We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, int...

Casson and Gordon gave the rectangle condition for strong irreducibility of Heegaard splittings [1]. We give a parity condition for irreducibility of Heegaard splittings of irreducible manifolds. As an application, we give examples of non-stabilized Heegaard splittings by doing a single Dehn twist.

In the current paper we prove the irreducibility of Severi varieties on Hirzebruch surfaces in arbitrary characteristic. Our approach is of purely algebro-geometric nature, and it works in any characteristic. As a result, we obtain a deformation-theoretic proof of the irreducibility of moduli spaces Mg in positive characteristic, which does not involve reduction to characteristic zero.

In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are rational and are at finite Hausdorff distance among them. As a consequence, we provide a projective linear subspace where all (irreducible) elements are solutio...

We study effectively the simultaneous approximation of n − 1 different complex numbers by conjugate algebraic integers of degree n over Z( √ −1). This is a refinement of a result of Motzkin [2] (see also [3], p. 50) who has no estimate for the remaining conjugate. If the n−1 different complex numbers lie symmetrically about the real axis, then Z( √ −1) can be replaced by Z. In Section 1 we prov...

We present a sequential deterministic polynomial-time algorithm for testing dense multivariate polynomials over a large finite field for irreducibility. All previously known algorithms were of a probabilistic nature. Our deterministic solution is based on our algorithm for absolute irreducibility testing combined with Berlekamp’s algorithm.

In the paper we introduce the notion of →-irreducibility and we show that the set of all →-irreducible elements of a finite Heyting lattice L forms the skeleton of L. We also discuss a parallel concept of ↔-irreducibility and give a similar characterization. Finally, we present generalizations of these results for some class of infinite Heyting lattices.