Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

New insights on the crystalline forms in binary systems of n-alkanes: Characterization of the solid ordered phases in the phase diagram tricosane + pentacosane

X-ray diffraction analyses of the pure components n-tricosane and n-pentacosane and of their binary mixed samples have enabled us to characterize the crystalline phases observed at low temperature. On the contrary to what was announced in literature on the structural behavior of mixed samples in odd-odd binary systems with D n = 2, the three domains are not all orthorhombic. This work has enabled us to show that two of the domains are, in fact, monoclinic, (Aa, Z = 4) and the other one is orthorhombic (Pca21, Z = 4). The conclusions drawn in this work can be easily transposed to other binary systems of n-alkanes.

Inhibition of glutathione efflux in the perfused rat liver and isolated hepatocytes by organic anions and bilirubin. Kinetics, sidedness, and molecular forms.

Using isolated, in situ, single-pass perfused rat livers, incubations of freshly isolated hepatocytes, and sinusoidal membrane-enriched vesicles, we and others have shown the saturability of transport (efflux) of hepatic glutathione (GSH). These observations have implicated a carrier mechanism. Our present studies were designed to provide further evidence in support of a carrier mechanism for hepatic GSH efflux by demonstrating competition by liver-specific ligands which are taken up by hepatocytes. Perfusing livers with different substances, we found that: (a) sulfobromophthalein-GSH (BSP-GSH) had a dose-dependent and fully reversible inhibitory effect on GSH efflux, while GSH alone did not have any effect; (b) taurocholate had no inhibitory effect; (c) all of the organic anions studied, i.e., BSP, rose bengal, indocyanine green, and unconjugated bilirubin (UCB), manifested potent, dose-dependent inhibitory effects, with absence of toxic effects and complete reversibility of inhibition in the case of UCB. The inhibitory effects of UCB could be overcome partially by raising (CoCl2-induced) hepatic GSH concentration. Because of the physiological importance of UCB, we conducted a detailed study of its inhibitory kinetics in the isolated hepatocyte model in the range of circulating concentrations of UCB. Studies with Cl- -free media, to inhibit the uptake of UCB by hepatocytes, showed that the inhibition of GSH efflux by UCB is apparently from inside the cell. This point was confirmed by showing that the inhibition is overcome only when bilirubin-loaded cells are cleared of bilirubin (incubation with 5% bovine serum albumin). Using Gunn rat hepatocytes and purified bilirubin mono- and diglucuronides, we found that both UCB and glucuronide forms of bilirubin inhibit GSH efflux in a dose-dependent manner. We conclude that the organic anions, although taken up by a mechanism independent of GSH, may competitively inhibit the carrier for GSH efflux from inside the hepatocyte.

Structure and spatial variability of Pinus uncinata Ram. growth forms at two contrasting treeline ecotones in the Spanish Pyrenees.

Describimos la distribución espacial de individuos de Pinus uncinata clasificados según su forma de crecimiento y tamaño en dos ecotonos poco perturbados del límite altitudinal del árbol situados en los Pirineos Centrales españoles (Ordesa, O; Tessó, T). En cada sitio situamos una parcela rectangular (30 140 m), que incluía los límites del árbol y del bosque, y cuyo lado mayor seguía el gradiente altitudinal. En ambos sitios, los individuos vivos eran más grandes y tenían un mayor número de cohortes de acículas pendiente abajo. La distribución de las clases de individuos según su forma de crecimiento y tamaño en el sitio O seguía una secuencia de mayor tamaño pendiente abajo, desde abundantes individuos policórmicos arbustivos (krummholz) con pocas cohortes de acículas (1-3) hasta individuos arbóreos mayores unicórmicos con varias cohortes de acículas (4-12). Por el contrario, los cambios estructurales en el ecotono del sitio T fueron graduales y no siguieron de forma tan clara dicha secuencia

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Phylogeography of competing sexual and parthenogenetic forms of a freshwater flatworm: patterns and explanations

Background: Models of the maintenance of sex predict that one reproductive strategy, sexual or parthenogenetic, should outcompete the other. Distribution patterns may reflect the outcome of this competition as well as the effect of chance and historical events. We review the distribution data of sexual and parthenogenetic biotypes of the planarian Schmidtea polychroa. Results: S. polychroa lives in allopatry or sympatry across Europe except for Central and North-Western Europe, where sexual individuals have never been reported. A phylogenetic relationship between 36 populations based on a 385 bp fragment of the mitochondrial cytochrome oxidase I gene revealed that haplotypes were often similar over large geographic distances. In North Italian lakes, however, diversity was extreme, with sequence differences of up to 5% within the same lake in both sexuals and parthenogens. Mixed populations showed "endemic" parthenogenetic lineages that presumably originated from coexisting sexuals, and distantly related ones that probably result from colonization by parthenogens independent from sexuals. Conclusions: Parthenogens originated repeatedly from sexuals, mainly in Italy, but the same may apply to other Mediterranean regions (Spain, Greece). The degree of divergence between populations suggests that S. polychroa survived the ice ages in separate ice-free areas in Central, Eastern and Southern Europe and re-colonised Europe after the retreat of the major glaciers. Combining these results with those based on nuclear markers, the data suggest that repeated hybridisation between sexuals and parthenogenetic lineages in mixed populations maintains high levels of genetic diversity in parthenogens. This can explain why parthenogens persist in populations that were originally sexual. Exclusive parthenogenesis in central and western populations suggests better colonisation capacity, possibly because of inbreeding costs as well

A crise europeia: excepcionalidade econômica, gestão autoritária e emergência de formas ativas de resistência civil = The European crisis: economic exceptionality, authoritarian rulings and the emergence of active forms of civil resistance

Thirty years after neo-liberalism hegemony, the states shows its incapacity for driving democratically exceptional situations like global economical crisis. In this context, it seems a particularly interesting issue to exam the popular alternatives that are growing to reject the institutional paralysis. This work take these problems since European perspective, especially this one of Spain, and its scope is justify the new forms of civil disobedience that are growing. They are analyzed not like"paradoxes" of democracy, but like necessary instruments of participative democracy into a really exceptional scenario

Morphological priming in Spanish verb forms: an ERP repetition priming study

The ERP repetition priming paradigm has been shown to be sensitive to the processing differences between regular and irregular verb forms in English and German. The purpose of the present study is to extend this research to a language with a different inflectional system, Spanish. The design (delayed visual repetition priming) was adopted from our previous study on English, and the specific linguistic phenomena we examined are priming relations between different kinds of stem (or root) forms. There were two experimental conditions: In the first condition, the prime and the target shared the same stem form, e.g., "ando-andar" [I walk-to walk], whereas in the second condition, the prime contained a marked (alternated) stem, e.g., "duermo-dormir" [I sleep-to sleep]. A reduced N400 was found for unmarked (nonalternated) stems in the primed condition, whereas marked stems showed no such effect. Moreover, control conditions demonstrated that the surface form properties (i.e., the different degree of phonetic and orthographic overlap between primes and targets) do not explain the observed priming difference. The ERP priming effect for verb forms with unmarked stems in Spanish is parallel to that found for regularly inflected verb forms in English and German. We argue that effective priming is possible because prime target pairs such as "ando-andar" access the same lexical entry for their stems. By contrast, verb forms with alternated stems (e.g., "duermo") constitute separate lexical entries, and are therefore less powerful primes for their corresponding base forms.