1,690 research outputs found
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
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
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
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
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