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

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

Superdiffusion of massive particles induced by multi-scale velocity fields

We study drag-induced diffusion of massive particles in scale-free velocity fields, where superdiffusive behavior emerges due to the scale-free size distribution of the vortices of the underlying velocity field. The results show qualitative resemblance to what is observed in fluid systems, namely the diffusive exponent for the mean square separation of pairs of particles and the preferential concentration of the particles, both as a function of the response time.Comment: 5 pages, 5 figures. Accepted for publication in EP

Tratamento de efluentes vitivinícolas : uma caso de estudo na região dos vinhos verdes

Um sistema de tratamento tem como objectivo remover os compostos presentes nos efluentes industriais que, se não forem eliminados, exercerão impactes negativos nos meios aquáticos, excedendo a resiliência dos ecossistemas. Nessa perspectiva, a presente comunicação foca as principais características dos efluentes da indústria vitivinícola e apresenta o caso de estudo de uma unidade de tratamento de águas residuais instalado numa unidade dedicada à produção de Vinho Verde. Assim, indicam-se os resultados da operação do sistema de tratamento, cuja concepção assentou na tecnologia de reactores descontínuos sequenciais (SBR). Os resultados obtidos procuram evidenciar a estratégia de operação e a capacidade de adaptação do sistema de tratamento aos diferentes caudais e cargas orgânicas afluentes, aspecto bastante importante neste tipo de sector industrial, caracterizado por uma acentuada sazonalidade

Paleolítico médio e superior em Portugal : datas 14C, estado actual dos conhecimentos, síntese e discussão

No âmbito des pesquisas do CEPUNL sobre o Paleolítico médio e superior foram obtidas novas datas de radiocarbono em situações bem definidas do ponto de vista estratigráfico; com outras, permitem uma visão cronológica global aproximada. As datas não parecem distribuir-se ao longo dos tempos de modo aleatório. No estado actual dos conhecimentos, parecem corresponder a vários conjuntos: (a) 14000 a 15000 anos BP, Solutrense superior; (b) cerca de 20 000 BP, Solutrense; (c) com datas cerca de 25000 BP, já Solutrense, e, a pouco mais de 26000 BP, ainda Musrierense; (d) entre 29 000 e 31 000 BP, Mustierense. Demonstra-se a persistência de Mustierense muito após o limite admitido; cerca de 34 000 BP - e, por conseguinte, a dos seus autores neandertalianos. Pela primeira vez, foi possível a datação do limite cronológico superior do terraço marinho de 5-8 mettos (Tirreniano III) da Arrábida, bem como de jazidas sem indústrias ou com indústrias incaracterísticas. As datas obtidas permitem correlacionar jazidas e depósitos com episódios da última glaciação. Parece haver nítida correlação entre a ocupação de grutas e abrigos pelo Homem e episódios de clima mais desfavorável.New radiocarbon measuremenrs were obtained from middle and upper Paleolithic sites currenrly under research by the CEPUNL, in well defined stratigraphical situations. Wirh other dates, they yield an approximarive chronological global view. Measurement distriburion in function of time does not seem to be an hazardous one. ln rhe actual status of our knowledge, rhis disrriburion seems ro fit in some assemblages: (a) 14000 to 15000 BP, Solurrean; (b) about 20 000 BP, Solucrean; (c) árca 25 000 BP, already Solutrean, and slighdy older than 26 000 BP, still Moust~rian; (d) berween 29 000 and 31 000 BP, Mousterian. The persistance of Mousterian much later than its acknowledged upper limit ar about 34 000 BP (and hence the survival of its neanderrhalian authors) is demonstrated. For the first time ir has been possible ro ascercain rhe upper time limit of the marine 5-8 metres raised beach (Tyrrhenian III) at Serra da Arrábida, and also rhe age of archaeological sires wirhour stone arrifacrs, or wirh uncharacteristic ones. The obtained measurements allow us to correlate localities and sedimencary units wirh lasr glaciation events. There seems to have been a distinct correlation berween cave and shelter human occupation and events marked by rhe worsening of climare.Dans le cadre des recherches du CEPUNL sur le Paléolithique moyen et supérieur ont été· obtenues de nouvelles dares 14C correspondant à des situarions bien définies du point de vue srrarigraphique; avec d'autres, elles permeccent une vision globale apptoximative de la chronologie. La discribution des dates en fonction des temps ne parait pas alléatoire. Dans I' état aCtuei des connaissances, certe discribution semble correspondre à quelques ensembles: (a) 14000 à 15 000 ans BP, Solutréen supérieur; (b) environ 20000 BP, Solutréen; (c) árca 25000 BP, Solurréen déjà, er avec un peu plus de 26 000 BP, Moustérien (encore); (d) enrre 29 000 et 31 000 BP, Moustérien. La persistance de Moustérien bien apres la date limite admise (34 000 BP environ) - et donc celle de ses auteurs neanderthaliens - est démontrée. Pour la premiere fois ii a éré possible de darer la limite chronologique supérieure de la terrasse marine de 5-8 merres (Tyrrhénien III) dans la Serra da Arrábida, ainsi que des sites dépourvus d'indusrries ou ayant livré des industries incaractéristiques. Les dates obtenues permettenr de corréler des gisements er dépôts avec des épisodes de la derniere glaciation. II semble avoir eu une nette correspondance enrre I'occupation de grottes et abris par I'Homme et des épisodes à climar plus défavorable

Leachate treatment process at a municipal stabilized landfill by catalytic ozonation: an exploratory study from Taguchi orthogonal array

Catalytic ozonation has been recognized in the scientific community as an efficient technique, reaching elevated rates of recalcitrant organic material mineralization, even at the presence of scavenger species of hydroxyl free radicals. This study presents the most significant factors involving the leachate treatment stabilized by the municipal landfill of the city of Guaratinguetá, State of São Paulo, Brazil, by using a catalytic ozonation activated by metallic ions Fe3+, Zn2+, Mn2+, Ni2+ and Cr3+. The Taguchi L16 orthogonal array and its associated statistical methods were also used in this study. Among the researched ions, the most notable catalysis was obtained with ferric ion, statistically significant in the reduction of COD with a confidence level of 99.5%.Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES