On uniform convergence of Fourier series

We consider the space $U(\mathbb T)$ of all continuous functions on the circle $\mathbb T$ with uniformly convergent Fourier series. We show that if $\varphi: \mathbb T\rightarrow\mathbb T$ is a continuous piecewise linear but not linear map, then $\|e^{in\varphi}\|_{U(\mathbb T)}\simeq\log n$

Séries de Taylor et séries trigonométriques universelles au sens de Menchoff

RésuméLe résultat principal de cet article est qu'il existe une série trigonométrique universelle au sens de Menchoff qui est la restriction au cercle unité d'une série de Taylor dont les coefficients tendent vers zéro.Il nous a paru bon, avant de présenter ce résultat et ses variantes, de récapituler des éléments connus de la théorie des séries trigonométrique universelles et de celle des séries de Taylor universelles.AbstractHere is the principal result: there exists a trigonometric series of the Taylor type, with coefficients tending to zero, and universal in the sense of Mens̆ov. The article recapitulates known results on universal trigonometric series and universal Taylor series before presenting the main result and its developments

Disk-Like Structure in the Semi-Regular Pulsating Star, X Her

The author reports a result of an interferometric observation of the semiragular pulsating star with an unusual narrow molecular line profile, X Her, in the CO J=1-0 line with the Berkeley-Illinois-Maryland array. In the CO spectrum, a double-component profile (including narrow and broad components) is seen as reported by previous observations. The narrow component consists of two spiky peaks. The spatial structure of the board component shows bipolar shape, and that of the narrow component shows an elliptical/spherical shape. The two peaks in the narrow component show a systematic difference in the integrated intensity map. The kinematical and geometrical properties of the narrow component are reminiscent of a Keplerian rotating disk with the central mass of 0.9 M_sun, though an interpretation by an expansion disk seems to be more natural. A secondary bipolar flow instead of the disk cannot be fully excluded as an interpretation of the narrow line.Comment: 12 pages, 4 figues, accepted for publication in Ap

Elastic and Raman scattering of 9.0 and 11.4 MeV photons from Au, Dy and In

Monoenergetic photons between 8.8 and 11.4 MeV were scattered elastically and in elastically (Raman) from natural targets of Au, Dy and In.15 new cross sections were measured. Evidence is presented for a slight deformation in the 197Au nucleus, generally believed to be spherical. It is predicted, on the basis of these measurements, that the Giant Dipole Resonance of Dy is very similar to that of 160Gd. A narrow isolated resonance at 9.0 MeV is observed in In.Comment: 31 pages, 11 figure

Approximated maximum likelihood estimation in multifractal random walks

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the R computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.Comment: 8 pages, 3 figures, 2 table

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

KPZ in one dimensional random geometry of multiplicative cascades

We prove a formula relating the Hausdorff dimension of a subset of the unit interval and the Hausdorff dimension of the same set with respect to a random path matric on the interval, which is generated using a multiplicative cascade. When the random variables generating the cascade are exponentials of Gaussians, the well known KPZ formula of Knizhnik, Polyakov and Zamolodchikov from quantum gravity appears. This note was inspired by the recent work of Duplantier and Sheffield proving a somewhat different version of the KPZ formula for Liouville gravity. In contrast with the Liouville gravity setting, the one dimensional multiplicative cascade framework facilitates the determination of the Hausdorff dimension, rather than some expected box count dimension.Comment: 14 page

Macroscopic objects in quantum mechanics: A combinatorial approach

Why we do not see large macroscopic objects in entangled states? There are two ways to approach this question. The first is dynamic: the coupling of a large object to its environment cause any entanglement to decrease considerably. The second approach, which is discussed in this paper, puts the stress on the difficulty to observe a large scale entanglement. As the number of particles n grows we need an ever more precise knowledge of the state, and an ever more carefully designed experiment, in order to recognize entanglement. To develop this point we consider a family of observables, called witnesses, which are designed to detect entanglement. A witness W distinguishes all the separable (unentangled) states from some entangled states. If we normalize the witness W to satisfy |tr(W\rho)| \leq 1 for all separable states \rho, then the efficiency of W depends on the size of its maximal eigenvalue in absolute value; that is, its operator norm ||W||. It is known that there are witnesses on the space of n qbits for which ||W|| is exponential in n. However, we conjecture that for a large majority of n-qbit witnesses ||W|| \leq O(\sqrt{n logn}). Thus, in a non ideal measurement, which includes errors, the largest eigenvalue of a typical witness lies below the threshold of detection. We prove this conjecture for the family of extremal witnesses introduced by Werner and Wolf (Phys. Rev. A 64, 032112 (2001)).Comment: RevTeX, 14 pages, some additions to the published version: A second conjecture added, discussion expanded, and references adde

Vocal aging and adductor spasmodic dysphonia: Response to botulinum toxin injection

Aging of the larynx is characterized by involutional changes which alter its biomechanical and neural properties and create a biological environment that is different from younger counterparts. Illustrative anatomical examples are presented. This natural, non-disease process appears to set conditions which may influence the effectiveness of botulinum toxin injection and our expectations for its success. Adductor spasmodic dysphonia, a type of laryngeal dystonia, is typically treated using botulinum toxin injections of the vocal folds in order to suppress adductory muscle spasms which are disruptive to production of speech and voice. A few studies have suggested diminished response to treatment in older patients with adductor spasmodic dysphonia. This retrospective study provides a reanalysis of existing pre-to-post treatment data as function of age. Perceptual judgments of speech produced by 42 patients with ADSD were made by two panels of professional listeners with expertise in voice or fluency of speech. Results demonstrate a markedly reduced positive response to botulinum toxin treatment in the older patients. Perceptual findings are further elucidated by means of acoustic spectrography. Literature on vocal aging is reviewed to provide a specific set of biological mechanisms that best account for the observed interaction of botulinum toxin treatment with advancing age