The aim of this study was to examine the suitability of different growth functions (linear, sinusoidal, Gompertz, Schumacher and Richards) to fit cumulative milk production data from buffalo cows. Cumulative milk production at each day in milk was calculated from two published datasets reporting (i) fortnightly test-day milk yield records of the first lactation of Murrah buffalo that had calved during 1977–2012 and (ii) the first lactation records of Jaffarabadi buffalo collected from history-cum-pedigree registers for each quinquennium between 1991 and 2010. Each function was fitted to the lactation curves using nonlinear regression procedures. The Richards and sinusoidal equations provided the smallest root mean square error values, Akaike's and Bayesian information criteria and, therefore, the best fit for the cumulative lactation curves for milk yield. The Richards equation appeared to provide the most accurate estimate of the cumulative milk production at peak milk yield. Sinusoidal and flexible classical growth functions are appropriate to describe cumulative milk production curves and estimate lactation traits in buffalo.

The aim of the work reported here was to investigate the appropriateness of a sinusoidal function by applying it to model the cumulative lactation curves for milk yield and composition in primiparous Holstein cows, and to compare it with three conventional growth models (linear, Richards and Morgan). Data used in this study were 911 144 test-day records for milk, fat and protein yields, which were recorded on 834 dairy herds from 2000 to 2011 by the Animal Breeding Centre and Promotion of Animal Products of Iran. Each function was fitted to the test-day production records using appropriate procedures in SAS (PROC REG for the linear model and PROC NLIN for the Richards, Morgan and sinusoidal equations) and the parameters were estimated. The models were tested for goodness of fit using adjusted coefficient of determination $\lpar {R_{{\rm adj}}^2 } \rpar $, root mean square error (RMSE), Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). $R_{{\rm adj}}^2 $ values were generally high (>0.999), implying suitable fits to the data, and showed little differences among the models for cumulative yields. The sinusoidal equation provided the lowest values of RMSE, AIC and BIC, and therefore the best fit to the lactation curve for cumulative milk, fat and protein yields. The linear model gave the poorest fit to the cumulative lactation curve for all production traits. The current results show that classical growth functions can be fitted accurately to cumulative lactation curves for production traits, but the new sinusoidal equation introduced herein, by providing best goodness of fit, can be considered a useful alternative to conventional models in dairy research.

In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra with at least one dihedral angle of the form $\frac{\pi }{k}$ for an integer $k\ge 7$. Combining a classical result by Parry with a previous result of ours, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.

Economic effects for three scenarios of antimicrobial drug use in livestock production—a no-ban scenario and two levels of bans—are examined through cost minimization and a partial equilibrium analysis. Results indicate that regulating antimicrobial drug use in livestock production would increase per-unit costs of producers previously using drugs and reduce beef supplies in the short run, reducing consumer surplus. Producers not previously using drugs would benefit from short-run price increases.

Beurling's inequality is proved to have an interpretation in terms of ingredients that do not depend on the effective numerical contribution of transition probabilities of circuit processes (those processes whose transition law is expressed by a denumerable class of directed weighted circuits). Connections with reversibility for Sk-state, k≧2, circuit processes, where S is a denumerable set, are revealed.