The apparent ileal digestibility of amino acids in 8 feed ingredients was determined using 14-, 28- and 42-d-old male broiler chickens. The ingredients included three cereals (wheat, sorghum and maize), one cereal by-product (mill run), three oilseed meals (canola, cottonseed and soybean meals) and one animal protein meal (meat and bone meal). Dietary crude protein in the assay diets was supplied solely by the test ingredient. All diets contained 20 g/kg acid-insoluble ash as an indigestible marker, and each diet was offered ad libitum in mash form to 5 replicate pens from 11 to 14 d, 25 to 28 d and 39 to 42 d post-hatching. There were 12, 6 and 6 birds per pen for the 14, 28 and 42 d samplings, respectively. The results suggest that the age of broilers significantly influenced the apparent ileal digestibility of amino acids. The effects, however, varied among amino acids and ingredients. In wheat, the digestibility of most amino acids was higher in 14- than in 28- and 42-d-old broilers. In maize, the digestibility coefficients of amino acids were higher at 28 and 42 d than at 14 d. The digestibility coefficients in maize and wheat at 28 and 42 d were similar. The digestibility of amino acids in sorghum at 42 d was higher than those at 28 d, but similar to those at 14 d except for histidine, lysine, serine and glycine, which were significantly higher at 42 d. Digestibility of amino acids in sorghum was similar between 14 and 28 d except for isoleucine, leucine, phenylalanine, glutamic acid and alanine. The digestibility of amino acids in mill run at 42 d was significantly higher than those at 14 and 28 d. There were no differences in digestibility between 14 and 28 d. In general, the digestibility of amino acids in canola meal, soybean meal and, meat and bone meal was higher at 28 and 42 d compared to those at 14 d, and similar between 28 and 42 d of age. In cottonseed meal, age had no effect on the digestibility coefficient of amino acids, except for lysine and arginine, which increased with age. Analysis of the combined results for the 8 feed ingredients showed that, in general, the digestibility coefficients of amino acids increased with advancing age of broiler chickens.

We propose a perturbative method to compute the deflection angle of both null and massive particles for source and detector at finite distance. This method applies universally to the motion of particles with general velocity in the equatorial plane of stationary axisymmetric spacetimes or static spherical symmetric spacetimes that are asymptotically flat. The resultant deflection angle automatically arranges into a quasi-inverse series form of the impact parameter, with coefficients depending on the metric functions, the signal velocity and the source and detector locations through the apparent angles. In the large impact parameter limit, the series coefficients are reduced to rational functions of sine/cosine functions of the zero order apparent angle.

The apparent ileal digestibility of amino acids in 7 feed ingredients was determined using broilers, layers, and roosters. The ingredients included 3 cereals (wheat, sorghum, and corn), 3 oilseed meals (canola, cottonseed, and soybean meals), and 1 animal protein meal (meat and bone meal). Dietary protein in the assay diets was supplied solely by the test ingredient. All diets contained 20 g/kg of acid-insoluble ash as an indigestible marker, and each diet was offered ad libitum in mash form to 5 replicate pens of broilers and layers, and 4 replicate pens of roosters. The digestibility coefficients of individual amino acids for wheat, corn, and sorghum were higher (P < 0.05) in broilers than in layers and roosters. The digestibility of most amino acids for corn and sorghum was higher (P < 0.05) in roosters compared with those in layers, whereas the digestibility for wheat in layers and roosters was similar. In general, the digestibility of amino acids in canola meal, cottonseed meal, and meat and bone meal was similar among the 3 classes of chickens. The digestibility of amino acids in soybean meal was higher (P < 0.05) for layers compared with those for broilers and roosters but similar between broilers and roosters. These results suggest that the class of chickens significantly influenced the apparent ileal digestibility of amino acids in some feed ingredients.

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