Distance-Redshift in Inhomogeneous Omega0=1Omega_0=1 Friedmann-Lemaitre-Robertson-Walker Cosmology

Distance--redshift relations are given in terms of associated Legendre functions for partially filled beam observations inspatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies. These models are dynamically pressure-free, flat FLRW on large scales but, due to mass inhomogeneities, differ in their optical properties. The partially filled beam area-redshift equation is a Lame$^{\prime}$ equation for arbitrary FLRW and is shown to simplify to the associated Legendre equation for the spatially flat, i.e. $\Omega_0=1$ case. We fit these new analytic Hubble curves to recent supernovae (SNe) data in an attempt to determine both the mass parameter $\Omega_m$ and the beam filling parameter $\nu$. We find that current data are inadequate to limit $\nu$. However, we are able to estimate what limits are possible when the number of observed SNe is increased by factor of 10 or 100, sample sizes achievable in the near future with the proposed SuperNova Acceleration Probe satellite.Comment: 9 pages, 3 figure

QED radiative corrections to the decay pi^0 to e^+e^-

We reconsider QED radiative corrections (RC) to the $\pi^{0}\to e^{+}e^{-}$ decay width. One kind of RC investigated earlier has a renormalization group origin and can be associated with the final state interaction of electron and positron. It determines the distribution of lepton pair invariant masses in the whole kinematic region. The other type of RC has a double-logarithmic character and is related to almost on-mass-shell behavior of the lepton form factors. The total effect of RC for the $\pi^{0}\to e^{+}e^{-}$ decay is estimated to be 3.2% and for the decay $\eta \to e^{+}e^{-}$ is 4.3%.Comment: 12 pages, 3 figure

Comparative Life Histories of Georgia and Virginia Cotton Rats

Adult hispid cotton rats (Sigmodon hispidus) were collected from the field monthly for \u3e2 years from populations near the northern edge of their range in Virginia and contemporaneously from south-central Georgia. Body measurements and weights were taken at capture, and after dissection embryos, corpora lutea, and placental scars were counted and measured; testes and seminal vesicles were dissected out, measured, and weighed. This allowed comparison of several life-history parameters between the populations and tests of several life-history hypotheses. The breeding season was up to 2 months longer in Georgia than in Virginia, where there was typically a 3-month or longer winter inactive period. Some reproductive activity was observed among Georgia females in all 12 calendar months, whereas pregnancies were never observed in Virginia during November– February. Average litter sizes were significantly higher in Virginia (5.91 ± 6 1.41, up to 13) than in Georgia (5.16 ± 6 1.79, up to 9); this difference may partly result from a higher incidence of embryo resorption and prenatal mortality in the Georgia population, primarily in the cooler 6 months of the year. Virginia rats averaged significantly smaller for both sexes, but this was likely the result of a younger age distribution. Among reproductive males and females, no body-size differences were found between populations except that pregnant females from Virginia averaged significantly longer. Fifty percent and 75% of the random sample of adult females and males, respectively, were reproductively active in Georgia, whereas only 35% and 40% were reproductively active in Virginia. Spermatogenically active males in Virginia had significantly greater relative gonadal mass than their Georgia counterparts. Overwinter survival of parous females was lower in Virginia. Virginia populations, in a more seasonal environment, displayed a more r-selected life history, with greater reproductive allocation, faster growth (except over winter), higher mortality, and less iteroparity

Some Simple Analytics of Peak-Load Pricing

We consider a public utility that provides its service at two different times. Capacity in place can be used in both periods. We study the effects of a change from uniform pricing throughout the day to peak-load pricing, when the utility is constrained to operate with a fixed rate of return on capital. The conventional wisdom seems to be that with peak-load pricing, the peak price will be higher and the off-peak price lower than under uniform pricing, and that peak-load pricing leads to a lower installed capacity. These effects are not generally true. There are plausible cases in which introducing peak-load pricing reduces the price of the service both in peak and off-peak times. Furthermore, peak-load pricing can lead either to greater or to smaller capacity than uniform pricing. We are able to find simple expressions that determine the size and direction of each of these effects. We also provide a criterion for determining whether a particular individual gains or loses from peak-load pricing.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/101093/1/ECON078.pd

Peak-Load Pricing - With and Without Constrained Rate of Return

We consider a public utility that offers its service at two different times. Capacity in place can be used in both periods. We study the effects of a change from uniform pricing throught the day to peak-load pricing, when the utility is constrained to operate with a fixed rate of return on capital. We show that therre are plausible circumstances in which the introduction of peak-load pricing reduces the price of the service both in peak and off-peak times. We show further that peak-load pricing can lead either to greater or to smaller capacity than uniform pricing. We are able to find simple expressions that determine the size and direction of each of these effects. We also provide a straightforward criterion for determining whether a particular individual gains or loses from peak-load pricing. Some of the results are extended under different assumptions about preferences, technology and market structure.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/101092/1/ECON077.pd

Can Heavy WIMPs Be Captured by the Earth?

If weakly interacting massive particles (WIMPs) in bound solar orbits are systematically driven into the Sun by solar-system resonances (as Farinella et al. have shown is the case for many Earth-crossing asteroids), then the capture of high-mass WIMPs by the Earth would be affected dramatically because high-mass WIMPs are captured primarily from bound orbits. WIMP capture would be eliminated for M_x>630 GeV and would be highly suppressed for M_x>~150 GeV. Annihilation of captured WIMPs and anti-WIMPs is expected to give rise to neutrinos coming from the Earth's center. The absence of such a neutrino signal has been used to place limits on WIMP parameters. At present, one does not know if typical WIMP orbits are in fact affected by these resonances. Until this question is investigated and resolved, one must (conservatively) assume that they are. Hence, limits on high-mass WIMP parameters are significantly weaker than previously believed.Comment: 8 pages + 1 figure. Submitted to Ap

Theory, models and biology

Theoretical ideas have a rich history in many areas of biology, and new theories and mathematical models have much to offer in the future

Determining the fraction of compact objects in the Universe using supernova observations

We investigate the possibility to determine the fraction of compact objects in the Universe by studying gravitational lensing effects on Type Ia supernova observations. Using simulated data sets from one year of operation of the proposed dedicated supernova detection satellite SNAP, we find that it should be possible to determine the fraction of compact objects to an accuracy of < 5 %.Comment: 6 pages, 5 figure

Relating Body Size to the Rate of Home Range Use in Mammals

The area occupied or traversed by an animal is a function of the time period considered, but few empirical estimates of the temporal component of home range use are available. We used a statistic called the "time to independence" to make an ecologically meaningful estimate of the amount of time required for an individual to traverse its home range. Data from 23 species of terrestrial mammals indicated the existence of a sizedependent time scale governing the rate of home range use. Foraging mode influenced the rate of home range use; central place foragers traversed their home ranges approximately five times as rapidly as comparably sized noncentral place foragers. Numerous physiological measures of time are related to body mass raised to the V* power. Our results suggest that the time scale governing the rate of space use by mammals is related similarly to body mass. This relationship permits a more critical examination of factors thought to influence home range size, including habitat productivity and social organization