The equivalence of a Gibbsian equilibrium condition and the KMS condition is proven for one-dimensional quantum lattice systems with a finite range interaction at arbitrary temperature, and for quantum lattice systems of arbitrary dimension, with a finite body interaction, at high temperature.

In a previous paper [6] it was shown that a certain two-parameter dilation of a given strongly continuous self-adjoint contraction semigroup, called the time-orthogonal unitary dilation, gives rise to noncommutative Feynman-Kac formulae through the mechanism of Boson second quantisation in Fock space. This paper explores the modifications of this theory which arise firstly by using Fermion rather than Boson second quantisation, and secondly by using Boson second quantisation based on extremal universally invariant states of the CCR algebra. In the second case it is found that the programme is successful if and only if the infinitesimal generator of the original semigroup is of trace class. § 1. Introduction In a previous paper [ 6 ] a certain two-parameter unitary evolution, called the time-orthogonal unitary dilation, was constructed for a given strongly continuous self-adjoint contraction one-parameter semigroup. Upon passing to second quantisations in Boson Fock space, one obtains a unitary evolution possessing properties of Euclidean covariance and independence which permit the construction of a non-commutative Feynman-Kac formula [5, 6] for perturbations of the semigroup which is the second quantisation of the originally

This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning work cumulatively, this study traces the evolution of the "here and now" using fixed-duration sliding windows. The analysis uses a suite of common network diagnostics, including the distributions of degrees, distances, and clustering, to track network structure. Several random models that call these diagnostics as parameters help tease them apart as factors from the values of others. Some behaviors are consistent over the entire interval, but most diagnostics indicate that the network's structural evolution is dominated by occasional dramatic shifts in otherwise steady trends. These behaviors are not distributed evenly across the network; stark differences in evolution can be observed between two major subnetworks, loosely thought of as "pure" and "applied", which approximately partition the aggregate. The paper characterizes two major events along the mathematics network trajectory and discusses possible explanatory factors.

Abstract. The Mathematics Subject Classification (MSC), maintained by the American Mathematical Society's Mathematical Reviews (MR) and FIZ Karlsruhe's Zentralblatt für Mathematik (Zbl), is a scheme for classifying publications in mathematics. While it is widely used, its traditional, idiosyncratic conceptualization and representation did not encourage wide reuse on the Web, and it made the scheme hard to maintain. We have reimplemented its current version MSC2010 as a Linked Open Dataset using SKOS, and our focus is concentrated on turning it into the new MSC authority. This paper explains the motivation and details of our design considerations and how we realized them in the implementation, presents use cases, and future applications.

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In a previous paper [6] it was shown that a certain two-parameter dilation of a given strongly continuous self-adjoint contraction semigroup, called the time-orthogonal unitary dilation, gives rise to noncommutative Feynman-Kac formulae through the mechanism of Boson second quantisation in Fock space. This paper explores the modifications of this theory which arise firstly by using Fermion rather than Boson second quantisation, and secondly by using Boson second quantisation based on extremal universally invariant states of the CCR algebra. In the second case it is found that the programme is successful if and only if the infinitesimal generator of the original semigroup is of trace class. § 1. IntroductionIn a previous paper [ 6 ] a certain two-parameter unitary evolution, called the time-orthogonal unitary dilation, was constructed for a given strongly continuous self-adjoint contraction one-parameter semigroup. Upon passing to second quantisations in Boson Fock space, one obtains a unitary evolution possessing properties of Euclidean covariance and independence which permit the construction of a non-commutative Feynman-Kac formula [5,6] for perturbations of the semigroup which is the second quantisation of the originally