Square root meadows

Let Q_0 denote the rational numbers expanded to a meadow by totalizing inversion such that 0^{-1}=0. Q_0 can be expanded by a total sign function s that extracts the sign of a rational number. In this paper we discuss an extension Q_0(s ,\sqrt) of the signed rationals in which every number has a unique square root.Comment: 9 page

Note on paraconsistency and reasoning about fractions

We apply a paraconsistent logic to reason about fractions.Comment: 6 page

Straight-line instruction sequence completeness for total calculation on cancellation meadows

A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the instruction set $\{x \Leftarrow 0, x \Leftarrow 1, x\Leftarrow -x, x\Leftarrow x^{-1}, x\Leftarrow x+y, x\Leftarrow x\cdot y\}$. It is proven that total functions on cancellation meadows can be computed by straight-line programs using at most 5 auxiliary variables. A similar result is obtained for signed meadows.Comment: 24 page

Equations for formally real meadows

We consider the signatures $\Sigma_m=(0,1,-,+, \cdot, \ ^{-1})$ of meadows and $(\Sigma_m, {\mathbf s})$ of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom scheme expressing formal realness; the second axiomatization presupposes an ordering. We apply these completeness results in order to obtain complete axiomatizations of the complex numbers.Comment: 24 pages, 14 tables, revised, new Theorem 3.

Tests of Power Corrections to Event Shape Distributions from e+e- Annihilation

A study of differential event shape distributions using e+e- data at centre-of-mass energies of 35 to 183 GeV is presented. We investigated non-perturbative power corrections for the thrust, C-parameter, total and wide jet broadening observables. We observe a good description of the distributions by the combined resummed QCD calculations plus power corrections from the dispersive approach. The single non-perturbative parameter \alpha_0 is measured to be \alpha_0 (2 GeV) = 0.502 +- 0.013 (stat.) ^{+0.046)_{-0.032} (exp. syst.) ^{+0.074}_{-0.053} (theo. syst.) and is found to be universal for the observables studied within the given systematic uncertainties. Using revised calculations of the power corrections for the jet broadening variables, improved consistency of the individual fit results is obtained. Agreement is also found with results extracted from the mean values of event shape distributions.Comment: 19 pages, LaTeX2e, 8 .eps-files included, paper contributed to the EPS-HEP99 conference in Tampere, Finlan

Effects of Nonmaternal Child Care on Inequality in Cognitive Skills

As a result of changing welfare policies, large numbers of children of poor, uneducated mothersare likely to receive care from others as their mothers enter the workforce. How will this change affect inequality in cognitive skills among young children? One view suggests that inequality will expand because children from economically advantaged families have access to better child care, and families with well-educated parents are more likely to reinforce the cognitive benefits of care. Another view argues that inequality will diminish because even though child care may be unequal, it may be less unequal than the home environments that are supplanted by nonmaternal care. A third view suggests that because the effects of care are inconsistent, there will be little overall change in inequality. Analysis of the children of mothers in the National Longitudinal Survey of Youth provides tentative evidence in support of the first view, that nonmaternal care tends to magnify inequality. Although ordinary least squares regressions reveal no effects of child care, fixed-effects models that control for differences between families indicate that children of high-income, well-educated mothers benefit from center-based care, but children of low-income, poorly educated mothers suffer a cognitive disadvantage from attending day care centers. Home-based care, however, is not associated with cognitive performance. Results from nonparametric analyses are consistent with the findings from fixed-effects models. The key results rely mainly on a relatively small sample of about 700 children in 300 families that sent their children to different types of care, and they do not pertain to families with only one child, so caution is warranted in generalizing the findings.

Tests of Power Corrections for Event Shapes in e+e- Annihilation

A study of perturbative QCD calculations combined with power corrections to model hadronisation effects is presented. The QCD predictions are fitted to differential distributions and mean values of event shape observables measured in e+e- annihilation at centre-of-mass energies from 14 to 189 GeV. We investigate the event shape observables thrust, heavy jet mass, C-parameter, total and wide jet broadening and differential 2-jet rate and observe a good description of the data by the QCD predictions. The strong coupling constant alpha_S(M_Z) and the free parameter of the power correction calculations alpha_0(2 GeV) are measured to be alpha_S(M_Z) = 0.1171 +/- 0.0032/0.0020 and alpha_0(2 GeV) = 0.513 +/- 0.066/0.045. The predicted universality of alpha_0 is confirmed within the uncertainties of the measurements.Comment: 28 pages, LaTeX2e, 21 .eps-files included, accepted by Eur. Phys. J.