Related papers: Free-Boolean independence with amalgamation
The key elements of the Unified Model are reviewed and checked against modern experimental data. For medium-mass or heavy nuclei it is found that separation between collective and intrinsic degrees freedom becomes invalid for after exciting…
A {\em maximal inequality} seeks to estimate $\mathbb{E}\max_i X_i$ in terms of properties of the $X_i$. When the latter are independent, the union bound (in its various guises) can yield tight upper bounds. If, however, the $X_i$ are…
An expression in terms of (cyclotomic) harmonic sums can be simplified by the quasi-shuffle algebra in terms of the so-called basis sums. By construction, these sums are algebraically independent within the quasi-shuffle algebra. In this…
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
We prove a new general multiplicity estimate applicable to sets of functions without any assumption on algebraic independence. The multiplicity estimates are commonly used in determining measures of algebraic independence of values of…
In this note we derive a property of maximal ideal-independent subsets of boolean algebras which has corollaries regarding the continuum cardinals p and s_mm(P(omega)/fin).
We propose a definition for background (in)/dependence in dynamical theories of the evolution of configurations that have a continuous symmetry and test this definition on particle models and on gravity. Our definition draws from Barbour's…
The grouplike elements of a coalgebra over a field are known to be linearly independent over said field. Here we prove three variants of this result. One is a generalization to coalgebras over a commutative ring (in which case the linear…
We introduce a family of quantum semigroups and their natural coactions on noncommutative polynomials. We present three invariance conditions, associated with these coactions, for the joint distribution of sequences of selfadjoint…
Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…
The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest…
We show that free objects on sets do not exist in the category $bal$ of bounded archimedean $\ell$-algebras. On the other hand, we introduce the category of weighted sets and prove that free objects on weighted sets do exist in $bal$. We…
We establish the MF property of the reduced group $ C^* $-algebra of an amalgamated free product of countable Abelian discrete groups. This result is then used to give a characterization of the amalgamated free products of Abelian groups…
We show that the level sets of automorphisms of free groups with respect to the Lipschitz metric are connected as subsets of Culler-Vogtmann space. In fact we prove our result in a more general setting of deformation spaces. As…
We prove unit-free versions of both the associative and the non-associative Vidav-Palmer theorems. Then these results are applied to prove a unit-free version of the Blecher-Ruan-Sinclair non-associative characterization of unital…
We present several approaches to equivariant intersection cohomology. We show that for a complete algebraic variety acted by a connected algebraic group $G$ it is a free module over $H^*(BG)$. The result follows from the decomposition…
We study lifting properties for full product C*-algebras with amalgamation over ${\mathbb C}1$ and give new proofs for some results of Kirchberg and Pisier. We extend the result of Choi on the quasidiagonality of $C^*({\mathbb F}_n)$,…
The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the…
Coupled Maxwell and time-dependent orbital-free calculations are implemented and tested to describe the interaction of electromagnetic waves and matter. The currents and induced fields predicted by the orbital-free calculations are compared…
We consider homogeneity properties of Boolean algebras that have nonprincipal ultrafilters which are countably generated.It is shown that a Boolean algebra B is homogeneous if it is the union of countably generated nonprincipal ultrafilters…