Image retrieval and image compression are both very active elds of research. Unfortunately, in the past they were pursued independently leading to image indexing methods being both eÆcient and e ective but restricted to uncompressed images. In this paper we introduce an image retrieval technique that operates in the compressed domain of vector quantised images. Vector quantization (VQ) achieves...

Let be a Pisot unit of degree 3 with a certain niteness condition. A large family of self similar plane tilings can be constructed, by the digit expansion in base . (cf. [7], [5], [8]) In this paper, we prove that the origin is an inner point of the central tile K. Further, in the case corresponds to the minimal Pisot number, we shall give a detailed study on the fractal boundary of each tile. ...

Hyperbolic branching Brownian motion is a branching di usion process in which individual particles follow independent Brownian paths in the hyperbolic plane H2, and undergo binary ssion(s) at rate ¿0. It is shown that there is a phase transition in : For 51=8 the number of particles in any compact region of H2 is eventually 0, w.p.1, but for ¿1=8 the number of particles in any open set grows to...

In a previous paper MR the authors introduced the inverse measure y of a probability measure on It was argued that the respective multifractal spectra are linked by the inversion formula fy f Here the statements of MR are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures Thereby f may stand for the Hausdor spectrum the packing spect...

This is a survey article on domain constants related to uniform perfectness. We gather comparison theorems for various domain constants, most of which are, more or less, known or elementary, but not stated quantitatively in literature, and some are new or improved results. Among these theorems, our main result is a comparison of the modulus and the injectivity radius of a hyperbolic Riemann sur...

The first main result of this paper is that the law of the (rescaled) two-dimensional uniform spanning tree is tight in a space whose elements are measured, rooted real trees continuously embedded into Euclidean space. Various properties of the intrinsic metrics, measures and embeddings of the subsequential limits in this space are obtained, with it being proved in particular that the Hausdor↵ ...

Let H0 be an arbitrary self-adjoint n × n matrix and H(n) be an n × n (random) Wigner matrix. We show that t 7→ Tr exp(H(n)−itH0) is positive definite in the average. This partially answers a long-standing conjecture. On the basis of asymptotic freeness our result implies that t 7→ τ(exp(a − itb)) is positive definite whenever the noncommutative random variables a and b are in free relation, wi...

O R IG IN A L A R T IC L E

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...