Related papers: Non-Hausdorff Separation Axioms
In discriminating between objects from different classes, the more separable these classes are the less computationally expensive and complex a classifier can be used. One thus seeks a measure that can quickly capture this separability…
In non-relativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In Algebraic Quantum Field Theory, though, local observables corresponding to space-like separated parties are just…
Trace formulas are investigated in non-commutative integration theory. The main result is to evaluate the standard trace of a Takesaki dual and, for this, we introduce the notion of interpolator and accompanied boundary objects. The formula…
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is…
One of the central notions to emerge from the study of persistent homology is that of interleaving distance. It has found recent applications in symplectic and contact geometry, sheaf theory, computational geometry, and phylogenetics. Here…
A transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some of the properties of transfers by using noncommutative determinants. These properties enable us…
We review the developments in the Lie theory for non-associative products from 2000 to date and describe the current understanding of the subject in view of the recent works, many of which use non-associative Hopf algebras as the main tool.
Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…
Quasi-set theory provides a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the quantum statistics into the scope of quasi-set theory and discuss the…
A corpus of vector-embedded text documents has some empirical distribution. Given two corpora, we want to calculate a single metric of distance (e.g., Mauve, Frechet Inception) between them. We describe an abstract quality, called…
Models play an important role in our understanding of the global structure of the solar wind and its interaction with the interstellar medium. A critical ingredient in many types of models are the charge-exchange collisions between ions and…
We show some results about the Hausdorff dimension of particular minimal but not uniquely ergodic interval exchange transformations. There is an appendix which shows that typical points for two different ergodic measures of an interval…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
We discuss quantum non-locality and contextuality using the notion of transition sets. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear…
Two differential calculi are developped on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same quantum group that is extended to a…
We rederive the thermodynamical properties of a non interacting gas in the presence of a minimal uncertainty in length. Apart from the phase space measure which is modified due to a change of the Heisenberg uncertainty relations, the…
The classical Hausdorff-Young inequalities for the Fourier transform acting between appropriate $L_p$ spaces are cornerstones of Fourier analysis. Here we extend it to weighted spaces of Besov or Sobolev type where the weight has the form…
We study the properties of a non-Gaussian density matrix for a O(N) scalar field in the context of the incomplete description picture. This is of relevance for studies of decoherence and entropy production in quantum field theory. In…
Ehrenfest urns with interaction that are connected in a ring is considered as a paradigm model for non-equilibrium thermodynamics and is shown to exhibit two distinct non-equilibrium steady states (NESS) of uniform and non-uniform particle…
We investigate the properties of arithmetic differentiation, an attempt to adapt the notion of differentiation to the integers by preserving the Leibniz rule, (ab)' = a'b + ab'. This has proved to be a very rich topic with many different…