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

Typability in partial groupoids

Adapting a claim of M. Kracht, we establish a characterization of the typable partial applicative algebras.Comment: 5 page

Completing partial combinatory algebras with unique head-normal forms

In this note, we prove that having unique head-normal forms is a sufficient condition on partial combinatory algebras to be completable. As application, we show that the pca of strongly normalizing CL-terms as well as the pca of natural numbers with partial recursive function application can be extended to total combinatory algebras

Simulated pre-industrial climate in Bergen Climate Model (version 2): model description and large-scale circulation features

The Bergen Climate Model (BCM) is a fully-coupled atmosphere-ocean-sea-ice model that provides state-of-the-art computer simulations of the Earth's past, present, and future climate. Here, a pre-industrial multi-century simulation with an updated version of BCM is described and compared to observational data. The model is run without any form of flux adjustments and is stable for several centuries. The simulated climate reproduces the general large-scale circulation in the atmosphere reasonably well, except for a positive bias in the high latitude sea level pressure distribution. Also, by introducing an updated turbulence scheme in the atmosphere model a persistent cold bias has been eliminated. For the ocean part, the model drifts in sea surface temperatures and salinities are considerably reduced compared to earlier versions of BCM. Improved conservation properties in the ocean model have contributed to this. Furthermore, by choosing a reference pressure at 2000 m and including thermobaric effects in the ocean model, a more realistic meridional overturning circulation is simulated in the Atlantic Ocean. The simulated sea-ice extent in the Northern Hemisphere is in general agreement with observational data except for summer where the extent is somewhat underestimated. In the Southern Hemisphere, large negative biases are found in the simulated sea-ice extent. This is partly related to problems with the mixed layer parametrization, causing the mixed layer in the Southern Ocean to be too deep, which in turn makes it hard to maintain a realistic sea-ice cover here. However, despite some problematic issues, the pre-industrial control simulation presented here should still be appropriate for climate change studies requiring multi-century simulations

Analytic Perturbation Theory for Practitioners and Upsilon Decay

Within the ghost-free Analytic Perturbation Theory (APT), devised in the last decade for low energy QCD, simple approximations are proposed for 3-loop analytic couplings and their effective powers, in both the space-like (Euclidean) and time-like (Minkowskian) regions, accurate enough in the large range (1--100 GeV) of current physical interest.\par Effectiveness of the new Model is illustrated by the example of $\Upsilon(1\mathrm{S})$ decay where the standard analysis gives $\alpha_s(M_{\Upsilon})=0.170\pm 0.004$ value that is inconsistent with the bulk of data for $\alpha_s$. Instead, we obtain $\alpha_s^{Mod}(M_{\Upsilon})=0.185\pm 0.005$ that corresponds to $\alpha_s^{Mod}(M_Z)=0.120\pm 0.002$ that is close to the world average.\par The issue of scale uncertainty for $\Upsilon$ decay is also discussed.Comment: 12 pages, 0 figures. Model slightly modified to increase its accuracy. Numerical results upgraded, references added. The issue of scale uncertainty is discusse