Pseudo-rip: Cosmological models intermediate between the cosmological constant and the little rip

If we assume that the cosmic energy density will remain constant or strictly increase in the future, then the possible fates for the universe can be divided into four categories based on the time asymptotics of the Hubble parameter H(t): the cosmological constant, for which H(t) = constant, the big rip, for which H(t) goes to infinity at finite time, the little rip, for which H(t) goes to infinity as time goes to infinity, and the pseudo-rip, for which H(t) goes to a constant as time goes to infinity. Here we examine the last of these possibilities in more detail. We provide models that exemplify the pseudo-rip, which is an intermediate case between the cosmological constant and the little rip. Structure disintegration in the pseudo-rip depends on the model parameters. We show that pseudo-rip models for which the density and Hubble parameter increase monotonically can produce an inertial force which does not increase monotonically, but instead peaks at a particular future time and then decreases.Comment: 4 pages, 2 figures, title changed to agree with published versio

Forced to be Rich? Returns to Compulsory Schooling in Britain

Do students benefit from compulsory schooling? In an important article, Oreopoulos (2006) studied the 1947 British compulsory schooling law change and found large returns to schooling of about 15% using the General Household Survey (GHS). Reanalysing this dataset, we find much smaller returns of about 3% on average with no evidence of any positive return for women and a return for men of 4-7%. Additionally, we utilize the New Earnings Survey Panel Data-set (NESPD) that has earnings information superior to that in the GHS and find similar estimates: zero returns for women and returns of 3 to 4% for men.Compulsory Schooling, Returns to Education

Forced to be Rich? Returns to Compulsory Schooling in Britain

Do students benefit from compulsory schooling? In an important article, Oreopoulos (2006) studied the 1947 British compulsory schooling law change and found large returns to schooling of about 15% using the General Household Survey (GHS). Reanalysing this dataset, we find much smaller returns of about 3% on average with no evidence of any positive return for women and a return for men of 4-7%. Additionally, we utilize the New Earnings Survey Panel Data-set (NESPD) that has earnings information superior to that in the GHS and find similar estimates: zero returns for women and returns of 3 to 4% for men.

Set Systems Containing Many Maximal Chains

The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size maximise the number of $(n+1)$-element chains in the power set $\mathcal{P}(\{1,2,\dots,n\})$? We will show that for each fixed $\alpha>0$ there is a family of $\alpha 2^n$ sets containing $(\alpha+o(1))n!$ such chains, and that this is asymptotically best possible. For smaller set systems we are unable to answer the question. We conjecture that a `tower of cubes' construction is extremal. We finish by mentioning briefly a connection to an extremal problem on posets and a variant of our question for the grid graph.Comment: 5 page

Ski-Lift Pricing, with an Application to the Labor Market

The market for ski runs or amusement rides often features lump-sum admission tickets with no explicit price per ride. Therefore, the equation of the demand for rides to the supply involves queues, which are systematically longer during peak periods, such as weekends. Moreover, the prices of admission tickets are much less responsive than the length of queues to variations in demand, even when these variations are predictable. We show that this method of pricing generates nearly efficient outcomes under plausible conditions. In particular, the existence of queues and the "stickiness" of prices do not necessarily mean that rides are allocated improperly or that firms choose inefficient levels of investment. We then draw an analogy between "ski-lift pricing" and the use of profit-sharing schemes in the labor market. Although firms face explicit marginal costs of labor that are sticky and less than workers' reservation wages, and although the pool of profits seems to create a common-property problem for workers, this method of pricing can approximate the competitive outcomes for employment and total labor compensation.

Heat transfer with very high free stream turbulence

Stanton numbers as much as 350 percent above the accepted correlations for flat plate turbulent boundary layer heat transfer have been found in experiments on a low velocity air flow with very high turbulence (up to 50 percent). These effects are far larger that have been previously reported and the data do not correlate as well in boundary layer coordinates (Stanton number and Reynolds number) as they do in simpler coordinates: h vs. X. The very high relative turbulence levels were achieved by placing the test plate in different positions in the margin of a large diameter free jet. The large increases may be due to organized structures of large scale which are present in the marginal flowfield around a free jet