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

Responses of CYP450 dependent system to aliphatic and aromatic hydrocarbons body burden in transplanted mussels from South coast of Portugal

Mussels Mytilus galloprovincialis were cross-transplanted at South Portugal from a reference site (site 1) to a site more contaminated with hydrocarbon compounds (site 2), and vice versa, in an active biomonitoring (ABM) concept, to assess the biotransformation capacity catalyzed by the mixed function oxygenase (MFO) system. Total alkanes (TAlk), the unresolved complex mixture (UCM), and total polycyclic aromatic hydrocarbons (TPAHs) concentration increased respectively 6, 4.4 and 4.2 fold relatively to control, in mussels transplanted from site 1 to 2. In the cross-transplant, a 48, 57 and 62% depuration of TAlk, UCM and TPAHs concentrations occurred by the end of the 3-4th week. Petrogenic and biogenic (marine and terrigenous) sources of AHs, and petrogenic and pyrolitic (biomass and oil/fuel incomplete combustion) sources of PAHs were detected at both sites. CYP450, CYT b (5) and NADPH-RED in mussels transplanted from site 1 to 2 were induced from day 0 to 28, with a total increase of 35, 32 and 35%, respectively, while biochemical equilibrium to lesser environmental contamination occurs in mussels transplanted from site 2 to 1. A significant relationship between CYP450 and NADPH-RED was found with TPAH, with distinctive behavior at the two sites. MFO system components increase with exposure time at one site and decreases in the other, reflecting an adaptation to distinct environmental hydrocarbon loads. The ABM strategy proved to be useful to understand the environment real impact on the biochemical responses in mussels' local populations. In this study, CYP450 and NADPH-RED are a useful biomarker for hydrocarbon exposure.FCT: PRAXIS XXI/BD/3740/94info:eu-repo/semantics/publishedVersio

A dynamical point of view of Quantum Information: entropy and pressure

Quantum Information is a new area of research which has been growing rapidly since last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more "dynamical point of view" of this theory. We want to consider the concepts of entropy and pressure for "stationary systems" acting on density matrices which generalize the usual ones in Ergodic Theory (in the sense of the Thermodynamic Formalism of R. Bowen, Y. Sinai and D. Ruelle). We consider the operator $\mathcal{L}$ acting on density matrices $\rho\in \mathcal{M}_N$ over a finite $N$-dimensional complex Hilbert space $\mathcal{L}(\rho):=\sum_{i=1}^k tr(W_i\rho W_i^*)V_i\rho V_i^*,$ where $W_i$ and $V_i$, $i=1,2,...k$ are operators in this Hilbert space. $\mathcal{L}$ is not a linear operator. In some sense this operator is a version of an Iterated Function System (IFS). Namely, the $V_i\,(.)\,V_i^*=:F_i(.)$, $i=1,2,...,k$, play the role of the inverse branches (acting on the configuration space of density matrices $\rho$) and the $W_i$ play the role of the weights one can consider on the IFS. We suppose that for all $\rho$ we have that $\sum_{i=1}^k tr(W_i\rho W_i^*)=1$. A family $W:=\{W_i\}_{i=1,..., k}$ determines a Quantum Iterated Function System (QIFS) $\mathcal{F}_{W}$, $\mathcal{F}_W=\{\mathcal{M}_N,F_i,W_i\}_{i=1,..., k}.

A dynamical point of view of Quantum Information: Wigner measures

We analyze a known version of the discrete Wigner function and some connections with Quantum Iterated Funcion Systems. This paper is a follow up of "A dynamical point of view of Quantum Information: entropy and pressure" by the same authors

Effects of adopting IFRS 10 and IFRS 11 on consolidated financial statements: an exploratory research

Purpose: This paper investigates how the adoption of IFRS 10 and IFRS 11 affected consolidated financial statements. Specifically, the paper explores whether entities adopted mandatorily or voluntarily both IFRS, whether expressly declared effects, whether considered those effects as material and whether those effects had impacts on selected items of financial statements and on selected financial ratios. Design/methodology/approach: The research is an exploratory study using public entities from France, Germany and the United Kingdom. The majority of the data are manually collected from financial statements. Findings: The results suggest that the adoption of the new IFRS 10 affected the composition of a large number of entity groups but that their financial information and economic-financial indicators do not present material changes. There is also evidence of a large and material impact on the changes in the classification and accounting for interests in arrangements under joint control through the new IFRS 11. The evidence thus suggests unequal effects of the adoption of IFRS 10 and IFRS 11 on the proportion of entities declaring materiality of effects, on the quantitative effects on selected items of financial statements, and on financial ratios. A comparison between the pre-adoption and post-adoption periods reveals that the majority of the effects are driven by the adoption of IFRS 11. Originality/value: This exploratory paper is the first presenting the effectiveness of adopting the most important standards under the “consolidation package” and opens an avenue for future research by academics, for future post-implementation reviews by IASB, and for analysis of peer reviews between accounting practitioners.info:eu-repo/semantics/acceptedVersio

Ensaio comparativo avançado de arroz de sequeiro em Altamira, Pará - ano agrícola 1998/1999.

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