A note on the algebraic growth rate of Poincar\'e series for Kleinian groups

In this note we employ infinite ergodic theory to derive estimates for the algebraic growth rate of the Poincar\'e series for a Kleinian group at its critical exponent of convergence.Comment: 8 page

Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces

We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and pressure for shifts acting on $X$ and obtain the existence of equilibrium states as additive probability measures for any bounded continuous potential. Furthermore, we establish convexity and other structural properties of the set of equilibrium states, prove a version of the Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity of the potential and show that the Yosida-Hewitt decomposition of these equilibrium states do not have a purely additive part. We then apply our results to the construction of invariant measures of time-homogeneous Markov chains taking values on a general Borel standard space and obtain exponential asymptotic stability for a class of Markov operators. We also construct conformal measures for an infinite collection of interacting random paths which are associated to a potential depending on infinitely many coordinates. Under an additional differentiability hypothesis, we show how this process is related after a proper scaling limit to a certain infinite dimensional diffusion.Comment: Accepted for publication in Discrete and Continuous Dynamical Systems. 23 page

Spectral Properties of the Ruelle Operator for Product Type Potentials on Shift Spaces

We study a class of potentials $f$ on one sided full shift spaces over finite or countable alphabets, called potentials of product type. We obtain explicit formulae for the leading eigenvalue, the eigenfunction (which may be discontinuous) and the eigenmeasure of the Ruelle operator. The uniqueness property of these quantities is also discussed and it is shown that there always exists a Bernoulli equilibrium state even if $f$ does not satisfy Bowen's condition. We apply these results to potentials $f:\{-1,1\}^\mathbb{N} \to \mathbb{R}$ of the form $$f(x_1,x_2,\ldots) = x_1 + 2^{-\gamma} \, x_2 + 3^{-\gamma} \, x_3 + ...+n^{-\gamma} \, x_n + \ldots$$ with $\gamma >1$. For $3/2 < \gamma \leq 2$, we obtain the existence of two different eigenfunctions. Both functions are (locally) unbounded and exist a.s. (but not everywhere) with respect to the eigenmeasure and the measure of maximal entropy, respectively.Comment: To appear in the Journal of London Mathematical Societ

Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

In this paper we construct spectral triples $(A,H,D)$ on the symbolic space when the alphabet is finite. We describe some new results for the associated Dixmier trace representations for Gibbs probabilities (for potentials with less regularity than H\"older) and for a certain class of functions. The Dixmier trace representation can be expressed as the limit of a certain zeta function obtained from high order iterations of the Ruelle operator. Among other things we consider a class of examples where we can exhibit the explicit expression for the zeta function. We are also able to apply our reasoning for some parameters of the Dyson model (a potential on the symbolic space $\{-1,1\}^\mathbb{N}$) and for a certain class of observables. Nice results by R. Sharp, M.~Kesseb\"ohmer and T.~Samuel for Dixmier trace representations of Gibbs probabilities considered the case where the potential is of H\"older class. We also analyze a particular case of a pathological continuous potential where the Dixmier trace representation - via the associated zeta function - is not true.Comment: the tile was modified and there are two more author

Investigation of the chemical vicinity of crystal defects in ion-irradiated Mg and AZ31 with coincident Doppler broadening spectroscopy

Crystal defects in magnesium and magnesium based alloys like AZ31 are of major importance for the understanding of their macroscopic properties. We have investigated defects and their chemical surrounding in Mg and AZ31 on an atomic scale with Doppler broadening spectroscopy of the positron annihilation radiation. In these Doppler spectra the chemical information and the defect contribution have to be thoroughly separated. For this reason samples of annealed Mg were irradiated with Mg-ions in order to create exclusively defects. In addition Al- and Zn-ion irradiation on Mg-samples was performed in order to create samples with defects and impurity atoms. The ion irradiated area on the samples was investigated with laterally and depth resolved positron Doppler broadening spectroscopy (DBS) and compared with preceding SRIM-simulations of the vacancy distribution, which are in excellent agreement. The investigation of the chemical vicinity of crystal defects in AZ31 was performed with coincident Doppler broadening spectroscopy (CDBS) by comparing Mg-ion irradiated AZ31 with Mg-ion irradiated Mg. No formation of solute-vacancy complexes was found due to the ion irradiation, despite the high defect mobility.Comment: Submitted to Physical Review B on March 20 20076. Revised version submitted on September 28 2007. Accepted on October 19 200

Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states

We study relations between $(H,\beta)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\mathcal{L}_{-\beta H}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,\beta)$--KMS states and eigenmeasures of $\mathcal{L}_{-\beta H}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then these are $\ast$--isomorphic to the given Cuntz--Krieger algebra. Finally, we apply these general results to study multifractal decompositions of limit sets of essentially free Kleinian groups $G$ which may have parabolic elements. We show that for the Cuntz--Krieger algebra arising from $G$ there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen--Series map associated with $G$. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous functions on the limit set of $G$. If $G$ has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with $G$.Comment: 30 pages, minor changes in the proofs of Theorem 3.9 and Fact

XMM-Newton EPIC Observation of SMC SNR 0102-72.3

Results from observations of the young oxygen-rich supernova remnant SNR 0102-72.3 in the Small Magellanic Cloud during the calibration phase of the XMM-Newton Observatory are presented. Both EPIC-PN and MOS observations show a ringlike structure with a radius of ~15'' already known from Einstein, ROSAT and Chandra observations. Spectra of the entire SNR as well as parts in the eastern half were analyzed confirming shocked hot plasma in non-uniform ionization stages as the origin of the X-ray emission. The spectra differ in the northeastern and the southeastern part of the X-ray ring, showing emission line features of different strength. The temperature in the northeastern part is significantly higher than in the southeast, reflected by the lines of higher ionization stages and the harder continuum. Comparison to radio data shows the forward shock of the blast wave dominating in the northern part of the SNR, while the southern emission is most likely produced by the recently formed reverse shock in the ejecta. In the case of the overall spectrum of SNR 0102-72.3, the two-temperature non-equilibrium ionization model is more consistent with the data in comparison to the single plane-parallel shock model. The structure of SNR 0102-72.3 is complex due to variations in shock propagation leading to spatially differing X-ray spectra

On random topological Markov chains with big images and preimages

We introduce a relative notion of the 'big images and preimages'-property for random topological Markov chains. This then implies that a relative version of the Ruelle-Perron-Frobenius theorem holds with respect to summable and locally Hoelder continuous potentials.Comment: Corrected and extended version of the article published in Stochastics and Dynamics 201

Genome-wide DNA methylation changes in a mouse model of infection-mediated neurodevelopmental disorders

Background Prenatal exposure to infectious or inflammatory insults increases the risk of neurodevelopmental disorders. Using a well-established mouse model of prenatal viral-like immune activation, we examined whether this pathological association involves genome-wide DNA methylation differences at single nucleotide resolution. Methods Prenatal immune activation was induced by maternal treatment with the viral mimetic polyriboinosinic-polyribocytidylic acid in middle or late gestation. Following behavioral and cognitive characterization of the adult offspring (n = 12 per group), unbiased capture array bisulfite sequencing was combined with subsequent matrix-assisted laser desorption/ionization time-of-flight mass spectrometry and quantitative real-time polymerase chain reaction analyses to quantify DNA methylation changes and transcriptional abnormalities in the medial prefrontal cortex of immune-challenged and control offspring. Gene ontology term enrichment analysis was used to explore shared functional pathways of genes with differential DNA methylation. Results Adult offspring of immune-challenged mothers displayed hyper- and hypomethylated CpGs at numerous loci and at distinct genomic regions, including genes relevant for gamma-aminobutyric acidergic differentiation and signaling (e.g., Dlx1, Lhx5, Lhx8), Wnt signaling (Wnt3, Wnt8a, Wnt7b), and neural development (e.g., Efnb3, Mid1, Nlgn1, Nrxn2). Altered DNA methylation was associated with transcriptional changes of the corresponding genes. The epigenetic and transcriptional effects were dependent on the offspring\u2019s age and were markedly influenced by the precise timing of prenatal immune activation. Conclusions Prenatal viral-like immune activation is capable of inducing stable DNA methylation changes in the medial prefrontal cortex. These long-term epigenetic modifications are a plausible mechanism underlying the disruption of prefrontal gene transcription and behavioral functions in subjects with prenatal infectious histories

Компресорні установки

Зміст видання відповідає освітньо-професійній програмі підготовки кадрів з вищою освітою напряму „Електротехніка та електротехнології“, зокрема – програмі дисципліни „Енергетичні установки“. Розглянуто основні положення теорії компресорних машин, будову, експлуатаційні особливості та методи регулювання режиму роботи поршневих, ротаційних, гвинтових, водокільцевих і відцентрових компресорів. Посібник адресовано студентам спеціальності „Енергетичний менеджмент“, які вивчають дисципліну „Енергетичні установки“. Він може бути корисним також студентам напрямів „Гірництво“, „Інженерна механіка“ та „Електромеханіка“ при вивченні стаціонарних установок гірничих підприємств