In the study of substitutative dynamical systems and Pisot number systems, an algebraic condition, which we call ‘weak finiteness’, plays a fundamental role. It is expected that all Pisot numbers would have this property. In this paper, we prove some basic facts about ‘weak finiteness’. We show that this property is valid for cubic Pisot units and for Pisot numbers of higher degree under a domi...

Anosov representations give a higher-rank analogue of convex cocompactness in rank-one Lie group which shares many its good geometric and dynamical properties; finiteness rank one may be seen as controlled weakening to allow for isolated failures hyperbolicity. We introduce relatively dominated relativization representations, or other words finiteness. prove that groups admitting must hyperboli...

We show for a finite abelian group G and any element in the image of the Swan homomorphism sw : Z/|G|∗ −→ K̃0(ZG) that it can be realized as the finiteness obstruction of a finitely dominated connected CW -complex X with fundamental group π1(X) = G such that π1(X) is equal to the subgroup G1(X) defined by Gottlieb. This is motivated by the observation that any H-space X satisfies π1(X) = G1(X) a...

Let MPd denote the space of polynomials f : C → C of degree d ≥ 2, modulo conjugation by Aut(C). Using properties of polynomial trees (as introduced in [DM]), we show that if fn is a divergent sequence of polynomials in MPd, then any subsequential limit of the measures of maximal entropy m(fn) will have finite support. With similar techniques, we observe that the iteration maps {MPd 99K MPdn : ...

Let Rb < φ be arbitrary. In [27], it is shown that r 6= e. We show that Heaviside’s condition is satisfied. Next, the work in [19] did not consider the parabolic, countably non-partial case. W. Robinson [7] improved upon the results of J. Johnson by constructing super-linear, universally contravariant equations.

In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...

Finiteness spaces constitute a categorical model of Linear Logic whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps. First, we recall definitions of finiteness spaces and describe their basic properties deduced from the general theory of linearly topologised spaces. Then we give...

Finite quantum field theories may be constructed from the most general renormalizable quantum field theory by forbidding, order by order in the perturbative loop expansion, all ultraviolet-divergent renormalizations of the physical parameters of the theory. The relevant finiteness conditions resulting from this requirement relate all dimensionless couplings in the theory. At first sight, Yukawa...

In this article we investigate the L1–norm of certain functions on groups called divisibility functions. Using these functions, their connection to residual finiteness, and integration theory on profinite groups, we define the residual average of a finitely generated group. One of the main results in this article is the finiteness of residual averages on finitely generated linear groups. Whethe...

PURPOSE The current study investigated finiteness marking (e.g., he walk s, he walk ed) in boys with fragile X syndrome (FXS); the boys were grouped based on receptive vocabulary (i.e., borderline, impaired). METHOD Twenty-one boys with the full mutation of fragile X, between the ages of 8 and 16 years participated. The boys completed probes from the Test of Early Grammatical Impairment (TE...