Related papers: A note on equivalences between various mixing scal…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
The review considers statistical systems composed of several phases that are intermixed in space at mesoscopic scale and systems representing a mixture of several components of microscopic objects. These types of mixtures should be…
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.
We show that topological mixing, weak mixing and total transitivity are equivalent for coded systems. We provide an example of a mixing coded system which cannot be approximated by any increasing sequence of mixing shifts of finite type,…
When one studies the structure (e.g. graded ideals, graded subspaces, radicals, ...) or graded polynomial identities of graded algebras, the grading group itself does not play an important role, but can be replaced by any other group that…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing…
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued…
A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…
Let (X,dX) and (Y,dY) be semimetric spaces with distance sets D(X) and, respectively, D(Y). A mapping F : X \to Y is a weak similarity if it is surjective and there exists a strictly increasing f : D(Y) \to D(X) such that dX = f \circ dY…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some…
We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.