A class of generalized Ornstein transformations with the weak mixing property
A class of nonstationary adic transformations
A class of stationary stochastic processes
Regular stationary stochastic vector processes whose spectral densities are the boundary values of matrix functions with bounded Nevanlinna characteristic are considered. A criterion for the representability of such processes as output data of linear time invariant dynamical systems is established.
A class of strongly cooperative systems without compactness
A class of tridiagonal operators associated to some subshifts
We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N....
A classification of bicritical rational maps with a pair of period two superattracting cycles
We give a Thurston classification of those bicritical rational maps which have two period two superattracting cycles. We also show that all such maps are constructed by the mating of two unicritical degree polynomials.
A classification of inverse limit spaces of tent maps with periodic critical points
We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps , with periodic critical points, we show that the inverse limit spaces and are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.
A classification of triangular maps of the square.
A Closing Lemma on the Interval.
A combinatorial invariant for escape time Sierpiński rational maps
An escape time Sierpiński map is a rational map drawn from the McMullen family z ↦ zⁿ + λ/zⁿ with escaping critical orbits and Julia set homeomorphic to the Sierpiński curve continuum. We address the problem of characterizing postcritically finite escape time Sierpiński maps in a combinatorial way. To accomplish this, we define a combinatorial model given by a planar tree whose vertices come with a pair of combinatorial data that encodes the dynamics of critical orbits. We show...
A combinatorial proof of the extension property for partial isometries
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
A comparative dynamical analysis of Hebrew texts.
A compositional approach to synchronize two dimensional networks of processors
A Compositional Approach to Synchronize Two Dimensional Networks of Processors
The problem of synchronizing a network of identical processors that work synchronously at discrete steps is studied. Processors are arranged as an array of m rows and n columns and can exchange each other only one bit of information. We give algorithms which synchronize square arrays of (n × n) processors and give some general constructions to synchronize arrays of (m × n) processors. Algorithms are given to synchronize in time n2, , and 2n a square array of (n × n) processors. Our approach...
A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours
A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs treatment....
A concentration Phenomenon in Mean curvature Flow.
A conservative evolution of the Brownian excursion.
A construction of realizations of perturbations of Poincaré maps
A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions
We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree.
A continuity property for the inverse of Mañé's projection
Let be a compact subset of a separable Hilbert space with finite fractal dimension , and an orthogonal projection in of rank greater than or equal to . For every , there exists an orthogonal projection in of the same rank as , which is injective when restricted to and such that . This result follows from Mañé’s paper. Thus the inverse of the restricted mapping is well defined. It is natural to ask whether there exists a universal modulus of continuity for the inverse of Mañé’s...