Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

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.

Influence of soil pH on inorganic phosphorus sorption and desorption in a humid brazilian Ultisol

Liming is a common practice to raise soil pH and increase phosphorus (P) bioavailability in tropical regions. However, reports on the effect of liming on P sorption and bioavailability are controversial. The process of phosphorus desorption is more important than P sorption for defining P bioavailability. However few studies on the relationship between soil pH and P desorption are available, and even fewer in the tropical soils. The effects of soil pH on P sorption and desorption in an Ultisol from Bahia, Brazil, were investigated in this study. Phosphorus sorption decreased by up to 21 and 34 % with pH increases from 4.7 to 5.9 and 7.0, respectively. Decreasing Langmuir K parameter and decreasing partition coefficients (Kd) with increasing pH supported this trend. Phosphorus desorption was positively affected by increased soil pH by both the total amount of P desorbed and the ratio of desorbed P to initially sorbed P. A decreased K parameter and increased Kd value, particularly at the highest pH value and highest P-addition level, endorsed this phenomenon. Liming the soil had the double effect of reducing P sorption (up to 4.5 kg ha-1 of remaining P in solution) and enhancing P desorption (up to 2.7 kg ha-1 of additionally released P into solution).

Properties of slow-release phosphorus fertilizers with special references to their use on drained peatland forests : A review

Tiivistelmä: Hidasliukoisten fosforilannoitteiden ominaisuudet ja käyttökelpoisuus suometsien lannoituksessa. Kirjallisuuteen perustuva tarkastelu

Activity of phosphorus of synthetic Fe-K-P compounds in superphosphate fertilizers as affected by pH and ionic strength

The concentration of orthophosphate ions released from Fe-K-P compounds (Fe3KH8(PO4)6 .6H2O and Fe3KH14(PO4)8 .4H2O) present in superphosphates increases with pH, which initially suggests that the agronomic effectiveness of P fertilizers containing high amounts of these compounds would also increase with soil pH but studies considering activity, instead of concentration, are necessary. With this purpose, both compounds were synthesized under laboratory conditions, characterized by elemental chemical analysis, optical microscopy, X ray diffractometry, scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS), and used in a solubility study. Solutions of 0.01, 0.05 and 0.1 mol L-1 NaCl with pH adjusted to 3.0, 4.0, 5.0, 5.5, 6.0, 6.5, 7.0 and 7.5 were prepared for the solubility study of H8-syn, H14-syn and a phosphate rock (PR) from Brazil. The orthophosphate activity as H2PO4- and HPO4(2-) was calculated in each situation as related to pH and ionic strength using software MINTEQ. The remaining precipitates after equilibrium were chemically analyzed and subjected to X ray, SEM and EDS. Results of chemical analysis and instrumental techniques confirmed the preparation method. The activity of orthophosphate ions of both compounds tended to decrease under increasing pH and/or ionic strength of the solution, which in turn suggests that an increase in the solution pH does not necessarily promote an increase in the P bioavailability for plant uptake. This can be important when evaluating agronomic data of P fertilizers with high contents of these two Fe-K-P compounds.

Leaf senescence of common bean plants as affected by soil phosphorus supply

Responses of leaf senescence to P supply could constitute adaptive mechanisms for plant growth under P-limiting conditions. The aim of this study was to evaluate the effects of soil P supply on leaf senescence of common bean (Phaseolus vulgaris L.). Eight P levels, ranging from 5 to 640 mg kg-1 P, were applied to pots containing four bean plants of cultivar Carioca in 10 kg of an Oxic Haplustult soil. Attached leaves were counted weekly, abscised leaves were collected every other day, and seeds were harvested at maturity. The number of live leaves increased until 48 days after emergence (DAE) and decreased afterwards, irrespective of applied P levels. At lower applied P levels, the initial increase and the final decrease of leaf number was weak, whereas at higher applied P levels the leaf number increased intensively at the beginning of the growth cycle and decreased strongly after 48 DAE. Dry matter and P accumulated in senesced leaves increased as soil P levels increased until 61 DAE, but differences between P treatments narrowed thereafter. The greatest amounts of dry mass and P deposited by senesced leaves were observed at 48-54 DAE for high P levels, at 62-68 DAE for intermediate P levels and at 69-76 DAE for low P levels. These results indicate that soil P supply did not affect the stage of maximal leaf number and the beginning of leaf senescence of common bean plants, but the stage of greatest deposition of senesced leaves occurred earlier in the growth cycle as the soil P supply was raised.

Relationships between grain yield and accumulation of biomass, nitrogen and phosphorus in common bean cultivars

Shoot biomass is considered a relevant component for crop yield, but relationships between biological productivity and grain yield in legume crops are usually difficult to establish. Two field experiments were carried out to investigate the relationships between grain yield, biomass production and N and P accumulation at reproductive stages of common bean (Phaseolus vulgaris) cultivars. Nine and 18 cultivars were grown on 16 m² plots in 1998 and 1999, respectively, with four replications. Crop biomass was sampled at four growth stages (flowering R6, pod setting R7, beginning of pod filling R8, and mid-pod filling R8.5), grain yield was measured at maturity, and N and P concentrations were determined in plant tissues. In both years, bean cultivars differed in grain yield, in root mass at R6 and R7 stages, and in shoot mass at R6 and R8.5, whereas at R7 and R8 differences in shoot mass were significant in 1998 only. In both years, grain yield did not correlate with shoot mass at R6 and R7 and with root mass at R6. Grain yield correlated with shoot mass at R8 in 1999 but not in 1998, with shoot mass at R8.5 and with root mass at R7 in both years. Path coefficient analysis indicated that shoot mass at R8.5 had a direct effect on grain yield in both years, that root mass at R7 had a direct effect on grain yield in 1998, and that in 1999 the amounts of N and P in shoots at R8.5 had indirect effects on grain yield via shoot mass at R8.5. A combined analysis of both experiments revealed that biomass accumulation, N and P in shoots at R6 and R7 as well as root mass at R6 were similar in both years. In 1998 however bean accumulated more root mass at R7 and more biomass and N and P in shoots at R8 and R8.5, resulting in a 57 % higher grain yield in 1998. This indicates that grain yield of different common bean cultivars is not intrinsically associated with vegetative vigor at flowering and that mechanisms during pod filling can strongly influence the final crop yield. The establishment of a profuse root system during pod setting, associated with the continuous N and P acquisition during early pod filling, seems to be relevant for higher grain yields of common bean.

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.

Biomass production and phosphorus use of forage grasses fertilized with two phosphorus sources

A major constraint to agricultural production in acid soils of tropical regions is the low soil P availability, due to the high adsorption capacity, low P level in the source material and low efficiency of P uptake and use by most of the modern varieties grown commercially. This study was carried out to evaluate the biomass production and P use by forage grasses on two soils fertilized with two P sources of different solubility. Two experiments were carried out, one for each soil (Cambisol and Latosol), using pots filled with 4 dm³ soil in a completely randomized design and a 4 x 2 factorial scheme. The treatments consisted of a combination of four forage plants (Brachiaria decumbens, Brachiaria brizantha, Pennisetum glaucum and Sorghum bicolor) with two P sources (Triple Superphosphate - TSP and Arad Reactive Phosphate - ARP), with four replications. The forage grasses were harvested at pre-flowering, when dry matter weight and P concentrations were measured. Based on the P concentration and dry matter production, the total P accumulation was calculated. With these data, the following indices were calculated: the P uptake efficiency of roots, P use efficiency, use efficiency of available P, use efficiency of applied P and agronomic efficiency. The use of the source with higher solubility (TSP) resulted, generally, in higher total dry matter and total P accumulation in the forage grasses, in both soils. For the less reactive source (ARP), the means found in the forage grasses, for use efficiency and efficient use of available P, were always higher when grown in Latosol, indicating favorable conditions for the solubility of ARP. The total dry matter of Brachiaria brizantha was generally higher, with low P uptake, accumulation and translocation, which indicated good P use efficiency for both P sources and soils. The forage plants differed in the P use potential, due to the sources of the applied P and of the soils used. Less than 10 % of the applied P was immobilized in the forage dry matter. Highest values were observed for TSP, but this was not reflected in a higher use efficiency of P from this source.

Effect of fertilization on soil phosphorus in a long-term field experiment in southern Finland

Selostus: Maan fosforitilan muutos pitkäaikaisessa kenttäkokeessa hietamaalla

Phosphorus and root distribution and corn growth as related to long-term tillage systems and fertilizer placement

Soil and fertilizer management during cultivation can affect crop productivity and profitability. Long-term experiments are therefore necessary to determine the dynamics of nutrient and root distribution as related to soil profile, as well as the effects on nutrient uptake and crop growth. An 18-year experiment was conducted at the Federal University of Rio Grande do Sul State (UFRGS), in Eldorado do Sul, Brazil, on Rhodic Paleudult soil. Black oat and vetch were planted in the winter and corn in the summer. The soil management methods were conventional, involving no-tillage and strip tillage techniques and broadcast, row-and strip-applied fertilizer placement (triple superphosphate). Available P (Mehlich-1) and root distribution were determined in soil monoliths during the corn grain filling period. Corn shoot dry matter production and P accumulation during the 2006/2007 growing season were determined and the efficiency of P utilization calculated. Regardless of the degree of soil mobilization, P and roots were accumulated in the fertilized zone with time, mainly in the surface layer (0-10 cm). Root distribution followed P distribution for all tillage systems and fertilizer treatments. Under no-tillage, independent of the fertilizer placement, the corn plants developed more roots than in the other tillage systems. Although soil tillage systems and fertilizer treatments affected P and root distribution throughout the soil profile, as well as P absorption and corn growth, the efficiency of P utilization was not affected.

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.

Leaf area of common bean genotypes during early pod filling as related to plant adaptation to limited phosphorus supply

Low phosphorus supply markedly limits leaf growth and genotypes able to maintain adequate leaf area at low P could adapt better to limited-P conditions. This work aimed to investigate the relationship between leaf area production of common bean (Phaseolus vulgaris) genotypes during early pod filling and plant adaptation to limited P supply. Twenty-four genotypes, comprised of the four growth habits in the species and two weedy accessions, were grown at two P level applied to the soil (20 and 80 mg kg-1) in 4 kg pots and harvested at two growth stages (pod setting and early pod filling). High P level markedly increased the leaf number and leaf size (leaf area per leaf), slightly increased specific leaf area but did not affect the net assimilation rate. At low P level most genotypic variation for plant dry mass was associated with leaf size, whereas at high P level this variation was associated primarily with the number of leaves and secondarily with leaf size, specific leaf area playing a minor role at both P level. Determinate bush genotypes presented a smaller leaf area, fewer but larger leaves with higher specific leaf area and lower net assimilation rate. Climbing genotypes showed numerous leaves, smaller and thicker leaves with a higher net assimilation rate. Indeterminate bush and indeterminate prostrate genotypes presented the highest leaf area, achieved through intermediate leaf number, leaf size and specific leaf area. The latter groups were better adapted to limited P. It is concluded that improved growth at low P during early pod filling was associated with common bean genotypes able to maintain leaf expansion through leaves with greater individual leaf area.

Sewage sludge as nitrogen and phosphorus source for cane-plant and first ratoon crops

The use of sewage sludge in Brazilian agriculture was regulated by the resolution no. 375 Conama, in 2006. However, there is a lack of research to adequate the mineral N and P fertilizer doses to be applied in agricultural fields treated with this residue. In a field experiment, the effects of application rates of sewage sludge and mineral N and P fertilizers on the productivity and technical characteristics of the cane-plant and first ratoon (residual effect) crops were evaluated. Four doses of sewage sludge (0, 3.6, 7.2 and 10.8 t ha-1, dry base), of N (0, 30, 60 and 90 kg ha-1) and of P2O5 (0, 60, 120 and 180 kg ha-1) were combined in a factorial and laid out on randomized block design, a with two replications. To evaluate the residual effect of the sludge, 120 kg ha-1 N and 140 kg ha-1 of K2O were applied in all plots. Sludge application at cane planting, with or without N and/or P fertilizer increased the stalk yield from 84 up to 118 t ha-1, with no alteration in the sugarcane quality, compared with the application of NPK fertilizer alone, resulting in a stalk yield of 91 t ha-1. The study of the response surface for stalk yield on lowfertility soil was the basis for a recommendation of mineral N and P fertilizer doses for sugarcane implantation as related to sewage sludge application rates. It was also concluded that a sludge application of 10.8 t ha-1, which is the sludge dose established based on the N criterion according to the resolution Conama nº 375, could a) reduce the use of mineral N by 100 % and of P2O5 by 30 %, with increments of 22 % in stalk yield, as a direct effect of sludge application to cane plant crop, and b) increase the stalk yield in the second harvest (first ratoon) by up to 12 % and sugar yield by up to 11 %, by the residual effect of sludge application to sugar cane.