Foliar Application of N and Fe to Kentucky Bluegrass

The goal of the professional lawn care industry is to provide the homeowner with a dark green weed-free lawn. Members of this industry are interested in techniques to enhance the color of a turfgrass stand in lieu of excessive N fertilization. The purpose of this research was to evaluate the use of foliar applications of Fe alone or in combination with N on the color response of Kentucky bluegrass (Poa pratensis L.). Iron sulfate or an iron chelate was applied at the rate of 1.1, 2.2, or 4.5 kg Fe ha–1 in combination with either 0, 25, or 49 kg N ha–1 to a mixed ‘Columbia’/‘Touchdown’ Kentucky bluegrass turf growing on a Catlin silt loam (fine-silty, mixed, mesic Typic Argiudoll). Color ratings and clipping weights were determined on a weekly basis until treatment effects were no longer significant. In a separate experiment, both sources of Fe were applied at rates of 1.1 to 72.4 kg Fe ha–1 to Kentucky bluegrass to evaluate phytotoxicity. The color enhancement due to Fe applications without N lasted from several weeks to several months depending on the weather following application. Use of Fe during cool wet periods enhanced turf color for only 2 to 3 weeks and therefore, was considered of limited value. Iron applications during cool dry periods enhanced turf color for several months. The treatment of 2.2 kg ha–1 of Fe from iron chelate was judged to be the most effective Fe treatment because the color enhancement was usually equal to that provided by a 4.5 kg rate of either source but it did not result in any discoloration as was found with the 4.5 kg rate. Combining Fe with the 25 kg ha–1 rate of N resulted in color enhancement equal to that caused by applying 49 kg ha–1 of N alone. The results of the study indicate that combining Fe with N can result in acceptable turfgrass color with lower rates of N. No permanent damage was caused to turfs receiving Fe at rates up to 72.2 kg ha–1 although foliar phytotoxicity was observed

Strong Approximation of Empirical Copula Processes by Gaussian Processes

We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm

Semiclassical approximations for Hamiltonians with operator-valued symbols

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter $\varepsilon\ll 1$ controls the separation of time scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time $\varepsilon\to 0$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the $\varepsilon$-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an \epsi-dependent classical Hamilton function and an $\varepsilon$-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order $\varepsilon^2$. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was remove

Nonlinear coherent states and Ehrenfest time for Schrodinger equation

We consider the propagation of wave packets for the nonlinear Schrodinger equation, in the semi-classical limit. We establish the existence of a critical size for the initial data, in terms of the Planck constant: if the initial data are too small, the nonlinearity is negligible up to the Ehrenfest time. If the initial data have the critical size, then at leading order the wave function propagates like a coherent state whose envelope is given by a nonlinear equation, up to a time of the same order as the Ehrenfest time. We also prove a nonlinear superposition principle for these nonlinear wave packets.Comment: 27 page

Evidence for validity and reliability of a french version of the FAAM

BACKGROUND: The Foot and Ankle Ability Measure (FAAM) is a self reported questionnaire for patients with foot and ankle disorders available in English, German, and Persian. This study plans to translate the FAAM from English to French (FAAM-F) and assess the validity and reliability of this new version.METHODS: The FAAM-F Activities of Daily Living (ADL) and sports subscales were completed by 105 French-speaking patients (average age 50.5 years) presenting various chronic foot and ankle disorders. Convergent and divergent validity was assessed by Pearson's correlation coefficients between the FAAM-F subscales and the SF-36 scales: Physical Functioning (PF), Physical Component Summary (PCS), Mental Health (MH) and Mental Component Summary (MCS). Internal consistency was calculated by Cronbach's Alpha (CA). To assess test re-test reliability, 22 patients filled out the questionnaire a second time to estimate minimal detectable changes (MDC) and intraclass correlation coefficients (ICC).RESULTS: Correlations for FAAM-F ADL subscale were 0.85 with PF, 0.81 with PCS, 0.26 with MH, 0.37 with MCS. Correlations for FAAM-F Sports subscale were 0.72 with PF, 0.72 with PCS, 0.21 with MH, 0.29 with MCS. CA estimates were 0.97 for both subscales. Respectively for the ADL and Sports subscales, ICC were 0.97 and 0.94, errors for a single measure were 8 and 10 points at 95% confidence and the MDC values at 95% confidence were 7 and 18 points.CONCLUSION: The FAAM-F is valid and reliable for the self-assessment of physical function in French-speaking patients with a wide range of chronic foot and ankle disorders

Vibration Response Imaging: evaluation of rater agreement in healthy subjects and subjects with pneumonia

<p>Abstract</p> <p>Background</p> <p>We evaluated pulmonologists variability in the interpretation of Vibration response imaging (VRI) obtained from healthy subjects and patients hospitalized for community acquired pneumonia.</p> <p>Methods</p> <p>The present is a prospective study conducted in a tertiary university hospital. Twenty healthy subjects and twenty three pneumonia cases were included in this study. Six pulmonologists blindly analyzed images of normal subjects and pneumonia cases and evaluated different aspects of VRI images related to the quality of data aquisition, synchronization of the progression of breath sound distribution and agreement between the maximal energy frame (MEF) of VRI (which is the maximal geographical area of lung vibrations produced at maximal inspiration) and chest radiography. For qualitative assessment of VRI images, the raters' evaluations were analyzed by degree of consistency and agreement.</p> <p>Results</p> <p>The average value for overall identical evaluations of twelve features of the VRI image evaluation, ranged from 87% to 95% per rater (94% to 97% in control cases and from 79% to 93% per rater in pneumonia cases). Inter-rater median (IQR) agreement was 91% (82-96). The level of agreement according to VRI feature evaluated was in most cases over 80%; intra-class correlation (ICC) obtained by using a model of subject/rater for the averaged features was overall 0.86 (0.92 in normal and 0.73 in pneumonia cases).</p> <p>Conclusions</p> <p>Our findings suggest good agreement in the interpretation of VRI data between different raters. In this respect, VRI might be helpful as a radiation free diagnostic tool for the management of pneumonia.</p

Localized instabilities of the Wigner equation as a model for the emergence of Rogue Waves

In this paper, we model Rogue Waves as localized instabilities emerging from homogeneous and stationary background wavefields, under NLS dynamics. This is achieved in two steps: given any background Fourier spectrum P(k), we use the Wigner transform and Penrose’s method to recover spatially periodic unstable modes, which we call unstable Penrose modes. These can be seen as generalized Benjamin–Feir modes, and their parameters are obtained by resolving the Penrose condition, a system of nonlinear equations involving P(k). Moreover, we show how the superposition of unstable Penrose modes can result in the appearance of localized unstable modes. By interpreting the appearance of an unstable mode localized in an area not larger than a reference wavelength λ0 as the emergence of a Rogue Wave, a criterion for the emergence of Rogue Waves is formulated. Our methodology is applied to δ spectra, where the standard Benjamin–Feir instability is recovered, and to more general spectra. In that context, we present a scheme for the numerical resolution of the Penrose condition and estimate the sharpest possible localization of unstable modes. Keywords: Rogue Waves; Wigner equation; Nonlinear Schrodinger equation; Penrose modes; Penrose conditio