Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

Distortion of wreath products in some finitely presented groups

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Lipschitz harmonic capacity and Bilipschitz images of cantor sets

For bilipschitz images of Cantor sets in Rd we estimate the Lipschitz harmonic capacity and show this capacity is invariant under bilipschitz homeomorphisms.

Distortion of Hausdorff measures and improved Painlevé removability for quasiregular mappings

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Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane

In this paper we prove the sharp distortion estimates for the quasiconformal mappings in the plane, both in terms of the Riesz capacities from non linear potential theory and in terms of the Hausdorff measures.

A type of perturbation of the harmonic oscillator

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Distortion theorems for quasiconformal mappings

L'any 1994, Astala publicà el reconegut teorema de distorió de l'àrea per aplicacions quasiconformes, un resultat innovador que va permetre que n'apareguessin nombrosos més dins d'aquest camp de l'anàlisi durant la darrera dècada. Ens centrem en les conseqüències que té en la distorsió de la mesura de Hausdorff. Seguim la demostració de Lacey, Sawyer i Uriarte-Tuero per la distorsió del contingut de Hausdorff, clarificant-ne alguns punts i canviant l'enfocament per l'acotació de la transformada de Beurling, on prenem les idees d'Astala, Clop, Tolsa, Uriarte-Tuero i Verdera.

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy

Distortion control for delay-sensitive sources

We investigate the problem of finding minimum-distortion policies for streaming delay-sensitive but distortion-tolerant data. We consider cross-layer approaches which exploit the coupling between presentation and transport layers. We make the natural assumption that the distortion function is convex and decreasing. We focus on a single source-destination pair and analytically find the optimum transmission policy when the transmission is done over an error-free channel. This optimum policy turns out to be independent of the exact form of the convex and decreasing distortion function. Then, for a packet-erasure channel, we analytically find the optimum open-loop transmission policy, which is also independent of the form of the convex distortion function. We then find computationally efficient closed-loop heuristic policies and show, through numerical evaluation, that they outperform the open-loop policy and have near optimal performance.

The minimax distortion redundancy in empirical quantizer design

We obtain minimax lower and upper bounds for the expected distortionredundancy of empirically designed vector quantizers. We show that the meansquared distortion of a vector quantizer designed from $n$ i.i.d. datapoints using any design algorithm is at least $\Omega (n^{-1/2})$ awayfrom the optimal distortion for some distribution on a bounded subset of${\cal R}^d$. Together with existing upper bounds this result shows thatthe minimax distortion redundancy for empirical quantizer design, as afunction of the size of the training data, is asymptotically on the orderof $n^{1/2}$. We also derive a new upper bound for the performance of theempirically optimal quantizer.

Harmonic oscillators driven by colored noise: crossovers, resonances and spectra

We study second-order properties of linear oscillators driven by exponentially correlated noise. We focus our attention on dynamical exponents and crossovers and also on resonance phenomena that appear when the driving noise is dichotomous. We also obtain the power spectrum and show its different behaviors according to the color of the noise.

Dimerization of polyacetylene treated as a spin-Peierls distortion of the Heisenberg Hamiltonian

Extracting a bond-length-dependent Heisenberg-like Hamiltonian from the potential-energy surfaces of the two lowest states of ethylene, it is possible to study the geometry of polyacetylene by minimization of the cohesive energy, using both variational-cluster and Rayleigh-Schrödinger perturbative expansions. The dimerization amplitude is satisfactorily reproduced. Optimizing the variational-cluster-expansion total energy with the equal-bond-length constraint, the barrier to reversal of alternation is obtained. The alternating-to-regular phase transition is treated from the Néel-state starting function and appears to be of second order.

ZnO nanorods for efficient third harmonic UV generation.

ZnO nanorods grown by both high temperature vapour phase transport and low temperature chemical bath deposition are very promising sources for UV third harmonic generation. Material grown by both methods show comparable efficiencies, in both cases an order of magnitude higher than surface third harmonic generation at the quartz-air interface of a bare quartz substrate. This result is in stark contrast to the linear optical properties of ZnO nanorods grown by these two methods, which show vastly different PL efficiencies. The third harmonic generated signal is analysed using intensity dependent measurements and interferometric frequency resolved optical gating, allowing extraction of the laser pulse parameters. The comparable levels of efficiency of ZnO grown by these very different methods as sources for third harmonic UV generation provides a broad suite of possible growth methods to suit various substrates, coverage and scalability requirements. Potential application areas range from interferometric frequency resolved optical gating characterization of few cycle fs pulses to single cell UV irradiation for biophysical studies.

The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing

By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.