Pigs subjected to heat stress (HS) decrease their feed intake and growth. The objectives of the experiment were to determine the effects of live yeast (LY) supplementation (Saccharomyces cerevisiae var boulardii CNCM I-1079) on feeding behaviour, energy metabolism and faecal microbiota composition of finishing boars (n 10) housed in a respiration chamber at thermoneutrality (7 d at 22°C) or during HS (seven plus six days at 28°C). Dietary LY supplementation increased DM intake (P = 0·01) whatever the ambient temperature, whereas HS decreased feed intake whatever the dietary supplementation (P = 0·01). Dietary LY supplementation increased the number of meals (P = 0·02). Energy retention was higher with dietary LY supplementation (P < 0·01) but decreased during HS (P < 0·01). The skin temperature of the supplemented pigs was lower at thermoneutrality and increased during HS to a lesser extent than that of non-supplemented pigs (P < 0·01). Faecal microbiota composition was determined using 16S rRNA gene sequencing. Treponema, Christensenellaceae R-7, Ruminococcaceae UCG-002, Rikenellaceae RC9, Clostridium sensu stricto 1 and Romboutsia genera and some bacteria belonging to Alloprevotella, Oxalobacter and Anaeroplasma genera were more abundant under HS. LY supplementation attenuated HS effects on Romboutsia abundance, while decreasing the abundance of some bacteria from Ruminoccocus, Coprococcus, Peptococcus and Oxalobacter genera and increasing the abundance of beneficial bacteria from Lactococcus and Subdoligranulum genera. Our results suggest that higher level of the keystone species Ruminococcus bromii at thermoneutrality may be one of the causes for higher energy retention observed under subsequent HS.

We analyse local aspects of chaos for nonautonomous periodic dynamical systems in the context of generating autonomous dynamical systems and the possibility of disturbing them.

We prove the Gross–Deligne conjecture on CM periods for motives associated with ${{H}^{2}}$ of certain surfaces fibered over the projective line. Then we prove for the same motives a formula which expresses the ${{K}_{1}}$-regulators in terms of hypergeometric functions $_{3}{{F}_{2}}$, and obtain a new example of non-trivial regulators.

Egg storage is a common and important practice in the poultry industry. Knowledge of the effects of storage on the egg, the embryo and incubation yield is important for planning incubation by hatcheries. Recommendations for storage environmental conditions depend mainly on the breeder age and storage time. Storage from seven days or more alters the characteristics of albumen, reduces incubation yield, increases incubation period and can damage embryonic development. When working with long storage periods, the adoption of management practices such as storing the egg with the thin tip down, egg turning during storage and pre-storage incubation should be considered to reduce the negative effects on the incubation yield.

When a ship is moored by a single anchor at the anchorage, its combined motions (i.e. yaw, sway, surge, etc.) are usually induced by external forces. Previous studies have gained some insights into the forces on anchor chains, but the motions for Capesize vessels still need to be further investigated. The length of anchor chain required for safe anchoring also needs to be carefully calculated rather than determined solely by the experience and judgement of Captains. The relationship between the length of chain and water depth, wind force, current velocity and the trim (draught difference forward/aft) requires further study. Our new methods consider all necessary factors which may exert significant influence on ships, including not only the water depth at the anchoring location but also the particulars of the ships, its equipment and the environmental conditions. Here, a numerical simulation model to describe the behaviour of an anchored Capesize ship is presented, with the comparison of results between simulations and real time model tests carried out. A discussion highlights the important features of the methods which provide mariners with theoretical solutions.

The mortality data (registered deaths and population size) over the years 1961–2007 for the population of England and Wales and for Scotland were obtained from the Office for National Statistics (ONS) and from the Scottish Registrar General. This paper addresses the following questions:

(i) Is there statistical evidence for a cohort effect (i.e. a generation effect separate from the period effect) being present in the data?

(ii) Do both males and females exhibit similar cohort (generation) effects?

(iii) Are period effects (i.e. the improvement in mortality with time) more significant than cohort effects?

(iv) How should one allow, in forecasts of population mortality, for age, period and cohort effects?

(v) Is it sensible to combine male and female mortality experience to determine the period effect and the cohort effect?

(vi) How do the forecasts for the expectation of life at birth, using the Extended-Lee–Carter-Combined (ELCC) model (described in the paper) differ from the (2008 based) Office of National Statistics (ONS) forecasts of the expectation of life at birth?

Let F = GF(q). To any polynomial G ∈ F[x] there is associated a mapping Ĝ on the set IF of monic irreducible polynomials over F. We present a natural and effective theory of the dynamics of Ĝ for the case in which G is a monic q-linearized polynomial. The main outcome is the following theorem.

Assume that G is not of the form , where l ≥ 0 (in which event the dynamics is trivial). Then, for every integer n ≥ 1 and for every integer k ≥ 0, there exist infinitely many μ ∈ IF. having preperiod k and primitive period n with respect to Ĝ.

Previously, Morton, by somewhat different means, had studied the primitive periods of Ĝ when G = xq – ax, α a non-zero element of F. Our theorem extends and generalizes Morton's result. Moreover, it establishes a conjecture of Morton for the class of q-linearized polynomials.

We present an on-line linear time and space algorithm to check if an integer array f is the border array of at least one string w built on a bounded or unbounded size alphabet Σ. First of all, we show a bijection between the border array of a string w and the skeleton of the DFA recognizing Σ*ω, called a string matching automaton (SMA). Different strings can have the same border array but the originality of the presented method is that the correspondence between a border array and a skeleton of SMA is independent from the underlying strings. This enables to design algorithms for validating and generating border arrays that outperform existing ones. The validating algorithm lowers the delay (maximal number of comparisons on one element of the array) from O(|w|) to 1 + min{|Σ|,1 + log2|ω|} compared to existing algorithms. We then give results on the numbers of distinct border arrays depending on the alphabet size. We also present an algorithm that checks if a given directed unlabeled graph G is the skeleton of a SMA on an alphabet of size s in linear time. Along the process the algorithm can build one string w for which G is the SMA skeleton.

We consider relational periods, where the relation is a compatibility relation on words induced by a relation on letters. We prove a variant of the theorem of Fine and Wilf for a (pure) period and a relational period.

We derive a new compound Poisson distribution with explicit parameters to approximate the number of overlapping occurrences of any set of words in a Markovian sequence. Using the Chen-Stein method, we provide a bound for the approximation error. This error converges to 0 under the rare event condition, even for overlapping families, which improves previous results. As a consequence, we also propose Poisson approximations for the declumped count and the number of competing renewals.