We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a distinct point in the bigger set. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision o...

We prove that for all $s\in(0,d)$ and $c\in (0,1)$ there exists a self-similar set $E\subset \mathbb{R}^d$ with Hausdorff dimension $s$ such $\mathcal{H}^s(E)=c|E|^s$. This answers question raised by Zhiying Wen[16].

In the paper we study (countably) compact and (absolutely) H-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive topological inverse semigroup embeds into a compact primitive topological inverse semigroup. In this paper all spaces are Hausdorff. A semigr...

Let M(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup S with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for M(S)∗ to have a topologically left invariant mean.

In a recent paper [l],1 W. F. Eberlein introduced the notion of Banach-Hausdorff limits. We employ throughout m to denote the space of all real bounded sequences [2, pp. 11 and 34]. The BanachHausdorff limits are real-valued functionals L(x), defined over m, which are Banach limits [2, p. 34], i.e., which satisfy the four conditions (i) L(ax+by)=aL(x)+bL(y) (a, b real), (ii)L(l) = l, (iii) L(x)...

Given a local homeomorphism σ : U → X where U ⊆ X is clopen and X is a compact and Hausdorff topological space, we obtain the possible transfer operators Lρ which may occur for α : C(X) → C(U) given by α(f) = f ◦ σ. We obtain examples of partial dynamical systems (XA, σA) such that the construction of the covariance algebra C (XA, σA) and the crossed product by partial endomorphism O(XA, α, L) ...

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces is equivalent to sequential compactness. We also show Hausdorff compact are metrizable. the second part article discuss significance bottom sets fixed point theorems for mappings acting spaces.

David maps are generalizations of classical planar quasiconformal maps for which the dilatation is allowed to tend to infinity in a controlled fashion. In this note we examine how these maps distort Hausdorff dimension. We show: – Given α and β in [0, 2] , there exists a David map φ: C → C and a compact set Λ such that dimH Λ = α and dimH φ(Λ) = β . – There exists a David map φ: C → C such that...

We study iterated function systems (IFSs) of contractive similitudes on Rd with overlaps. We introduce a generalized finite type condition which extends a more restrictive condition in [S.-M. Ngai, Y. Wang, Hausdorff dimension of self-similar sets with overlaps, J. London Math. Soc. (2) 63 (3) (2001) 655–672] and allows us to include some IFSs of contractive similitudes whose contraction ratios...

Consider two (n − 1)-dimensional manifolds, S and S ′ in R . We say that they are projection-homeomorphic when the closest projection of each one onto the other is a homeomorphism. We give tight conditions under which S and S ′ are projection-homeomorphic. These conditions involve the local feature size for S and for S and the Hausdorff distance between them. Our results hold for arbitrary n.