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.

Phosphate forms in plant and their internal buffering in five soybean cultivars

Differences among plants in their ability to support nutritional stress periods may be caused by a differential vacuole capacity of ion storage and release and may also depend on the intensity of nutrient re-translocation under such conditions. In five soybean cultivars, submitted to eight days of P deprivation, the dry matter production and the contents of three phosphorus (P) forms - inorganic (Pi), organic (Po), and acid-soluble total (Pts) of different plant organs were determined. Pi release velocity (RSPi) was estimated as the tangent to the equations obtained for Pi f(t) at the point t = 2 days (the mean point in the period of greatest Pi decrease), considering that -deltaPi/deltat expresses the rate of Pi release. The internal Pi buffering capacity (IBCPi) was calculated as the inverse of the RSPi. Cultivars' differences in size of the non-metabolic Pi pool, RSPi, and the ability to transport Pi from less to more actively metabolizing regions were evaluated. The preferential Pi source and sink compartments under limited P absorption conditions were also evaluated. The cultivar Santa Rosa showed the highest Pi storage ability when the external supply was high, and a more intensive release under low P supply conditions than IAC8 and UFV1. The cultivar Uberaba was superior to Doko in its ability to store and use Pi. In all cultivars, upper leaves and roots were the main sink of Pi stored in the middle and lower leaves. Roots and upper leaves showed larger RSPi and lower IBCPi values than middle and lower leaves.

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.

Phosphorous forms in cultivated indian black earth (anthrosols) of varying texture in the brazilian Amazon

Despite the agricultural importance of Indian Black Earth (IBE) in the Amazon region, there are few studies that report on the relation between soil texture and chemical fertility of IBE. These soils of pre-Colombian origin, with high contents of P, Ca and other nutrients are found across the Amazon valley. IBE profiles were studied to evaluate the total contents of P, its primary chemical forms and the P transformation phases in areas with IBE soils of variable texture and in adjacent reference soils. The soil texture strongly influenced soil fertility, changing in terms of transformation of the primary P forms and, consequently, predominant P forms in IBE. Soils with texture varying between clay and heavy clay had higher total P contents and primary Ca-P forms. Highest P-Al and lowest total P amounts were observed at the site Rio Preto da Eva, where texture varies from sandy loam to sandy clay loam. In the IBE with clay texture the amounts of soluble P, extracted with NH4Cl were highest, although different from Mehlich 1-extractable amounts.

Mobility of inorganic and organic phosphorus forms under different levels of phosphate and poultry litter fertilization in soils

The eutrophication of aquifers is strongly linked to the mobility of P in soils. Although P mobility was considered irrelevant in a more distant past, more recent studies have shown that P, both in organic (Po) and inorganic forms (Pi), can be lost by leaching and eluviation through the soil profile, particularly in less weathered and/or sandier soils with low P adsorption capacity. The purpose of this study was to determine losses of P forms by leaching and eluviation from soil columns. Each column consisted of five PVC rings (diameter 5 cm, height 10 cm), filled with two soil types: a clayey Red-Yellow Latosol and a sandy loam Red-Yellow Latosol, which were exposed to water percolation. The soils were previously treated with four P rates (as KH2PO4 ) to reach 0, 12.5, 25.0 and 50 % of the maximum P adsorption capacity (MPAC). The P source was homogenized with the whole soil volume and incubated for 60 days. After this period the soils were placed in the columns; the soil of the top ring was mixed with five poultry litter rates of 0, 20, 40, 80, and 160 t ha-1 (dry weight basis). Treatments consisted of a 4 x 5 x 2 factorial scheme corresponding to four MPAC levels, five poultry litter rates, two soils, with three replications, arranged in a completely randomized block design. Deionized water was percolated through the columns 10 times in 35 days to simulate about 1,200 mm rainfall. In the leachate of each column the inorganic P (reactive P, Pi) and organic P forms (unreactive P, Po) were determined. At the end of the experiment, the columns were disassembled and P was extracted with the extractants Mehlich-1 (HCl 0.05 mol L-1 and H2SO4 0.0125 mol L-1) and Olsen (NaHCO3 0.5 mol L-1; pH 8.5) from the soil of each ring. The Pi and Po fractions were measured by the Olsen extractant. It was found that under higher poultry litter rates the losses of unreactive P (Po) were 6.4 times higher than of reactive P (Pi). Both the previous P fertilization and increasing poultry litter rates caused a vertical movement of P down the soil columns, as verified by P concentrations extracted by Mehlich-1 and NaHCO3 (Olsen). The environmental critical level (ECL), i.e., the P soil concentration above which P leaching increases exponentially, was 100 and 150 mg dm-3 by Mehlich-1 and 40 and 60 mg dm-3 by Olsen, for the sandy loam and clay soils, respectively. In highly weathered soils, where residual P is accumulated by successive crops, P leaching through the profile can be significant, particularly when poultry litter is applied as fertilizer.

Forms of inorganic phosphorus in soil under different long term soil tillage systems and winter crops

The cultivation of crops with different capacity of P uptake and use under long-term soil tillage systems can affect the distribution of P cycling and inorganic forms in the soil, as a result of higher or lower use efficiency of P applied in fertilizers. The purpose of this study was to evaluate the effect of long-term cultivation of different winter species under tillage systems on the distribution of inorganic P forms in the soil. In 1986, the experiment was initiated with six winter crops (blue lupin, hairy vetch, oat, oilseed radish, wheat and fallow) on a Rhodic Hapludox in southwestern Paraná, under no-tillage (NT) and conventional tillage (CT). The application of phosphate fertilizer in NT rows increased inorganic P in the labile and moderately labile forms, and soil disturbance in CT redistributed the applied P in the deeper layers, increasing the moderately labile P concentration in the subsurface layers. Black oat and blue lupin were the most efficient P-recyclers and under NT, they increased the labile P content in the soil surface layers.

Equivalence of paper and pencil vs internet forms of the ZKPQ-50-CC in Spanish and French samples

This study was designed to check for the equivalence of the ZKPQ-50-CC (Spanish and French versions) through Internet on-line (OL) and paper and pencil (PP) answer format. Differences in means and devia- tions were significant in some scales, but effect sizes are minimal except for Sociability in the Spanish sample. Alpha reliabilities are also very similar in both versions with no significant differences between formats. A robust factorial structure was found for the two formats and the average congruency coefficients were 0.98. The goodness-of-fit indexes obtained by confirmatory factorial analysis are very similar to those obtained in the ZKPQ-50-CC validation study and they do not differ between the two formats. The multi-group analysis confirms the equivalence among the OL-PP formats in both countries. These results in general support the validity and reliability of the Internet as a method in investigations using the ZKPQ-50-CC.

Spectroscopic quantification of soil phosphorus forms by 31p-nmr after nine years of organic or mineral fertilization

Long-standing applications of mineral fertilizers or types of organic wastes such as manure can cause phosphorus (P) accumulation and changes in the accumulated P forms in the soil. The objective of this research was to evaluate the forms of P accumulated in soils treated with mineral fertilizer or different types of manure in a long-term experiment. Soil was sampled from the 0-5 cm layer of plots fertilized with five different nutrient sources for nine years: 1) control without fertilizer; 2) mineral fertilizer at recommended rates for local conditions; 3) 5 t ha-1 year-1 of moist poultry litter; 4) 60 m³ ha-1 year-1 of liquid cattle manure and 5) 40 m³ ha-1 year-1 of liquid swine manure. The 31P-NMR spectra of soil extracts detected the following P compounds: orthophosphate, pyrophosphate, inositol phosphate, glycerophosphate, and DNA. The use of organic or mineral fertilizer over nine years did not change the soil P forms but influenced their concentration. Fertilization with mineral or organic fertilizers stimulated P accumulation in inorganic forms. Highest inositol phosphate levels were observed after fertilization with any kind of manure and highest organic P concentration in glycerophosphate form in after mineral or no fertilization.

Forms and accumulation of copper and zinc in a sandy typic hapludalf soil after long-term application of pig slurry and deep litter

Successive applications of pig slurry and pig deep litter may lead to an accumulation of copper (Cu) and zinc (Zn) fractions in the soil profile. The objective of this study was to evaluate the Cu and Zn forms and accumulation in a Sandy Typic Hapludalf soil after long-term application of pig slurry and deep litter. In March 2010, eight years after initiating an experiment in Braço do Norte, Santa Catarina (SC), Brazil, on a Sandy Typic Hapludalf soil, soil samples were collected from the 0-2.5, 2.5-5.0, 5-10 and 10-15 cm layers in treatments consisting of no manure application (control) and with applications of pig slurry and deep litter at two levels: the single and double rate of N requirement for maize and black oat succession. The soil was dried, ground in an agate mortar and analyzed for Cu and Zn contents by 0.01 mol L-1 EDTA and chemically fractionated to determine Cu and Zn. The applications of Pig deep litter and slurry at doses equivalent to 90 kg ha-1 N increased the contents of available Cu and Zn in the surface soil layer, if the double of this dose was applied in pig deep litter or double this dose in pig slurry, Cu and Zn migrated to a depth of 15 cm. Copper is accumulated mainly in the organic and residual fractions, and zinc preferentially in the fraction linked to clay minerals, especially in the surface soil layers.

Ammonia volatilization from coated urea forms

Nitrogen fertilization is a major component of the cost of agricultural production, due to the high cost and low efficiency of fertilizers. In the case of urea, the low efficiency is mainly due to losses by volatilization, which are more pronounced in cultivation systems in which plant residues are left on the soil. The objective of this work was to compare the influence of urea coated with sulfur or boric acid and copper sulfate with conventional N fertilizers on N volatilization losses in sugar cane harvested after stubble burning. The sources urea, sulfur-coated urea, urea coated with boric acid and copper sulfate, as well as nitrate and ammonium sulfate, were tested at amounts containing N rates of 120 kg ha-1 N. The integration of new technologies in urea fertilization can reduce N losses by volatilization. These losses were most reduced when using nitrate and ammonium sulfate. The application of a readily acidified substance (boric acid) to urea was more efficient in reducing volatilization losses and nutrient removal by sugar cane than that of a substance with gradual acidification (elemental sulfur).

Available content, surface runoff and leaching of phosphorus forms in a typic hapludalf treated with organic and mineral nutrient sources

The application of animal manure to soil can increase phosphorus availability to plants and enhance transfer of the nutrient solution drained from the soil surface or leached into the soil profile. The aim of this study was to evaluate the effect of successive applications of organic and mineral nutrient sources on the available content, surface runoff and leaching of P forms in a Typic Hapludalf in no-tillage systems. Experiment 1 was set up in 2004 in the experimental area of UFSM, in Santa Maria (RS, Brazil). The treatments consisted of: control (without nutrient application) and application of pig slurry (PS), pig deep-litter (PL), cattle slurry (CS), and mineral fertilizers (NPK). The rates were determined to meet the N crop requirements of no-tillage black oat and maize, grown in the 2010/2011 growing season. The soil solution was collected after each event (rain + runoff or leaching) and the soluble, particulate and total P contents were measured. In November 2008, soil was collected in 2 cm intervals to a depth of 20 cm, in 5 cm intervals to a depth of 40 cm, and in 10 cm intervals to a depth of 70 cm. The soil was dried and ground, and P determined after extraction by anion exchange resin (AER). In experiment 2, samples collected from the Typic Hapludalf near experiment 1 were incubated for 20, 35, 58, 73 and 123 days after applying the following treatments: soil, soil + PS, soil + PL, soil + CS and soil + NPK. Thereafter, the soil was sampled and P was analyzed by AER. The applications of nutrient sources over the years led to an increase in available P and its migration in the soil profile. This led to P transfer via surface runoff and leaching, with the largest transfer being observed in PS and PL treatments, in which most P was applied. The soil available P and P transfer via surface runoff were correlated with the amounts applied, regardless of the P source. However, P transfer by leaching was not correlated with the applied nutrient amount, but rather with the solution amount leached in the soil profile.

Forms of phosphorus in an oxisol under different soil tillage systems and cover plants in rotation with maize

Phosphorus fractions play a key role in sustaining the productivity of acid-savanna Oxisols and are influenced by tillage practices. The aim of this study was to quantify different P forms in an Oxisol (Latossolo Vermelho-Amarelo) from the central savanna region of Brazil under management systems with cover crops in maize rotation. Three cover crops (Canavalia brasiliensis, Cajanus cajan (L.), and Raphanus sativus L.) were investigated in maize rotation systems. These cover crops were compared to spontaneous vegetation. The inorganic forms NaHCO3-iP and NaOH-iP represented more than half of the total P in the samples collected at the depth of 5-10 cm during the rainy season when the maize was grown. The concentration of inorganic P of greater availability (NaHCO3-iP and NaOH-iP) was higher in the soil under no-tillage at the depth of 5-10 cm during the rainy season. Concentrations of organic P were higher during the dry season, when the cover crops were grown. At the dry season, organic P constituted 70 % of the labile P in the soil planted to C. cajan under no-tillage. The cover crops were able to maintain larger fractions of P available to the maize, resulting in reduced P losses to the unavailable pools, mainly in no-tillage systems.

Regulation of nonphosphorylated and phosphorylated forms of neurofilament proteins in the prefrontal cortex of human opioid addicts.

The neurofilament (NF) proteins (NF-H, NF-M, and NF-L for high, medium, and low molecular weights) play a crucial role in the organization of neuronal shape and function. In a preliminary study, the abundance of total NF-L was shown to be decreased in brains of opioid addicts. Because of the potential relevance of NF abnormalities in opioid addiction, we quantitated nonphosphorylated and phosphorylated NF in postmortem brains from 12 well-defined opioid abusers who had died of an opiate overdose (heroin or methadone). Levels of NF were assessed by immunoblotting techniques using phospho-independent and phospho-dependent antibodies, and the relative (% changes in immunoreactivity) and absolute (changes in ng NF/microg total protein) amounts of NF were calculated. Decreased levels of nonphosphorylated NF-H (42-32%), NF-M (14-9%) and NF-L (30-29%) were found in the prefrontal cortex of opioid addicts compared with sex, age, and postmortem delay-matched controls. In contrast, increased levels of phosphorylated NF-H (58-41%) and NF-M (56-28%) were found in the same brains of opioid addicts. The ratio of phosphorylated to nonphosphorylated NF-H in opioid addicts (3.4) was greater than that in control subjects (1.6). In the same brains of opioid addicts, the levels of protein phosphatase of the type 2A were found unchanged, which indicated that the hyperphosphorylation of NF-H is not the result of a reduced dephosphorylation process. The immunodensities of GFAP (the specific glial cytoskeletol protein), alpha-internexin (a neuronal filament related to NF-L) and synaptophysin (a synapse-specific protein) were found unchanged, suggesting a lack of gross changes in glial reaction, other intermediate filaments of the neuronal cytoskeletol, and synaptic density in the prefrontal cortex of opioid addicts. These marked reductions in total NF proteins and the aberrant hyperphosphorylation of NF-H in brains of opioid addicts may play a significant role in the cellular mechanisms of opioid addiction.

Soil water erosion under different cultivation systems and different fertilization rates and forms over 10 years

The action of rain and surface runoff together are the active agents of water erosion, and further influences are the soil type, terrain, soil cover, soil management, and conservation practices. Soil water erosion is low in the no-tillage management system, being influenced by the amount and form of lime and fertilizer application to the soil, among other factors. The aim was to evaluate the effect of the form of liming, the quantity and management of fertilizer application on the soil and water losses by erosion under natural rainfall. The study was carried out between 2003 and 2013 on a Humic Dystrupept soil, with the following treatments: T1 - cultivation with liming and corrective fertilizer incorporated into the soil in the first year, and with 100 % annual maintenance fertilization of P and K; T2 - surface liming and corrective fertilization distributed over five years, and with 75 % annual maintenance fertilization of P and K; T3 - surface liming and corrective fertilization distributed over three years, and with 50 % annual maintenance fertilization of P and K; T4 - surface liming and corrective fertilization distributed over two years, and with 25 % annual maintenance fertilization of P and K; T5 - fallow soil, without liming or fertilization. In the rotation the crops black oat (Avena strigosa ), soybean (Glycine max ), common vetch (Vicia sativa ), maize (Zea mays ), fodder radish (Raphanus sativus ), and black beans (Phaseolus vulgaris ). The split application of lime and mineral fertilizer to the soil surface in a no-tillage system over three and five years, results in better control of soil losses than when split in two years. The increase in the amount of fertilizer applied to the soil surface under no-tillage cultivation increases phytomass production and reduces soil loss by water erosion. Water losses in treatments under no-tillage cultivation were low in all crop cycles, with a similar behavior as soil losses.