Abstract. We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier modes. We prove that the essential spectrum coincides with the imaginary axis, and give an estimate from above for the number of isolated nonimaginary eigenvalues. In addition, we prove that the spectral mapping theorem holds for the group generated by the linearized 2D Euler operator.
In vivo and in vitro experiments were conducted to determine whether P in a low-phytate corn (LPC) containing the lpa 1-1 allele is more available than P in a near-isogenic wild-type corn hybrid (NC). The LPC was analyzed to contain 0.18% nonphytate P and 0.26% total P (TP), whereas NC contained 0.05% nonphytate P and 0.25% TP. For these studies, nonphytate P was considered to be available P (AP). In the in vivo study, 150 1-d-old male chicks were randomly assigned to five treatments (six pens of five chicks each) for 21 d. The dietary treatments included: A) a diet containing 60% NC, 0.2% AP, and 0.8% Ca; B) a diet containing 60% LPC, 0.28% AP, and 0.8% Ca; C) an NC diet similar to Diet A, but with KH2PO4 added to increase the AP to 0.28% to match the AP in Diet B; D) an LPC diet containing 0.45% AP and 1% Ca; and E) an NC diet supplemented with KH2PO4 to provide 0.45% AP and 1% Ca. Diets A, B, and C were semipurified diets, with corn being the sole source of phytate. The only differences between Diets A and B were the source of corn and the amount of AP present in the diets. The levels of AP in these diets were deficient in order to measure the animal response to the different levels of AP. Diets D and E were typical corn-soybean meal diets, and were formulated to contain an optimal level of AP. Performance and bone ash were similar (P > 0.05) in chicks fed Diets B and C and in chicks fed Diets D and E. Chicks fed LPC diets (B and D) retained more P (P < 0.05) than chicks fed NC diets (C and E). Chicks fed Diet B had significantly higher (P < 0.05) Ca retention compared with chicks fed Diet A. An in vitro digestion procedure that simulated the physiological conditions of the gastrointestinal tract of broilers was used to determine P release from LPC and NC. Results showed that 65% (1,420 mg/kg) of the TP in LPC was released, compared with 23% (543 mg/kg) from NC. Results of these experiments indicate that the P in LPC is more available than the P in NC, and reducing the phytate content did not compromise the nutritional value of LPC. The increased P retention in chicks fed LPC suggests that substituting LPC for NC leads to a reduction in manure P. Also, the in vitro procedure accurately predicted differences in in vivo P availability between the two corns.
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