROUND: Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy. METHODS: We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets. RESULTS: Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall. CONCLUSIONS: For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt

Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators

Let B=A+K where A is a bounded selfadjoint operator and K is an element of the von Neumann-Schatten ideal S_p with p>1. Let {\lambda_n} denote an enumeration of the discrete spectrum of B. We show that \sum_n \dist(\lambda_n, \sigma(A))^p is bounded from above by a constant multiple of |K|_p^p. We also derive a unitary analog of this estimate and apply it to obtain new estimates on zero-sets of Cauchy transforms.Comment: Differences to previous version: Extended Introduction, new Section 5, additional references. To appear in Int. Eq. Op. Theor

Core pinning by intragranular nanoprecipitates in polycrystalline MgCNi_3

The nanostructure and magnetic properties of polycrystalline MgCNi_3 were studied by x-ray diffraction, electron microscopy, and vibrating sample magnetometry. While the bulk flux-pinning force curve F_p(H) indicates the expected grain-boundary pinning mechanism just below T_c = 7.2 K, a systematic change to pinning by a nanometer-scale distribution of core pinning sites is indicated by a shift of F_p(H) with decreasing temperature. The lack of scaling of F_p(H) suggests the presence of 10 to 20% of nonsuperconducting regions inside the grains, which are smaller than the diameter of fluxon cores 2xi at high temperature and become effective with decreasing temperature when xi(T) approaches the nanostructural scale. Transmission electron microscopy revealed cubic and graphite nanoprecipitates with 2 to 5 nm size, consistent with the above hypothesis since xi(0) = 6 nm. High critical current densities, more than 10^6 A/cm^2 at 1 T and 4.2 K, were obtained for grain colonies separated by carbon. Dirty-limit behavior seen in previous studies may be tied to electron scattering by the precipitates, indicating the possibility that strong core pinning might be combined with a technologically useful upper critical field if versions of MgCNi_3 with higher T_c can be found.Comment: 5 pages, 6 figures, submitted to PR