Finiteness spaces were introduced by Ehrhard as a model of linear logic, which relied on a finitess property of the standard relational interpretation and allowed to reformulate Girard’s quantitative semantics in a simple, linear algebraic setting. We review recent results obtained in a joint work with Christine Tasson, providing a very simple and generic construction of finiteness spaces: basi...

After results by the author (1980, 1981) and Vinberg (1981), finiteness of the number of maximal arithmetic groups generated by reflections in Lobachevsky spaces was not known in dimensions 2 ≤ n ≤ 9 only. Recently (2005), the finiteness was proved in dimension 2 by Long, Maclachlan and Reid, and in dimension 3 by Agol. Here we use these results in dimensions 2 and 3 to prove finiteness in all ...

The purpose of this paper is to develop a geometric approach to Wall's finiteness obstruction. We will do this for equivariant CW-complexes. The main advantage will be that we can derive all the formal properties of the equivariant finiteness obstruction easily from this geometric description. Namely, the obstruction property, homotopy invariance, the sum and product formulas, and the restricti...

Let Rt = sup0≤s≤t Xs − Xt be a Lévy process reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times above power law boundaries at infinity. Information as to when the expected passage time for Rt is finite, is given. We also discuss the almost sure finiteness of lim sup t→0 Rt/t , for each κ ≥ 0.

Young's experiment is the quintessential quantum experiment. It is argued here that quantum interference is a consequence of the finiteness of information. The observer has the choice of whether that information manifests itself as path information or in the interference pattern or partly in both to the extent defined by the finiteness of information.

We provide a characterization of countably n-rectifiable measures in terms $\sigma$-finiteness the integral Menger curvature. also prove that finiteness condition on pointwise curvature can characterize rectifiability Radon measures. Motivated by partial converse Meurer's work Kolasiński we under suitable density assumptions there is comparability between pointwise-Menger and sum over scales ce...

This paper deals with the joint spectral radius of a finite set of matrices. We say that a set of matrices has the finiteness property if the maximal rate of growth, in the multiplicative semigroup it generates, is given by the powers of a finite product. Here we address the problem of establishing the finiteness property of pairs of 2× 2 sign-matrices. Such problem is related to the conjecture...

In the present paper, synchronous, tabled chain code picture systems based on Lindenmayer systems (sT0L systems) are studied with respect to the finiteness of their picture languages. The finiteness is proved to be decidable. Additionally, a method is given for deciding whether an sT0L system generates a finite picture language or not.

We show that an artin algebra Λ having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with vanishing radical cube. We also give an equivalence between the finiteness of fin.dim.Λ and the finiteness of a given class of Λ-modules of infinite projective dimension.