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Main result: If a C*-algebra is simple, $\sigma$-unital, has finitely many extremal traces, and has strict comparison of positive elements by traces, then its multiplier also has strict comparison of positive elements by traces. The same…
There are just 10 closed flat 3-manifolds, following [1], we call them platycosms. The aim of this paper is to classify types of n-coverings over amphicosms, i.e. some kinds of platycosms, and enumerate the numbers of them. Key words:…
Many instructors choose to assess their students using open-ended written exam items that require students to show their understanding of physics by solving a problem and/or explaining a concept. Grading these items is fairly time…
We explore a novel link between two seemingly disparate mathematical concepts: Egyptian fractions and fractals. By examining the decomposition of rationals into sums of distinct unit fractions, a practice rooted in ancient Egyptian…
The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
This paper discusses experiments with single-particle systems, some of whose states appear to be entangled. It shows that the interpretation of the experiments in terms of entanglement is ill-defined. Three forms of ambiguity are discussed.…
The Hochschild and (cotriple) cyclic homologies of crossed modules of (not-necessarily-unital) associative algebras are investigated. Wodzicki's excision theorem is extended for inclusion crossed modules in the category of crossed modules…
The recently proposed Euclidean index offers a novel approach to measure the citation impact of academic authors, in particular as an alternative to the h-index. We test if the index provides new, robust information, not covered by existing…
We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…
Scaling arguments provide valuable analysis tools across physics and complex systems yet are often employed as one generic method, without explicit reference to the various mathematical concepts underlying them. A careful understanding of…
An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…
The Everett-interpretation description of isolated measurements, i.e., measurements involving interaction between a measuring apparatus and a measured system but not interaction with the environment, is shown to be unambiguous, claims in…
An ensemble technique is characterized by the mechanism that generates the components and by the mechanism that combines them. A common way to achieve the consensus is to enable each component to equally participate in the aggregation…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to…
Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…