Structures in BC_N Ruijsenaars-Schneider models

We construct the classical r-matrix structure for the Lax formulation of BC_N Ruijsenaars-Schneider systems proposed in hep-th 0006004. The r-matrix structure takes a quadratic form similar to the A_N Ruijsenaars-Schneider Poisson bracket behavior, although the dynamical dependence is more complicated. Commuting Hamiltonians stemming from the BC_N Ruijsenaars-Schneider Lax matrix are shown to be linear combinations of particular Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for specific values of the exponential one-body couplings. Uniqueness of such commuting Hamiltonians is established once the first of them and the general analytic structure are given.Comment: 18 pages, gzip latex fil

Adposition and Case Supersenses v2.5: Guidelines for English

This document offers a detailed linguistic description of SNACS (Semantic Network of Adposition and Case Supersenses; Schneider et al., 2018), an inventory of 50 semantic labels ("supersenses") that characterize the use of adpositions and case markers at a somewhat coarse level of granularity, as demonstrated in the STREUSLE corpus (https://github.com/nert-gu/streusle/; version 4.3 tracks guidelines version 2.5). Though the SNACS inventory aspires to be universal, this document is specific to English; documentation for other languages will be published separately. Version 2 is a revision of the supersense inventory proposed for English by Schneider et al. (2015, 2016) (henceforth "v1"), which in turn was based on previous schemes. The present inventory was developed after extensive review of the v1 corpus annotations for English, plus previously unanalyzed genitive case possessives (Blodgett and Schneider, 2018), as well as consideration of adposition and case phenomena in Hebrew, Hindi, Korean, and German. Hwang et al. (2017) present the theoretical underpinnings of the v2 scheme. Schneider et al. (2018) summarize the scheme, its application to English corpus data, and an automatic disambiguation task

Supersymmetric extension of qKZ-Ruijsenaars correspondence

We describe the correspondence of the Matsuo-Cherednik type between the quantum $n$-body Ruijsenaars-Schneider model and the quantum Knizhnik-Zamolodchikov equations related to supergroup $GL(N|M)$. The spectrum of the Ruijsenaars-Schneider Hamiltonians is shown to be independent of the ${\mathbb Z}_2$-grading for a fixed value of $N+M$, so that $N+M+1$ different qKZ systems of equations lead to the same $n$-body quantum problem. The obtained results can be viewed as a quantization of the previously described quantum-classical correspondence between the classical $n$-body Ruijsenaars-Schneider model and the supersymmetric $GL(N|M)$ quantum spin chains on $n$ sites.Comment: 17 page

A new description of equivariant cohomology for totally disconnected groups

We consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced by Baum and Schneider can be described using equivariant periodic cyclic homology. This provides a new approach to the construction of Baum and Schneider as well as a computation of equivariant periodic cyclic homology for a natural class of examples. In addition we discuss the relation between cosheaf homology and equivariant Bredon homology. Since the theory of Baum and Schneider generalizes cosheaf homology we finally see that all these approaches to equivariant cohomology for totally disconnected groups are closely related

On the superintegrability of the rational Ruijsenaars-Schneider model

The rational and hyperbolic Ruijsenaars-Schneider models and their non-relativistic limits are maximally superintegrable since they admit action variables with globally well-defined canonical conjugates. In the case of the rational Ruijsenaars-Schneider model we present an alternative proof of the superintegrability by explicitly exhibiting extra conserved quantities relying on a generalization of the construction of Wojciechowski for the rational Calogero model.Comment: added 2 references and some comments in v2, 10 page

THE LECTOTYPE AND TYPE LOCALITY OF CANDOIA CARINATA (REPTILIA, SERPENTES)

The lectotype of Boa carinata Schneider, 1801, has been rediscovered and is now ZMFK35503, having been transferred in 1977 from the Göttingen Museum, its original location. Its typelocality has not been reported previously, but is indicated as “Amboina” on a label with the lectotype.The specimen is redescribed and fi gured, and conforms with expectations for material from the vicinityof the type locality. A brief history of Schneider and of the syntypes of Boa carinata, now Candoiacarinata, is reviewed

Does the specification of uncertainty hurt the progress of scientometrics?

In "Caveats for using statistical significance tests in research assessments,"--Journal of Informetrics 7(1)(2013) 50-62, available at arXiv:1112.2516 -- Schneider (2013) focuses on Opthof & Leydesdorff (2010) as an example of the misuse of statistics in the social sciences. However, our conclusions are theoretical since they are not dependent on the use of one statistics or another. We agree with Schneider insofar as he proposes to develop further statistical instruments (such as effect sizes). Schneider (2013), however, argues on meta-theoretical grounds against the specification of uncertainty because, in his opinion, the presence of statistics would legitimate decision-making. We disagree: uncertainty can also be used for opening a debate. Scientometric results in which error bars are suppressed for meta-theoretical reasons should not be trusted

What\u27s Wrong With the Movies

Non-fiction by John Schneider