The rank of the semigroup of transformations stabilising a partition of a finite set

Let $\mathcal{P}$ be a partition of a finite set $X$. We say that a full transformation $f:X\to X$ preserves (or stabilizes) the partition $\mathcal{P}$ if for all $P\in \mathcal{P}$ there exists $Q\in \mathcal{P}$ such that $Pf\subseteq Q$. Let $T(X,\mathcal{P})$ denote the semigroup of all full transformations of $X$ that preserve the partition $\mathcal{P}$. In 2005 Huisheng found an upper bound for the minimum size of the generating sets of $T(X,\mathcal{P})$, when $\mathcal{P}$ is a partition in which all of its parts have the same size. In addition, Huisheng conjectured that his bound was exact. In 2009 the first and last authors used representation theory to completely solve Hisheng's conjecture. The goal of this paper is to solve the much more complex problem of finding the minimum size of the generating sets of $T(X,\mathcal{P})$, when $\mathcal{P}$ is an arbitrary partition. Again we use representation theory to find the minimum number of elements needed to generate the wreath product of finitely many symmetric groups, and then use this result to solve the problem. The paper ends with a number of problems for experts in group and semigroup theories

Exact gravitational lensing and rotation curve

Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein's equations. Then lensing is considered in the weak field approximation of general relativity. From the null geodesics we derive the lensing equation and corrections to it.Comment: 12 pages, 1 figur

A review of high beam current RFQ accelerators and funnels

The authors review the design features of several high-current (> 20-mA) and high-power (> 1-mA average) proton or H{sup {minus}} injectors, RFQs, and funnels. They include a summary of observed performance and will mention a sampling of new designs, including the proposed incorporation of beam choppers. Different programs and organizations have chosen to build the RFQ in diverse configurations. Although the majority of RFQs are either low-current or very low duty-factor, several versions have included high-current and/or high-power designs for either protons or H{sup {minus}} ions. The challenges of cooling, handling high space-charge forces, and coupling with injectors and subsequent accelerators are significant. In all instances, beam tests were a valuable learning experience, because not always did these as-built structures perform exactly as predicted by the earlier design codes. They summarize the key operational parameters, indicate what was achieved, and highlight what was learned in these tests. Based on this generally good performance and high promise, even more challenging designs are being considered for new applications that include even higher powers, beam funnels and choppers

Asymptotics and local constancy of characters of p-adic groups

In this paper we study quantitative aspects of trace characters $\Theta_\pi$ of reductive $p$-adic groups when the representation $\pi$ varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of $\Theta_\pi$ relative to the formal degree of $\pi$, which we are able to prove in the case where $\pi$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul

The Collective Action On Governing The Commons In The Surroundings Of Protected Areas

This work has as its theme the common natural resources and the management models that allow new governance systems in the rural areas in the surrounding of protected areas. In this sense, this paper aims to discuss the collective action of social actors in the management of common natural resources in the surroundings of the National Park of Serra da Bodoquena (PNSB). Based on institutional approach for the study of the self-organisation and self-governance in common-pool resources situations developed by Elinor Ostrom, the investigation sought the theoretical explanation of phenomena. The conclusions point out that the expected mobilisation of groups of individuals in the pursuit of common goals is twofold. In this case, the participants of the action arena create different goals and different collective actions according to their interests.194213

Prime ideals in nilpotent Iwasawa algebras

Let G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of G, and use this to show that the prime spectrum of kG is a disjoint union of commutative strata. We also show that every prime ideal of kG is completely prime. The key ingredient in the proof is the construction of a non-commutative valuation on certain filtered simple Artinian rings

Determining the accuracy of gestation feed drops

An experiment was conducted to determine the accuracy of three different gestation feed drops. Each drop was tested at three different angles (90, 75, 60°) from the feed line. Feed was collected and weighed at feeder settings of 2, 4, 6, 8, and 10 lb for the Econo- Drop and Accu-Drop feed dispensers. Samples were taken at 2, 4, 6, and 8 lb for the Ultra- Drop feed dispenser due to a smaller storage capacity for feed with this feed drop. There were five replications (five drops of each type) at each feed setting. There was a drop type by angle interaction (P<0.01) for the feed dispenser settings versus the actual pounds of feed dropped. At angles of 90 or 60 degrees, the Accu-Drop and the Ultra-Drop feed dispensers more (P<0.10) accurately dropped the correct amount of feed at the respective feeder settings. The amount of feed dropped at each dispenser setting was influenced more by angle to the feed line with the Econo-Drop than with the Accu-Drop or Ultra- Drop feed dispensers. This study demonstrated that the Accu-Drop and the Ultra-Drop feed dispensers are more accurate than the Econo-Drop feed dispenser. Therefore, producers should consider the additional feed cost over the lifetime of the feed drops and not rely solely on initial price

Effect of restricted feed intake on finishing pigs weighing between 150 and 250 lb fed twice or six times daily

Two 42-d trials and two 28-d trials were conducted to evaluate the effects of restricted feed intake and feeding frequency (2 or 6 times daily) on the performance of pigs weighing between 150 to 250 lb (initially 148 lb in Exp. 1; 155 lb in Exp. 2; 156 lb in Exp. 3; and 156 lb in Exp. 4). In all experiments, pigs were housed in 6 × 10 ft pens with half-solid concrete and half-slatted flooring and with one nipple waterer. Pigs were fed a corn-soybean meal-based diet formulated to 1.15% TID lysine and 1,491 kcal of ME/lb. In Exp. 1 to 3, energy and lysine were supplied to pigs to target an average growth rate of 1.75 lb/d based on NRC (1998) values. In Exp. 4, the diet was supplied to pigs to target growth rates of 1.75 lb/d (low feed intake) or 2.1 lb/d (high feed intake) based on NRC (1998) values to determine if the amount of energy above maintenance and feeding frequency has an effect on performance. Pigs were fed by dropping similar daily amounts of feed, either 2 (0700 and 1400) or 6 times (3 meals within 2 h at AM and PM feedings) per day, by an Accu-Drop Feed Dispenser® on the solid concrete flooring. In Exp. 1 and 2, increasing the feeding frequency of pigs fed a restricted diet from 2 to 6 times per day improved (P0.05) in performance between pigs fed 2 times per day when feed was dropped from the feed drop or by the modified method. In Exp. 4, increasing the feeding frequency from 2 to 6 feeding periods improved (P<0.01) ADG and F/G for pigs fed a low level of feed intake and tended to increase (P<0.06) ADG and improve (P<0.05) F/G for pigs fed a high level of feed intake. In conclusion, these studies indicate that increasing the frequency of feeding from 2 to 6 times a day improves pig performance compared with feeding 2 times per day

Determining the total sulfur amino acid to lysine requirement of the lactating sow

A total of 163 sows were used in a study to determine the requirement for total sulfur amino acids (TSAA), relative to lysine, during lactation. All experimental diets were cornsoybean meal-based and formulated to contain 0.88% true ileal digestible (TID) lysine (0.97% total lysine). The experimental diets contained 0.37% L-lysine HCl, with other crystalline amino acids added to ensure that TSAA was first limiting. The dietary TID TSAA rates were formulated to 0.44, 0.48, 0.53, 0.57, and 0.62%, corresponding to 50, 55, 60, 65, and 70% of lysine, respectively. Sows farrowed in six farrowing groups, and were randomly allotted to the dietary treatments on the basis of parity. Over the entire lactation period, there were no differences (P>0.14) in ADFI, weight loss, backfat loss, or plasma urea nitrogen among sows fed increasing TSAA:Lys ratios. Increasing TSAA, relative to lysine, had no effect (P>0.25) on litter weaning weight or preweaning mortality. In summary, there were no differences in litter performance with increasing TID TSAA:Lys ratio. These results suggest that the requirement for TID TSAA is no more than 50% of lysine. Additional research is needed to confirm this relatively low TSAA requirement, and that the relatively high feed (and amino acid) intake of sows, coupled with possible tissue breakdown as a source of TSAA, did not decrease the dietary requirement

How does flow in a pipe become turbulent?

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by three-dimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We will also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs.Comment: for the proceedings of statphys 2