Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

Comment on the Adiabatic Condition

The experimental observation of effects due to Berry's phase in quantum systems is certainly one of the most impressive demonstrations of the correctness of the superposition principle in quantum mechanics. Since Berry's original paper in 1984, the spin 1/2 coupled with rotating external magnetic field has been one of the most studied models where those phases appear. We also consider a special case of this soluble model. A detailed analysis of the coupled differential equations and comparison with exact results teach us why the usual procedure (of neglecting nondiagonal terms) is mathematically sound.Comment: 9 page

Caracterização parcial e avaliação da maturidade de composto e biofertilizante para a aplicação em áreas de produção orgânica.

Este trabalho teve por objetivo acompanhar o desenvolvimento e a determinação da maturidade de compostos e biofertilizantes

Control of state and state entanglement with a single auxiliary subsystem

We present a strategy to control the evolution of a quantum system. The novel aspect of this protocol is the use of a \emph{single auxiliary subsystem}. Two applications are given, one which allows for state preservation and another which controls the degree of entanglement of a given initial state

The effect of different remineralizing agents on caries-like lesions – a pilot study

Poster apresentado no XXV Congresso da Ordem dos Médicos Dentistas, 10-12 Novembro 2016, Porto, PortugalSob uma licença CC-BY-NC - http://creativecommons.org/licenses/by-nc/4.0/Aim: To quantify the surface microhardness of enamel when using different remineralizing agents, after the induction of artificial dental caries.N/

Use of filamentous fungi for improving electricity production and textile dye treatment in a microbial fuel cell

Urban and industrial wastewaters have received an increased interest towards energy harvesting using microbial fuel cells (MFC). The combined use of microbial anode oxidizing organic substrates and enzymatic cathode reducing oxygen is a promising new approach for the simultaneous treatment of wastewater and generation of electricity. In this context, our study evaluated the performance of a two-chambered MFC operated with three laccase producing strains of filamentous fungi (Ff), immobilized on the cathodic compartment and filled up with simulated textile dye effluent (TDE) and urban wastewater in the anodic compartment. The result indicated a rapid TDE decolourisation (>86 % within 72 h). Electrochemical monitoring of the MFC during TDE decolourisation indicated power density (>35 mW m2, control 3,61) and laccase activity (989.6 U l–1) in the presence of Pleurotus ostreatus on the cathodic compartment. Considering the initial COD value of 464 ± 20 mg.l-1, the organic removal in the anodic compartment after 20 days of MFC operation was 90.2%. Final toxicity measurements in the TDE treated indicated a much lower impact when compared to the original TDE. These are the initial studies to select Ff as models for MFC application and further adaptation for wastewater treatment and bioelectricity generatio