Explosion of smoothness from a point to everywhere for conjugacies between Markov families

For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics.

Hausdorff dimension versus smoothness

There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.

Adhesion and wear behaviour of NCD coatings on Si3N4 by micro-abrasion tests

Nanocrystalline diamond (NCD) coatings offer an excellent alternative for tribological applications, preserving most of the intrinsic mechanical properties of polycrystalline CVD diamond and adding to it an extreme surface smoothness. Silicon nitride (Si3N4) ceramics are reported to guarantee high adhesion levels to CVD microcrystalline diamond coatings, but the NCD adhesion to Si3N4 is not yet well established. Micro-abrasion tests are appropriate for evaluating the abrasive wear resistance of a given surface, but they also provide information on thin film/substrate interfacial resistance, i.e., film adhesion. In this study, a comparison is made between the behaviour of NCD films deposited by hot-filament chemical vapour deposition (HFCVD) and microwave plasma assisted chemical vapour deposition (MPCVD) techniques. Silicon nitride (Si3N4) ceramic discs were selected as substrates. The NCD depositions by HFCVD and MPCVD were carried out using H2–CH4 and H2–CH4–N2 gas mixtures, respectively. An adequate set of growth parameters was chosen for each CVD technique, resulting in NCD films having a final thickness of 5 m. A micro-abrasion tribometer was used, with 3 m diamond grit as the abrasive slurry element. Experiments were carried out at a constant rotational speed (80 r.p.m.) and by varying the applied load in the range of 0.25–0.75 N. The wear rate for MPCVD NCD (3.7±0.8 × 10−5 m3N−1m−1) is compatible with those reported for microcrystalline CVD diamond. The HFCVD films displayed poorer adhesion to the Si3N4 ceramic substrates than the MPCVD ones. However, the HFCVD films show better wear resistance as a result of their higher crystallinity according to the UV Raman data, despite evidencing premature adhesion failure.

Adaptive filtering for high quality HMM based speech synthesis

In this work an adaptive filtering scheme based on a dual Discrete Kalman Filtering (DKF) is proposed for Hidden Markov Model (HMM) based speech synthesis quality enhancement. The objective is to improve signal smoothness across HMMs and their related states and to reduce artifacts due to acoustic model's limitations. Both speech and artifacts are modelled by an autoregressive structure which provides an underlying time frame dependency and improves time-frequency resolution. Themodel parameters are arranged to obtain a combined state-space model and are also used to calculate instantaneous power spectral density estimates. The quality enhancement is performed by a dual discrete Kalman filter that simultaneously gives estimates for the models and the signals. The system's performance has been evaluated using mean opinion score tests and the proposed technique has led to improved results.