5,275 research outputs found
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 . 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 of meadows
and 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.
Universality of Univariate Mixed Fractions in Divisive Meadows
Univariate fractions can be transformed to mixed fractions in the equational
theory of meadows of characteristic zero.Comment: 12 page
Chirality of tensor perturbations for complex values of the Immirzi parameter
In this paper we generalise previous work on tensor perturbations in a de
Sitter background in terms of Ashtekar variables to cover all complex values of
the Immirzi parameter gamma (previous work was restricted to imaginary gamma).
Particular attention is paid to the case of real gamma. Following the same
approach as in the imaginary case, we can obtain physical graviton states by
invoking reality and torsion free conditions. The Hamiltonian in terms of
graviton states has the same form whether gamma has a real part or not; however
changes occur for the vacuum energy and fluctuations. Specifically, we observe
a gamma dependent chiral asymmetry in the vacuum fluctuations only if gamma has
an imaginary part. Ordering prescriptions also change this asymmetry. We thus
present a measurable result for CMB polarisation experiments that could shed
light on the workings of quantum gravity.Comment: 6 pages, 1 figur
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.
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