101 research outputs found

    Fast and slow points of Birkhoff sums

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    International audienceWe investigate the growth rate of the Birkhoff sums Sn,αf(x)=k=0n1f(x+kα)S_{n,\alpha}f(x)=\sum_{k=0}^{n-1}f(x+k\alpha),where ff is a continuous function with zero mean defined on the unit circle T\mathbb T and (α,x)(\alpha,x) isa ``typical'' element of T2\mathbb T^2. The answer depends on the meaning given to the word ``typical''. Part of the work will be done in a more general context

    Wavelets techniques for pointwise anti-Holderian irregularity

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    In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise Holder regularity. We build a class of wavelet series satisfying the multifractal formalism and thus show the optimality of the upper bound. We also show that the weak spectrum of singularities is disconnected from the casual one (denoted here strong spectrum of singularities) by exhibiting a multifractal function made of Davenport series whose weak spectrum di ers from the strong one

    Fast and slow points of Birkhoff sums

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    Equilibrium states of the pressure function for products of matrices

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    Let {Mi}i=1\{M_i\}_{i=1}^\ell be a non-trivial family of d×dd\times d complex matrices, in the sense that for any nNn\in \N, there exists i1...in{1,...,}ni_1... i_n\in \{1,..., \ell\}^n such that Mi1...Min0M_{i_1}... M_{i_n}\neq {\bf 0}. Let P ⁣:(0,)RP \colon (0,\infty)\to \R be the pressure function of {Mi}i=1\{M_i\}_{i=1}^\ell. We show that for each q>0q>0, there are at most dd ergodic qq-equilibrium states of PP, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

    Multifractal Analysis of inhomogeneous Bernoulli products

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    We are interested to the multifractal analysis of inhomogeneous Bernoulli products which are also known as coin tossing measures. We give conditions ensuring the validity of the multifractal formalism for such measures. On another hand, we show that these measures can have a dense set of phase transitions

    Some Aspects of Multifractal analysis

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    The aim of this survey is to present some aspects of multifractal analysis around the recently developed subject of multiple ergodic averages. Related topics include dimensions of measures, oriented walks, Riesz products etc

    Inhibition of G Protein-Activated Inwardly Rectifying K+ Channels by Different Classes of Antidepressants

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    Various antidepressants are commonly used for the treatment of depression and several other neuropsychiatric disorders. In addition to their primary effects on serotonergic or noradrenergic neurotransmitter systems, antidepressants have been shown to interact with several receptors and ion channels. However, the molecular mechanisms that underlie the effects of antidepressants have not yet been sufficiently clarified. G protein-activated inwardly rectifying K+ (GIRK, Kir3) channels play an important role in regulating neuronal excitability and heart rate, and GIRK channel modulation has been suggested to have therapeutic potential for several neuropsychiatric disorders and cardiac arrhythmias. In the present study, we investigated the effects of various classes of antidepressants on GIRK channels using the Xenopus oocyte expression assay. In oocytes injected with mRNA for GIRK1/GIRK2 or GIRK1/GIRK4 subunits, extracellular application of sertraline, duloxetine, and amoxapine effectively reduced GIRK currents, whereas nefazodone, venlafaxine, mianserin, and mirtazapine weakly inhibited GIRK currents even at toxic levels. The inhibitory effects were concentration-dependent, with various degrees of potency and effectiveness. Furthermore, the effects of sertraline were voltage-independent and time-independent during each voltage pulse, whereas the effects of duloxetine were voltage-dependent with weaker inhibition with negative membrane potentials and time-dependent with a gradual decrease in each voltage pulse. However, Kir2.1 channels were insensitive to all of the drugs. Moreover, the GIRK currents induced by ethanol were inhibited by sertraline but not by intracellularly applied sertraline. The present results suggest that GIRK channel inhibition may reveal a novel characteristic of the commonly used antidepressants, particularly sertraline, and contributes to some of the therapeutic effects and adverse effects
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