Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

Use of Megasphaera elsdenii NCIMB41125 as a probiotic for early-lactation dairy cows: effects on rumen pH and fermentation patterns

Multiparous rumen-fistulated Holstein cows were fed, from d 1 to 28 post-calving, an ad libitum TMR containing (g/kg DM) grass silage (196), corn silage (196), wheat (277), soybean meal (100), and other feeds (231) with CP, NDF, starch and water soluble carbohydrate concentrations of 176, 260, 299 and 39 g/kg DM respectively and ME of 12.2 MJ/kg DM. Treatments consisting of a minimum of 1010 cfu Megasphaera elsdenii NCIMB 41125 in 250 ml solution (MEGA) or 250 ml of autoclaved M. elsdenii (CONT) were administered via the rumen cannula on d 3 and 12 of lactation (n=7 per treatment). Mid-rumen pH was measured every 15 minutes and eating and ruminating behavior was recorded for 24 h on d 2, 4, 6, 8, 11, 13, 15, 17, 22 and 28. Rumen fluid for VFA and lactic acid (LA) analysis was collected at 11 timepoints on each of d 2, 4, 6, 13 and 15. Data were analysed as repeated measures using the Glimmix (LA data) or Mixed (all other data) procedures of SAS with previous 305 d milk yield and d 2 measurements as covariates where appropriate. Milk yield was higher (CONT 43.0 vs MEGA 45.4 ±0.75 kg/d, P=0.051) and fat concentration was lower (CONT 45.6 vs MEGA 40.4 ±1.05 g/kg, P=0.005) in cows that received MEGA. Time spent eating (263 ±15 min/d) and ruminating (571 ±13 min/d), DM intake (18.4 ±0.74 kg/d), proportion of each 24 h period with rumen pH below 5.6 (3.69 ±0.94 h) and LA concentrations (2.00 mM) were similar (P>0.327) across treatments. Ruminal total VFA concentration (104 ±3 mM) was similar (P=0.404) across treatments, but a shift from acetate (CONT 551 vs MEGA 524 ±14 mmol/mol VFA, P=0.161) to propionate production (CONT 249 vs MEGA 275 ±11 mmol/mol VFA, P=0.099) meant that the acetate:propionate ratio (CONT 2.33 vs MEGA 1.94 ±0.15) was reduced (P=0.072) in cows that received MEGA. This study provides evidence that supplementation of early lactation dairy cows with MEGA alters rumen fermentation patterns in favour of propionate, with potential benefits for animal health and productivity.

UK Food Standards Agency alpha-linolenic acid workshop report

The UK Food Standards Agency convened a group of expert scientists to review current research investigating whether n-3 polyunsaturated fatty acids (PUFA) from plant oils (a-linolenic acid; ALA) were as beneficial to cardiovascular health as the n-3 PUFA from the marine oils, eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA). The workshop also aimed to establish priorities for future research. Dietary intake of ALA has been associated with a beneficial effect on CHD; however, the results from studies investigating the effects of ALA supplementation on CHD risk factors have proved equivocal. The studies presented as part of the present workshop suggested little, if any, benefit of ALA, relative to linoleic acid, on risk factors for cardiovascular disease; the effects observed with fish-oil supplementation were not replicated by ALA supplementation. There is a need, therefore, to first prove the efficacy of ALA supplementation on cardiovascular disease, before further investigating effects on cardiovascular risk factors. The workshop considered that a beneficial effect of ALA on the secondary prevention of CHD still needed to be established, and there was no reason to look further at existing CHD risk factors in relation to ALA supplementation. The workshop also highlighted the possibility of feeding livestock ALA-rich oils to provide a means of increasing the dietary intake in human consumers of EPA and DHA.