Supplementation with a β- adrenergic agonist (β-AA) for 21 days in Brahman steers under heat stress conditions (HS) was evaluated with respect to feedlot performance and carcass merit. Twenty-four Brahman steers (kg = 338 ± 39) were housed in two controlled environment chambers with one of two environmental (ENV) conditions 1) heat stress (HS; THI = 73 to 85) and 2) thermoneutral (TN; THI = 68) with either Zilpaterol hydrochloride (ZL) or soymeal supplementation (CN) using a randomly assigned in a 2 x 2 factorial design (n=6/group). Daily data were collected for dry matter intake, water intake, respiratory rate (RR), and rectal temperature (RT). At the end of 21 d period, total weight gain was used to calculate average daily gain (ADG) and gain to feed. Blood samples were collected from the jugular vein on days -7, 3, 10, and 21 for cortisol analysis, and biological impedance analysis (BIA) was determined on days 3, 10, and 21 on each animal. Steers were harvested at 544 kg on average post supplementation/environment conditions, and carcass merit was determined. There were no differences (P > 0.05) in feedlot performance. Brahmans exposed to heat stress had greater RR during the heat stress periods of the experiment, regardless of supplementation. Environment and day interactions (P < 0.04) were observed for RT, HS steers had a greater RT on d 8 but similar RT on d 15 and 19. Stressed steers with ZL had higher RT (P < 0.05) than TN/CN steers on d 11. There was no interaction (P > 0.05) between environmental conditions and CN and ZH supplementation for cortisol concentrations. Regardless of environmental treatment or supplementation, no difference (P > 0.05) was associated with BIA characteristics. There were no differences (P > 0.05) for hot carcass weight, cold carcass weight, USDA yield grade, 12th rib loin eye area, marbling score, KPH percentage, and 12th rib fat thickness between groups. Twelfth-rib loin eye area lean color from HS/CN had higher lightness (L*) (P < 0.05) than TN/CN steers. HS/CN steers present a similar (L*) to ZL in TN and HS conditions. Redness-greenness (a*) was greater (P = 0.01) in carcasses from HS steers with or without ZL than TN/ZL but similar to TN/CN. Steers exposed to HS and CN had a higher (P = 0.02) change of 12th rib lean color from yellow to blue (b*) than TN steers with CN and ZL. Supplementation with β-AA did not negatively impact growth, carcass performance, or carcass merit in heat-stressed steers.
In this survey we give very simple proofs of Kepler's Laws and other facts about central force fields using only Newton's second law, Newton's law of universal gravitation, basic notions of vector calculus, and an elementary double integral.Hopefully, this article will help undergraduate students of mathematics and engineering who wish to understand these fundamental scientific discoveries.In many textbooks (see, for instance, [1, 2, 3, 4, 5]), Kepler's Laws are obtained using conservation of energy and angular momentum, differential equations, mobile reference systems, or notions not so well-defined such as differentials or ‘infinitesimal elements’. Some of the arguments appear to be rather involved if one is not accustomed to them, whereas the proof of Kepler's Laws may actually be obtained from quite simple facts.
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