The density of primes in orbits of z^d + c

Given a polynomial f(z) = z^d + c over a global field K and a_0 in K, we study the density of prime ideals of K dividing at least one element of the orbit of a_0 under f. The density of such sets for linear polynomials has attracted much study, and the second author has examined several families of quadratic polynomials, but little is known in the higher-degree case. We show that for many choices of d and c this density is zero for all a_0, assuming K contains a primitive dth root of unity. The proof relies on several new results, including some ensuring the number of irreducible factors of the nth iterate of f remains bounded as n grows, and others on the ramification above certain primes in iterated extensions. Together these allow for nearly complete information when K is a global function field or when K=Q(zeta_d).Comment: 27 page

Physical activity, weight status and diet in adolescents: are children meeting the guidelines?

Childhood obesity is on the increase and maintaining regular physical activity and consuming a healthy diet have become essential tools to combat the condition. The United Kingdom government has recommended guidelines for optimal levels of diet and activity in children. The aim of this paper is to describe and compare self-reported physical activity levels, diet, and Body Mass Indices (BMI) amongst adolescent children, aged 11-15, in the South West (SW) and North West (NW) regions of England and to see if these children were meeting the current targets for optimal levels of: physical activity; fruit/vegetable consumption; fat consumption and BMI. We report the results of a cross-sectional survey of four secondary schools and 1,869 children using the self-reported Western Australian Child and Adolescent Physical Activity and Nutrition Survey (CAPANS) physical activity instrument and a food intake screener questionnaire, in summer and winter. We found that 25% (469/1869) 95% CI: 23% to 27%, of children engaged in 60 minutes of moderate to vigorous physical activity per day; 53% (995/1866) 95% CI: 51% to 56%, took 5 portions of fruit and vegetables per day; while 22% (407/1861) 95% CI: 20% to 24% consumed recommended amount of fats, and 23.7% (276/1164) 95% CI: 21% to 26%, of pupils were obese or overweight as classified by their BMI. Self reported physical activity in young people regardless of area is lower than previously reported and the lack of students engaging in 60 minutes moderate to vigorous activity could have serious public health consequences. If sustained, this could lead to more overweight adults, and more ill health

Physical activity among adolescents and barriers to delivering physical education in Cornwall and Lancashire, UK: a qualitative study of heads of PE and heads of schools. BMC Public Health Journal 2008 Aug 1;8:273.

BACKGROUND: Recent initiatives have been introduced by the UK government into secondary schools to increase pupils' access to physical activity (PA). Despite this, not enough is known about pupils' levels of physical activity or whether the delivery of these initiatives in schools facilitates or creates a barrier for pupils' PA. The aim of this study was to gain an understanding of adolescents PA levels from the perspective of those responsible for delivering physical education (PE) in schools; heads of PE (HOPE) and heads of school (HS). METHODS: Seventeen semi-structured qualitative interviews were carried out with a snowball sample of HOPE and HS in schools in the Northwest and Southwest of England. Thematic data analysis using NVIVO was used to identify emergent themes.RESULTS:17 core themes were generated, 12 of which confirmed the findings from similar research. However, five themes relating to 'ethos of performance/elitism', 'lower fitness leads to lower ability', 'undervaluing activities within PE dept' or school as a whole', 'role of the school' and 'PE department doing all it can' offer valuable new insight into the factors which may encourage or prevent PA inside or outside the curriculum. CONCLUSION: Despite many positive perceptions of the delivery of PE in schools, it is evident that barriers still exist within that delivery which discourages physical activity. More research is needed to particularly address the complex issues of elitism and the ethos of PA in schools

Inhaled corticosteroids versus long-acting beta -agonists for chronic obstructive pulmonary disease (Review).

Long-acting beta(2)-agonists and inhaled corticosteroids can be used as maintenance therapy by patients with moderate to severe chronic obstructive pulmonary disease. These interventions are often taken together in a combination inhaler. However, the relative added value of the two individual components is unclear

A study of the local pressure field in turbulent shear flow and its relation to aerodynamic noise generation Semiannual status report, 1 Aug. 1970 - 31 Jan. 1971

Relation of Eulerian and Lagrangian structure of pseudosound pressure and velocity fields in turbulent shear flow to aerodynamic noise generatio

Vertical Foreclosure and International Trade Policy

We examine conditions under which a low cost vertically integrated manufacturer has an incentive to export an intermediate product to its higher cost (vertically integrated) rival rather than to vertically foreclose, fully cutting off supplies. The nature of supply conditions in the importing country, the size of an import tariff on the final good and optimal policy by the exporting country are all shown to be important for this decision. The exporting country may gain by taxing exports of the final (Cournot) product even though, under Cournot competition, an export subsidy is optimal in the absence of a market for intermediates. In this case, optimal policy also requires an export tax on intermediates, but the higher tax on final goods serves to divert sales to the more profitable market for intermediates increasing the extent of vertical supply. It is optimal to tax the export of both goods or to subsidize the export of both goods. It is never optimal to tax one and subsidize the other.

Letter from [Alice Spencer Jones] to John Muir, 1910 Sep 2.

[1][letterhead]Sept 2.— 1910—Dear Good Man,Mr John Muir.—I was just delighted to get your letter. Oh so often we talk about you- and wonder where you are, and what you have been about.—Uncle is now on Mt Wilson with other stars, he will return this (Friday Evening)- He went by auto yesterday, and will bring down a load for dinner at 325 - then they take the 8 P.M train North, Prof W.W. Campbell, among them04866 [2][letterhead][to?] make preparations for the visit of the Notables to his observatory at Mt HamiltonI am so glad aunt [Katharine?] returns so soon, and that you too are soon coming Home, as the old song says- what a meeting that will be when all the saints get Home —I am taking care of the Hooker office for a little while, while Mr Burlew, goes to jury Duty—Later. Sept. 3. I was interrupted in my office work- and now finish- Uncle returned full of high04866 [3][letterhead]spirits from the mountain top- for dinner was served and the gentlemen guests - have gone on their way - rejoicing -Uncle has just read your letter and says, isent that a fine letter ? He send his regards to you Genial John of Mountains. and says Come [on?] - that John of stars will meet John of Mountains when ever you sing out. Mrs Stott is here for Luncheon and sends greetings.Dont stay too long - but come Home Soon- so saysThe Lark.OVER. 04866 [4]The scientists were all intensely interested in uncles Cabinet of Slides — Prof. H. H. [illegible] of Oxford Eng- said — Mr Hooker there is not an observatory in the whole world that can give the fine display of the Heavens, that you can in this room