Related papers: A non commutative sewing lemma
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
We give a new proof that bounded non-commutative functions on polynomial polyhedra can be represented by a realization formula, a generalization of the transfer function realization formula for bounded analytic functions on the unit disk.
In this paper we study the notion of strong non-reflection, and its contrapositive weak reflection. We say theta strongly non-reflects at lambda iff there is a function F: theta ---> lambda such that for all alpha < theta with cf(alpha)=…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
We study the extension of integrable equations which possess the Lax representations to noncommutative spaces. We construct various noncommutative Lax equations by the Lax-pair generating technique and the Sato theory. The Sato theory has…
We provide a combinatorial formula for the expansion of immaculate noncommutative symmetric functions into complete homogeneous noncommutative symmetric functions. To do this, we introduce generalizations of Ferrers diagrams which we call…
We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough…
Let $(X,\mathcal{F},\mu,T)$ be a not necessarily invertible non-atomic measure-preserving dynamical system where the $\sigma$-algebra $\mathcal{F}$ is generated by the intervals according to some total order. The main result is that the…
We consider non oscillatory functions and prove an everywhere Fourier Inversion Theorem for functions of very moderate decrease. The proofs rely on some ideas in nonstandard analysis.
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
We prove that Tietze Extension does not always exist in constructive mathematics if closed sets on which the function we are extending are defined as sequentially closed sets. Firstly, we take a discrete metric space as our topological…
We establish the first common fixed point theorem for commutative set-valued mappings. This may help to generalize common fixed point theorems in single-valued setting to those in set-valued. We also prove the existence of a fixed point in…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…
Application of the noncommutative geometry to several physical models is considered.
In this paper some properties of the superstring with noncommutative worldsheet are studied. We study the noncommutativity of the spacetime, generalization of the Poincar\'e symmetry of the superstring, the changes of the metric,…
The goal of this work is to develop, in a systematic way and in a full natural generality, the foundations of a theory of functions of (free) noncommuting variables.
Fortin and Reutenauer defined the non-commutative rank for a matrix with entries that are linear functions. The non-commutative rank is related to stability in invariant theory, non-commutative arithmetic circuits, and Edmonds' problem. We…