The new class of Banach spaces, so-called asymptotic lp spaces, is introduced and it is shown that every Banach space with bounded distortions contains a subspace from this class. The proof is based on an investigation of certain functions, called enveloping functions, which are intimately connected with stabilization properties of the norm. 0 Introduction During the last year several problems ...

Given a graph G = (V,E) with two distinguished vertices s, t ∈ V and an integer parameter L > 0, an L-bounded cut is a subset F of edges (nodes) such that the every path between s and t in G \ F has length more than L. The task is to find an L-bounded cut of minimum cardinality. Though the problem is very simple to state and has been studied since the beginning of the 70’s, it is not much under...

DAEs: Infinite-dimensional LTI Index-1 Case 3.1 Infinite-dimensional Linear Algebra We first collect some useful infinite-dimensional definitions and statements which will be used in this and the next section. Details and proofs of these statements can be found in standard functional analysis references such as [11], [26], [28] and [38]: Proposition 3.1. Let L(X,Y ) denote the space of bounded ...

An algebra M = (M ; ,∨,∧,→, 0, 1) of type 〈2, 2, 2, 2, 0, 0〉 is called a bounded commutative R`-monoid iff (i) (M ; , 1) is a commutative monoid, (ii) (M ;∨,∧, 0, 1) is a bounded lattice, and (iii) x y ≤ z ⇐⇒ x ≤ y → z, (iv) x (x → y) = x ∧ y, for each x, y, z ∈ M . In the sequel, by an R`-monoid we will mean a bounded commutative R`-monoid. (Note that bounded commutative R`-monoids are just bo...

In this paper we consider translation invariant operators with additional symmetry coming from group actions. As the classic Hilbert and Riesz transforms can be characterized up to scalar by means of relative invariance of conformal transformation groups, certain multiplier operators are characterized by relative invariance of some other affine subgroups. In this article, we formalize a geometr...

This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X → V , and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a Banach space. Here, we consider the case V = L, where differentiability fails. We establish another kind of differentiability for certain X , including R and H, the Heisenberg group with its Carnot-Ca...

introduction: heavy metals are types of elements naturally present in soil or enter into soil as a result of human activities. the most important route of exposure to heavy metals is daily intake of food. crops grown in contaminated soil (due to mining activities, industrial operations and agriculture) may contain high concentrations of heavy metals. also closeness to cities and industrial cent...