On the microlocal properties of the range of systems of principal type

The purpose of this paper is to study microlocal conditions for inclusion relations between the ranges of square systems of pseudodifferential operators which fail to be locally solvable. The work is an extension of earlier results for the scalar case in this direction, where analogues of results by L. H\"ormander about inclusion relations between the ranges of first order differential operators with coefficients in $C^\infty$ which fail to be locally solvable were obtained. We shall study the properties of the range of systems of principal type with constant characteristics for which condition (\Psi) is known to be equivalent to microlocal solvability.Comment: Added Theorem 4.7, Corollary 4.8 and Lemma A.4, corrected misprints. The paper has 40 page

Forage Production of Hay-Type Sorghum Cultivars

Forage production was measured from three cuttings of 14 hay-type sorghum-sudan entries. Total annual yield was greater from ‘AS5201’, ‘Sweet Sioux WMR’, and ‘AS9302’ than from five lower-yielding cultivars

Nitrogen, Phosphorus, and Potassium Fertilization for Newly Established Tall Fescue

First-year spring yields of tall fescue in 2013 responded to phosphorus (P) fertilization, but lodging at the R5 growth stage in the spring with higher P fertilization rates may have influenced subsequent fall harvest yields, which declined with increasing P rates. As N rates increased, R5 yields declined but fall harvest yields increased

Nitrogen Management for Teff Hay Production

Fertilization of teff with nitrogen (N) resulted in increased forage production, but amounts above 25 lb/a did not often increase yields in this study. Urea as the N source produced at least as much yield response as the alternate, an extended source of nitrogen (ESN)

Nitrogen Management for Teff Hay Production

Fertilization of teff with the ESN source of nitrogen (N) at the higher rates, 100 and 125 lb N/a resulted in increased seasonal forage production. The primary increase occurred in the second of three cuttings

Nitrogen, Phosphorus, and Potassium Fertilization for Newly Established Tall Fescue

First-year production of tall fescue (Site 1 in 2013 and Site 2 in 2014) was affected by nitrogen (N) and phosphorus (P) but not potassium (K) fertilization. Environmental conditions likely influenced the growth of the fescue and the response to fertilizer N and P in the first year of production at the two sites

Nitrogen, Phosphorus, and Potassium Fertilization for Newly Established Tall Fescue

(Abstract only. Link to: http://newprairiepress.org/kaesrr/vol1/iss4/1/) Article is nearly identical to Nitrogen, Phosphorus, and Potassium Fertilization for Newly Established Tall Fescue previously published in Southeast Agricultural Research Center 2015, included in this PDF. First-year production of tall fescue (Site 1 in 2013 and Site 2 in 2014) was affected by nitrogen (N) and phosphorus (P), but not potassium (K) fertilization. Environmental conditions likely influenced the growth of the fescue and the response to fertilizer N and P in the first year of production at the two sites

Interminiband Rabi oscillations in biased semiconductor superlattices

Carrier dynamics at energy level anticrossings in biased semiconductor superlattices, was studied in the time domain by solving the time-dependent Schroedinger equation. The resonant nature of interminiband Rabi oscillations has been explicitly demonstrated to arise from interference of intrawell and Bloch oscillations. We also report a simulation of direct Rabi oscillations across three minibands, in the high field regime, due to interaction between three strongly coupled minibands.Comment: 13 pages, 16 figure

Scanner Invariant Representations for Diffusion MRI Harmonization

Purpose: In the present work we describe the correction of diffusion-weighted MRI for site and scanner biases using a novel method based on invariant representation. Theory and Methods: Pooled imaging data from multiple sources are subject to variation between the sources. Correcting for these biases has become very important as imaging studies increase in size and multi-site cases become more common. We propose learning an intermediate representation invariant to site/protocol variables, a technique adapted from information theory-based algorithmic fairness; by leveraging the data processing inequality, such a representation can then be used to create an image reconstruction that is uninformative of its original source, yet still faithful to underlying structures. To implement this, we use a deep learning method based on variational auto-encoders (VAE) to construct scanner invariant encodings of the imaging data. Results: To evaluate our method, we use training data from the 2018 MICCAI Computational Diffusion MRI (CDMRI) Challenge Harmonization dataset. Our proposed method shows improvements on independent test data relative to a recently published baseline method on each subtask, mapping data from three different scanning contexts to and from one separate target scanning context. Conclusion: As imaging studies continue to grow, the use of pooled multi-site imaging will similarly increase. Invariant representation presents a strong candidate for the harmonization of these data