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...

We consider the Mullins’ equation of a single surface grooving when diffusion is not considered as very slow. This problem can be formed by profiles in finite space region. The finiteness region allows to apply Fourier series analysis for one groove and also Mullins coefficient well slope root time-dependent. solve inverse finding time-dependent from total mass measurement. For both these probl...

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.

This paper gathers together different conditions which are all equivalent to geometric ergodicity of time-homogeneous Markov chains on general state spaces. A total 34 presented (27 for plus 7 reversible chains), some old and new, in terms such notions as convergence bounds, drift conditions, spectral properties, etc., with assumptions about the distance metric used, finiteness function moments...

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 investigate when a finite algebra admits only a finite number of compatible relations (modulo a natural equivalence). This finiteness condition is closely related to others in the literature, and arises naturally in duality theory. We find necessary conditions for a finite algebra to admit only finitely many compatible relations, as well as a family of examples of such algebras. The classic ...

Let R be an integral domain with quotient field L. An overring T of R is t-linked over R if I = R implies that (T : IT ) = T for each finitely generated ideal I of R. Let Ot(R) denotes the set of all t-linked overrings of R and O(R) the set of all overrings of R. The purpose of this paper is to study some finiteness conditions on the set Ot(R). Particularly, we prove that if Ot(R) is finite, th...

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.