We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in [2]. Our main results are as follows. (i) It was shown in [26] that for an arbitrary countable infinite group G, any free ergodic probability measure preserving G-system admits a minimal model. In contrast we show here, using URS’s, th...

Throughout the paper we will use the standard definitions and notation ([ABR], [E]). Let X and Y be metric spaces. The goal is to study some intermediate classes of functions between the class Cuc(X,Y ) of all uniformly continuous mappings (briefly, UC) from X into Y and the class C(X,Y ) of all continuous functions f :X → Y . These classes, defined below, have been intensively studied in [BD] ...

This paper investigates the network location problem for single-server facilities that are subject to congestion. In each network edge, customers are uniformly distributed along the edge and their requests for service are assumed to be generated according to a Poisson process. A number of facilities are to be selected from a number of candidate sites and a single server is located at each facil...

Let A and B denote two families of subsets of an n-element set. The pair (A,B) is said to be `-cross-intersecting iff |A∩B| = ` for all A ∈ A and B ∈ B. Denote by P`(n) the maximum value of |A||B| over all such pairs. The best known upper bound on P`(n) is Θ(2), by Frankl and Rödl. For a lower bound, Ahlswede, Cai and Zhang showed, for all n ≥ 2`, a simple construction of an `-cross-intersectin...

This paper discussed the characterizations of uniformly convexity of N -functions. Definition 1. A function M(u): R → R is called an N -function if it has the following properties: (1) M is even, continuous, convex; (2) M(0) = 0 and M(u) > 0 for all u = 0; (3) lim u→0 M(u) u = 0 and lim u→+∞ M(u) u = +∞. The N -function generates the Orlicz spaces. So it is important to analysis it. It is well-...

A word u appears as a factor of another word v as it is; in one piece. When u is a subword of v, u may be scattered as several factors. We consider the in-between case and put some restrictions on the number of factors as which u is allowed to be scattered. A large class of partial orders which are generalizations of factors and subwords is obtained. For all of them, the property of being well ...

Ladner [18] showed that there are no minimal recursive sets under polynomial-time reductions. Given any recursive set A, Ladner constructs a set B such that B strictly reduces to A but B does not lie in P. The set B does have very long sequences of input lengths of easily computable instances. We examine whether Ladner’s results hold if we restrict ourselves to “uniformly hard languages” which ...

Duplication is the replacement of a factor w within a word by ww. This operation can be used iteratively to generate languages starting from words or sets of words. By undoing duplications, one can eventually reach a square-free word, the original word’s duplication root. The duplication root is unique, if the length of duplications is fixed. Based on these unique roots we define the concept of...

LetG be a graph with vertex set V (G) and edge setE(G). A labeling f : V (G) → {0, 1} induces an edge labeling f ∗ : E(G) → {0, 1}, defined by f ∗(xy) = |f (x) − f (y)| for each edge xy ∈ E(G). For i ∈ {0, 1}, let ni(f ) = |{v ∈ V (G) : f (v) = i}| and mi(f )=|{e ∈ E(G) : f ∗(e)= i}|. Let c(f )=|m0(f )−m1(f )|.A labeling f of a graphG is called friendly if |n0(f )−n1(f )| 1. A cordial labeling ...