On axiomatic definitions of non-discrete affine buildings

In this paper we prove equivalence of sets of axioms for non-discrete affine buildings, by providing different types of metric, exchange and atlas conditions. We apply our result to show that the definition of a Euclidean building depends only on the topological equivalence class of the metric on the model space. The sharpness of the axioms dealing with metric conditions is illustrated in an appendix. There it is shown that a space X defined over a model space with metric d is possibly a building only if the induced distance function on X satisfies the triangle inequality.Comment: Errors corrected, results extended. (This replaces the two earlier, separate preprints "Axioms of affine buidlings" arXiv:0909.2967v1 and "Affine $\Lambda$ buildings II" arXiv:0909.2059v1.

Discrete Velocity Fields with Explicitly Computable Lagrangian Law

We introduce a class of random velocity fields on the periodic lattice and in discrete time having a certain hidden Markov structure. The generalized Lagrangian velocity (the velocity field as viewed from the location of a single moving particle) has similar hidden Markov structure, and its law is found explicitly. Its rate of convergence to equilibrium is studied in small numerical examples and in rigorous results giving absolute and relative bounds on the size of the second–largest eigenvalue modulus. The effect of molecular diffusion on the rate of convergence is also investigated; in some cases it slows convergence to equilibrium. After repeating the velocity field periodically throughout the integer lattice, it is shown that, with the usual diffusive rescaling, the single–particle motion converges to Brownian motion in both compressible and incompressible cases. An exact formula for the effective diffusivity is given and numerical examples are shown

Finding Common Ground: Collaboration Across the Disciplines in the Scholarship of Teaching

Many recent writings on the scholarship of teaching discuss the need to locate this scholarship within the disciplines. The authors argue that while scholarship within the disciplines is important, it should not come at the expense of work across the disciplines. They demonstrate the usefulness of cross-disciplinary collaboration for the scholarship of teaching and learning through the specific example of how collaboration contributed to their understanding of the role of such scholarship in the teaching of mathematics and negotiations courses. The authors also outline some of the pitfalls of cross-disciplinary collaboration, and they offer suggestions for beginning collaborative initiatives

Bounds on New Physics from the New Data on Parity Violation in Atomic Cesium

We assume the latest experimental determination of the weak charge of atomic cesium and analyze its implications for possible new physics. We notice that the data would imply positive upper and lower bounds on the new physics contribution to the weak charge, $\delta_NQ_W$. The required new physics should be of a type not severely constrained by the high energy precision data. A simplest possibility would be new neutral vector bosons almost un-mixed to the $Z$ and with sizeable couplings to fermions. The lower positive bound would however forbid zero or negative $\delta_NQ_W$ and exclude not only the standard model but also models with sequential $Z^\prime$, in particular simple-minded towers of $Z$-like excitations from extra-dimensions. The bound would also imply an upper limit on the $Z^\prime$ mass within the models allowed. Conclusions are also derived for models of four-fermion contact interactions.Comment: 11 pages, Latex, 1 PS figure, final version for Physics Letter

Drawing a Triangle on the Thurston Model of Hyperbolic Space

In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem

SM Kaluza-Klein Excitations and Electroweak Precision Tests

We consider a minimal extension to higher dimensions of the Standard Model, having one compactified dimension, and we study its experimental tests in terms of electroweak data. We discuss tests from high-energy data at the $Z$-pole, and low-energy tests, notably from atomic parity violation data. This measurement combined with neutrino scattering data strongly restricts the allowed region of the model parameters. Furthermore this region is incompatible at 95% CL with the restrictions from high-energy experiments. Of course a global fit to all data is possible but the $\chi^2_{\rm min}$ for degree of freedom is unpleasantly large.Comment: LaTex, 14 pages, 2 figures. More refs. and one comment about the validity of our results for any number of extra dimensions adde

Against strong pluralism

Strong pluralists hold that not even permanent material coincidence is enough for identity. Strong pluralism entails the possibility of purely material objects -- even if not coincident -- alike in all general respects, categorial and dispositional, relational and non-relational, past, present and future, at the microphysical level, but differing in some general modal, counterfactual or dispositional repscts at the macrophysical level. It is objectionable because it thus deprives us of the explanatory resources to explain why evident absurdities are absurd. A second objection is to the suggestion that cases involving artefacts can illustrate strong pluralism. This offends against the principle that gien a complex intrinsic microphysical property instantiated in some regiion, the number of material things possessing it in that region cannot depend on the existence and nature of intentional activity taking place outside it