Distortion of boundary sets under inner functions and applications

10 pages, no figures.-- MSC2000 codes: 30C85, 30D50.MR#: MR1183352 (93k:30014)Zbl#: Zbl 0765.30011An inner function is a bounded holomorphic function from the unit disc $\Delta$ of the complex plane such that the radial boundary values have modulus 1 a.e. . If $E$ is a Borel subset of $\partial\Delta$ we also define f(E)=\{e\sp{i\theta}/\lim\sb{r\to 1} f(re\sp{i\theta}) exists and belongs to $E\}$. Let M\sb \alpha, \text{cap}\sb \alpha and dim denote respectively the $\alpha$-dimensional content, $\alpha$- dimensional capacity and the Hausdorff dimension. In relation to the available results the authors in this paper prove that if $f$ is inner, $f(0)=0$, and $E$ is a Borel subset of $\partial\Delta$ then M\sb \alpha(f\sp{-1}(E)) \geq C\sb \alpha M\sb \alpha(E) and for $0\leq\alpha<1$, \text{cap}\sb \alpha(f\sp{-1}(E)) \geq C\sb \alpha \text{cap}\sb \alpha(E). An immediate consequence of course is \dim(f\sp{-1}(E))\geq \dim E. They also give examples to show that the inequalities cannot be reversed [source: Zentralblatt MATH].The first author was supported in part by a grant from CICYT, Ministerio de Educación y Ciencia, Spain.Publicad

Quantitative mixing results and inner functions

19 pages, no figures.-- MSC2000 codes: 30D05, 30D50, 37A05, 37A25, 37F10, 28D05, 11K55.MR#: MR2262783 (2007j:37003)Zbl#: Zbl 1125.30019We study in this paper estimates on the size of the sets of points which are well approximated by orbits of other points under certain dynamical systems. We apply the results obtained to the particular case of the dynamical system generated by inner functions in the unit disk of the complex plane.D. Pestana was supported by Grants BFM2003-04780 and BFM-2003-06335-C03-02, Ministerio de Ciencia y Tecnología, Spain. J. L. Fernández and M. V. Melián were supported by Grant BFM2003-04780 from Ministerio de Ciencia y Tecnología, Spain.Publicad

Distortion of boundary sets under inner functions. II

33 pages, no figures.-- MSC2000 codes: 32A30, 30C85, 30D50.MR#: MR1379286 (97b:30035)Zbl#: Zbl 0847.32005We present a study of the metric transformation properties of inner functions of several complex variables. Along the way we obtain fractional dimensional ergodic properties of classical inner functions.Publicad

Hardy's inequalities for monotone functions on partially ordered measure spaces

We characterize the weighted Hardy's inequalities for monotone functions in ${\mathbb R^n_+}.$ In dimension $n=1$, this recovers the classical theory of $B_p$ weights. For $n>1$, the result was only known for the case $p=1$. In fact, our main theorem is proved in the more general setting of partially ordered measure spaces.Comment: 14 page

Evolution of small-scale magnetic elements in the vicinity of granular-size swirl convective motions

Advances in solar instrumentation have led to a widespread usage of time series to study the dynamics of solar features, specially at small spatial scales and at very fast cadences. Physical processes at such scales are determinant as building blocks for many others occurring from the lower to the upper layers of the solar atmosphere and beyond, ultimately for understanding the bigger picture of solar activity. Ground-based (SST) and space-borne (Hinode) high-resolution solar data are analyzed in a quiet Sun region displaying negative polarity small-scale magnetic concentrations and a cluster of bright points observed in G-band and Ca II H images. The studied region is characterized by the presence of two small-scale convective vortex-type plasma motions, one of which appears to be affecting the dynamics of both, magnetic features and bright points in its vicinity and therefore the main target of our investigations. We followed the evolution of bright points, intensity variations at different atmospheric heights and magnetic evolution for a set of interesting selected regions. A description of the evolution of the photospheric plasma motions in the region nearby the convective vortex is shown, as well as some plausible cases for convective collapse detected in Stokes profiles.Comment: 9 figure

Health risks arising from the dietary intake of chemical contaminants: a case study of the consumption of edible marine species in Catalonia, NE Spain

Actualment, està ben establert que la ingesta dietètica és la principal via d'exposició humana a metalls i compostos orgànics persistents (COP). L'any 2000, el nostre laboratori va començar una exhaustiva investigació sobre l'exposició dietètica a diversos metalls i contaminants orgànics per la població general de Catalunya. Entre els onze grups d'aliments analitzats, els nivells més elevats de la major part dels contaminants es van trobar, en termes generals, al peix i marisc. Aquest grup va suposar les contribucions més elevades de la ingesta d'As, Hg i Pb, dioxines i furans (PCDD/PCDF), policlorbifenils (PCB), difenil èters polibromats (PBDE) i difenil èters policlorats (PCDE). El peix i marisc va ser també un contribuent important en la ingesta de Cd, hexaclorobenzè, hidrocarburs aromàtics policíclics (PHA) i naftalens policlorats (PCN). Tanmateix, els nivells dels contaminants es van determinar solament en tres espècies de peix fresc i en dues de conservat, la qual cosa suposava un factor limitant per tal de poder establir recomanacions sobre el consum de peix i marisc. Per això, recentment hem dut a terme un estudi addicional amb la intenció d'incrementar les dades de l'anterior investigació. Els resultats són aquí presentats. En termes generals, la major part d'espècies marines analitzades no haurien de suposar efectes adversos sobre la salut dels consumidors. Tanmateix, el tipus de peix, la freqüència de consum i la quantitat consumida són aspectes essencials per a establir un equilibri entre els beneficis i els riscos d'un consum regular de peix.Dietary intake is the main means of human exposure to toxic metals and persistent organic pollutants (POPs). In 2000, our laboratory initiated research into dietary exposure to a number of metals and organic pollutants. Among 11 food groups analyzed, the highest levels of most pollutants were detected in fish and seafood. This group contributed most to the intake of As, Hg and Pb, polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/PCDFs), polychlorinated biphenyls (PCBs), polybrominated diphenyl ethers (PBDEs) and polychlorinated diphenyl ethers (PCDEs). Fish and seafood also made an important contribution to the daily intake of Cd, hexachlorobenzene, polycyclic aromatic hydrocarbons (PAHs), and polychlorinated naphthalenes (PCNs). However, the levels of contaminants were only determined in three species of fresh fish and in two species of tinned fish, which was a limiting factor for the purposes of establishing recommendations concerning human consumption of fish and other seafood. Taking into account the potentially important contribution made by marine species to the dietary intake of environmental pollutants, as well as the reduced number of species analyzed, we recently performed additional research to extend our previous study. This paper presents our results from both the preliminary and the extended studies. In general terms, most marine species analyzed do not pose adverse health risks for consumers. However, the type of fish, frequency of consumption, and meal size are essential factors in balancing the health benefits and risks of regular fish consumption

Complex noise in diffusion-limited reactions of replicating and competing species

We derive exact Langevin-type equations governing quasispecies dynamics. The inherent multiplicative noise has both real and imaginary parts. The numerical simulation of the underlying complex stochastic partial differential equations is carried out employing the Cholesky decomposition for the noise covariance matrix. This noise produces unavoidable spatio-temporal density fluctuations about the mean field value. In two dimensions, the fluctuations are suppressed only when the diffusion time scale is much smaller than the amplification time scale for the master species.Comment: 10 pages, 2 composite figure