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Refinable functions and distributions with integer dilations have been studied extensively since the pioneer work of Daubechies on wavelets. However, very little is known about refinable functions and distributions with non-integer dilations, particularly concerning its regularity. In this paper we study the decay of the Fourier transform of refinable functions and distributions. We prove that ...

I show that the zeros of the chromatic polynomials PG(q) for the generalized theta graphs Θ(s,p) are, taken together, dense in the whole complex plane with the possible exception of the disc |q − 1| < 1. The same holds for their dichromatic polynomials (alias Tutte polynomials, alias Potts-model partition functions) ZG(q, v) outside the disc |q + v| < |v|. An immediate corollary is that the chr...

We study the chromatic polynomials (= zero-temperature antiferromagnetic Potts-model partition functions) PG(q) for m × n rectangular subsets of the square lattice, with m ≤ 8 (free or periodic transverse boundary conditions) and n arbitrary (free longitudinal boundary conditions), using a transfer matrix in the Fortuin-Kasteleyn representation. In particular, we extract the limiting curves of ...

The aim of the paper is to propose a new description of extraction in plain TAG. Contrary to Kroch 1987’s analysis, our description is based on the fact that the power of a relative clause to adjoin on a noun can be attached to the wh-word rather than to a verb. This analysis solves some problems of the previous analysis, notably by giving the right semantic dependency in case of pied-piping. W...

Architecture, in the real world as well fictional of children’s literature, seems always to be connected with ideology, i.e. a system beliefs held by social group or society whole. This is shown respect German literature dealing famous buildings 20th century, namely semi-detached house Le Corbusier and Pierre Jeanneret Stuttgart Weißenhofsiedlung that portrayed Hannelore erlebt die Großstadt Cl...

The Khinchin–Kahane inequality is a fundamental result in the probability literature, with most general version to date holding Banach spaces. Motivated by modern settings and applications, we generalize this arbitrary metric groups which are abelian. If instead of abelian one assumes group's be norm (i.e., Z>0-homogeneous), then explain how improves same as This occurs via “transfer principle”...

A multiplicative random cascade refers to a positive T -martingale in the sense of Kahane on the ultrametric space T = {0, 1, . . . , b− 1}. A new approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) non-degeneracy criterion, (ii) dimension spectra of carrying sets, and (iii) divergence of moments criterion. Specific applications are ...

We use the recently-developed multiparameter theory of additive Lévy processes to establish novel connections between an arbitrary Lévy process X in R, and a new class of energy forms and their corresponding capacities. We then apply these connections to solve two long-standing problems in the folklore of the theory of Lévy processes. First, we compute the Hausdorff dimension of the image X(G) ...