Related papers: Product Disintegrations: Some Examples
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density…
Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.
We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define…
This is the central article of a series of three papers on cross product bialgebras. We present a universal theory of bialgebra factorizations (or cross product bialgebras) with cocycles and dual cocycles. We also provide an equivalent…
This note presents some numerical examples worked out in order to show the reader how to implement, within a widely accessible computational setting, the methodology for achieving zero cancellation in linear multivariable systems discussed…
We introduce the concept of constructible ideal and we relate this concept with the notion of constructible simplicial complex. Several properties of constructible ideals are studied.
Two-dimensional dilational materials, for which the only easy mode of deformation is a dilation are reviewed and connections are drawn between models previously proposed in the literature. Some models which appear to be dilational…
We introduce the notion of a transformation digroup and prove that every digroup is isomorphic to a transformation digroup.
The cocycle bicrossed product construction allows certain freedom in producing examples of locally compact quantum groups. We give an overview of some recent examples of this kind having remarkable properties.
This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…
Higher-rank versions of Wold decomposition are shown to hold for doubly commuting isometric representations of product systems of C*-correspondences over N^k, generalising the classical result for a doubly commuting pair of isometries due…
A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…
Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…
We motivate and explore the basic features of generalized contagion, a model mechanism that unifies fundamental models of biological and social contagion. Generalized contagion builds on the elementary observation that spreading and…
We discuss a class of linear representations of the product poset of totally ordered sets $P= T_1 \times \cdots \times T_n$ which decompose into interval representations for block intervals. These can be characterised in terms of a…
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…
We introduce an analytically solvable model for a fragmented object that, despite of a low degree of randomness and of the extreme simplicity of the breaking process, displays non self-averaging effects in its thermodynamic limit.
The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…
We review mechanisms of dynamical supersymmetry breaking. Several observations that narrow the search for possible models of dynamical supersymmetry breaking are summarized. These observations include the necessary and sufficient conditions…