Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom

We study the universality between a discrete spin model with icosahedral symmetry and the O(3) model in two dimensions. For this purpose we study numerically the renormalized two-point functions of the spin field and the four point coupling constant. We find that those quantities seem to have the same continuum limits in the two models. This has far reaching consequences, because the icosahedron model is not asymptotically free in the sense that the coupling constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in the short distance limit. By universality this then also applies to the O(3) model, contrary to the predictions of perturbation theory.Comment: 18 pages, 8 figures Color coding in Fig. 5 changed to improve visibilit

Effects of different cultivation techniques on vineyard fauna

Green covering compared to soil cultivation enhanced the number of individuals of Araneae living on or near soil. No differences between the different soil management systems were found for the number of individuals of Staphylinidae and Carabidae. The typical main species of the two systems were different for all groups analyzed (Araneae, Staphylinidae and Carabidae)

On the Number of Solutions of Exponential Congruences

For a prime $p$ and an integer $a \in \Z$ we obtain nontrivial upper bounds on the number of solutions to the congruence $x^x \equiv a \pmod p$, $1 \le x \le p-1$. We use these estimates to estimate the number of solutions to the congruence $x^x \equiv y^y \pmod p$, $1 \le x,y \le p-1$, which is of cryptographic relevance

Coadjoint orbits of the Virasoro algebra and the global Liouville equation

The classification of the coadjoint orbits of the Virasoro algebra is reviewed and is then applied to analyze the so-called global Liouville equation. The review is self-contained, elementary and is tailor-made for the application. It is well-known that the Liouville equation for a smooth, real field $\phi$ under periodic boundary condition is a reduction of the SL(2,R) WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction yields, for the field $Q=\kappa g_{22}$ where $\kappa\neq 0$ is a constant, what we call the global Liouville equation. Corresponding to the winding number of the SL(2,R) WZNW model there is a topological invariant in the reduced theory, given by the number of zeros of Q over a period. By the substitution $Q=\pm\exp(- \phi/2)$, the Liouville theory for a smooth $\phi$ is recovered in the trivial topological sector. The nontrivial topological sectors can be viewed as singular sectors of the Liouville theory that contain blowing-up solutions in terms of $\phi$. Since the global Liouville equation is conformally invariant, its solutions can be described by explicitly listing those solutions for which the stress-energy tensor belongs to a set of representatives of the Virasoro coadjoint orbits chosen by convention. This direct method permits to study the `coadjoint orbit content' of the topological sectors as well as the behaviour of the energy in the sectors. The analysis confirms that the trivial topological sector contains special orbits with hyperbolic monodromy and shows that the energy is bounded from below in this sector only.Comment: Plain TEX, 48 pages, final version to appear in IJMP

Dynamical r-matrices and the chiral WZNW phase space

The dynamical generalization of the classical Yang-Baxter equation that governs the possible Poisson structures on the space of chiral WZNW fields with generic monodromy is reviewed. It is explained that for particular choices of the chiral WZNW Poisson brackets this equation reduces to the CDYB equation recently studied by Etingof--Varchenko and others. Interesting dynamical r-matrices are obtained for generic monodromy as well as by imposing Dirac constraints on the monodromy.Comment: Talk given at XXIII International Colloquium on Group Theoretical Methods in Physics, July 31 - August 5, 2000, Dubna, Russia. LaTeX, 9 page

An ideal toy model for confining, walking and conformal gauge theories: the O(3) sigma model with theta-term

A toy model is proposed for four dimensional non-abelian gauge theories coupled to a large number of fermionic degrees of freedom. As the number of flavors is varied the gauge theory may be confining, walking or conformal. The toy model mimicking this feature is the two dimensional O(3) sigma model with a theta-term. For all theta the model is asymptotically free. For small theta the model is confining in the infra red, for theta = pi the model has a non-trivial infra red fixed point and consequently for theta slightly below pi the coupling walks. The first step in investigating the notoriously difficult systematic effects of the gauge theory in the toy model is to establish non-perturbatively that the theta parameter is actually a relevant coupling. This is done by showing that there exist quantities that are entirely given by the total topological charge and are well defined in the continuum limit and are non-zero, despite the fact that the topological susceptibility is divergent. More precisely it is established that the differences of connected correlation functions of the topological charge (the cumulants) are finite and non-zero and consequently there is only a single divergent parameter in Z(theta) but otherwise it is finite. This divergent constant can be removed by an appropriate counter term rendering the theory completely finite even at theta > 0.Comment: 9 pages, 2 figures, minor modification, references adde

Fluoridation of Public Water Systems: Valid Exercise of State Police Power or Constitutional Violation

The addition of fluoride to public water systems is naively accepted by most Americans as a purported method of reducing tooth decay, but the toxic properties of fluoride and its effect on the human body are virtually unbeknownst to the public. Many lawsuits have been brought over the last thirty years seeking to enjoin the artificial fluoridation of public water, but courts have always upheld the statutes as a valid exercise of state police power. However, this police power is not absolute; statutes enacted to protect the health of citizens must not violate any constitutionally guaranteed rights. Those statutes which impinge on fundamental rights must pass the demanding standard of judicial review called strict scrutiny. Because two recent Supreme Court decisions have held that compulsory medication against one\u27s will is a constitutional violation of the 14th Amendment liberty interest, this Comment argues that fluoridation statutes will not pass a strict scrutiny analysis and that the United States Supreme Court should find these statutes to be in contravention of the Constitution

PACS photometer calibration block analysis

The absolute stability of the PACS bolometer response over the entire mission lifetime without applying any corrections is about 0.5% (standard deviation) or about 8% peak-to-peak. This fantastic stability allows us to calibrate all scientific measurements by a fixed and time-independent response file, without using any information from the PACS internal calibration sources. However, the analysis of calibration block observations revealed clear correlations of the internal source signals with the evaporator temperature and a signal drift during the first half hour after the cooler recycling. These effects are small, but can be seen in repeated measurements of standard stars. From our analysis we established corrections for both effects which push the stability of the PACS bolometer response to about 0.2% (stdev) or 2% in the blue, 3% in the green and 5% in the red channel (peak-to-peak). After both corrections we still see a correlation of the signals with PACS FPU temperatures, possibly caused by parasitic heat influences via the Kevlar wires which connect the bolometers with the PACS Focal Plane Unit. No aging effect or degradation of the photometric system during the mission lifetime has been found.Comment: 15 pages, accepted for publication in Experimental Astronom