The Hasse-Minkowski Theorem

The Hasse-Minkowski theorem concerns the classification of quadratic forms over global fields (i.e., finite extensions of Q and rational function fields with a finite constant field). Hasse proved the theorem over the rational numbers in his Ph.D. thesis in 1921. He extended the research of his thesis to quadratic forms over all number fields in 1924. Historically, the Hasse-Minkowski theorem was the first notable application of p-adic fields that caught the attention of a wide mathematical audience. The goal of this thesis is to discuss the Hasse-Minkowski theorem over the rational numbers and over the rational function fields with a finite constant field of odd characteristic. Our treatments of quadratic forms and local fields, though, are more general than what is strictly necessary for our proofs of the Hasse-Minkowski theorem over Q and its analogue over rational function fields (of odd characteristic). Our discussion concludes with some applications of the Hasse-Minkowski theorem.

Field operations of the Bureau of Soils /

Report for each year issued in two volumes: text, and portfolio.

Field operations of the Division of Soils /

With accompanying papers by assistants in charge of field parties.

A field experiment on a steel Gerber-truss bridge for damage detection utilizing vehicle-induced vibrations

A field experiment was conducted on a real continuous steel Gerber-truss bridge with artificial damage applied. This article summarizes the results of the experiment for bridge damage detection utilizing traffic-induced vibrations. It investigates the sensitivities of a number of quantities to bridge damage including the identified modal parameters and their statistical patterns, Nair’s damage indicator and its statistical pattern and different sets of measurement points. The modal parameters are identified by autoregressive time-series models. The decision on bridge health condition is made and the sensitivity of variables is evaluated with the aid of the Mahalanobis–Taguchi system, a multivariate pattern recognition tool. Several observations are made as follows. For the modal parameters, although bridge damage detection can be achieved by performing Mahalanobis–Taguchi system on certain modal parameters of certain sets of measurement points, difficulties were faced in subjective selection of meaningful bridge modes and low sensitivity of the statistical pattern of the modal parameters to damage. For Nair’s damage indicator, bridge damage detection could be achieved by performing Mahalanobis–Taguchi system on Nair’s damage indicators of most sets of measurement points. As a damage indicator, Nair’s damage indicator was superior to the modal parameters. Three main advantages were observed: it does not require any subjective decision in calculating Nair’s damage indicator, thus potential human errors can be prevented and an automatic detection task can be achieved; its statistical pattern has high sensitivity to damage and, finally, it is flexible regarding the choice of sets of measurement points.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.

Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).

Sequence analysis of coding DNA fragments of pfcrt and pfmdr-1 genes in Plasmodium falciparum isolates from Odisha, India

The global emergence and spread of malaria parasites resistant to antimalarial drugs is the major problem in malaria control. The genetic basis of the parasite's resistance to the antimalarial drug chloroquine (CQ) is well-documented, allowing for the analysis of field isolates of malaria parasites to address evolutionary questions concerning the origin and spread of CQ-resistance. Here, we present DNA sequence analyses of both the second exon of the Plasmodium falciparum CQ-resistance transporter (pfcrt) gene and the 5' end of the P. falciparum multidrug-resistance 1 (pfmdr-1) gene in 40 P. falciparum field isolates collected from eight different localities of Odisha, India. First, we genotyped the samples for the pfcrt K76T and pfmdr-1 N86Y mutations in these two genes, which are the mutations primarily implicated in CQ-resistance. We further analyzed amino acid changes in codons 72-76 of the pfcrt haplotypes. Interestingly, both the K76T and N86Y mutations were found to co-exist in 32 out of the total 40 isolates, which were of either the CVIET or SVMNT haplotype, while the remaining eight isolates were of the CVMNK haplotype. In total, eight nonsynonymous single nucleotide polymorphisms (SNPs) were observed, six in the pfcrt gene and two in the pfmdr-1 gene. One poorly studied SNP in the pfcrt gene (A97T) was found at a high frequency in many P. falciparum samples. Using population genetics to analyze these two gene fragments, we revealed comparatively higher nucleotide diversity in the pfcrt gene than in the pfmdr-1 gene. Furthermore, linkage disequilibrium was found to be tight between closely spaced SNPs of the pfcrt gene. Finally, both the pfcrt and the pfmdr-1 genes were found to evolve under the standard neutral model of molecular evolution.

Queen execution in the Argentine ant, Iridomyrmex humilis

Field censuses and laboratory experiments show that in the Argentine ant, Iridomyrmex humilis (Mayr), c. 90% of the queens are executed by workers in May, at the beginning of the reproductive season. The reduction in the number of queens probably decreases the inhibition exerted by queens on the differentiation of sexuals and thus allows the production of new queens and males shortly thereafter. In the laboratory, there was no correlation between the percentage of queens executed and their weight or fecundity. At the time of execution of queens, nearly all queens were of the same age; less than 1 year. Therefore it is not likely that the age of queens plays any role in the choice that workers make in the queens they executed. Execution of these queens results in a heavy energetic cost for the colony which amounts c. 8% of the total biomass. This behaviour of workers executing nestmate queens is discussed with regard to possible evolutionary significance at the queen and worker level.

The influence of different artificial soil types on the acute toxicity of carbendazim to the earthworm Eisenia fetida in laboratory toxicity tests

Field populations of earthworms have shown a varied response in mortality to the fungicide carbendazim, the toxic reference substance used in agrochemical field trials. The aim of this study was to determine the influence of soil conditions as a potential cause of this variation. Laboratory acute toxicity tests were conducted using a range of artificial soils with varying soil components (organic matter, clay, pH and moisture). Batch adsorption/desorption studies were run to determine the influence of the soil properties on carbendazim behaviour. Adsorption was shown to be correlated with organic matter content and pH and this in turn could be linked to Eisenia fetida mortality, with lower mortality occurring with increased adsorption. Overall while E.fetida mortality did vary significantly between several of the soils the calculated LC50 values in the different soils did not cover a wide range (6.04-16.00 mg kg(-1)), showing that under these laboratory conditions soil components did not greatly influence carbendazim toxicity to E.fietida. (c) 2007 Elsevier Masson SAS. All rights reserved.

Poor survival on an artificial diet of two genotypes of the aphid Myzus persicae: a fitness cost of insecticide resistance?

A fully susceptible genotype (4106A) of Myzus persicae survived the longest on an artificial diet and, in several of the eight replicates, monitoring was terminated when the culture was still thriving. A genotype with elevated carboxylesterase FE4 at the R3 level (800F) had a mean survival of only 98.13 days, whereas 794J, which combines R3 E4 carboxylesterase with target-site resistance (knockdown resistance), survived for the even shorter mean time of 84.38 days. The poorer survival of the two genotypes with extremely elevated carboxylesterase-resistance was not the result of a reluctance to transfer to new diet at each diet change. Although available for only two replicates, a revertant clone of 794J (794Jrev), which has the same genotype as 794J but the amplified E4 genes are not expressed leading to a fully susceptible phenotype, did not appear to survive any better than this clone. This suggests that the poor survival on an artificial diet of the extreme-carboxylesterase genotypes is not the result of the cost of over-producing the enzyme. The frequency of insecticide-resistant genotypes is low in the population until insecticide is applied, indicating that they have reduced fitness, although this does not necessarily reflect a direct cost of expressing the resistance mechanism.

Moderating mycorrhizas: arbuscular mycorrhizas modify rhizosphere chemistry and maintain plant phosphorus status within narrow boundaries

Pastures often experience a pulse of phosphorus (P) when fertilized. We examined the role of arbuscular mycorrhizal fungi (AMF) in the uptake of P from a pulse. Five legumes (Kennedia prostrata, Cullen australasicum, Bituminaria bituminosa, Medicago sativa and Trifolium subterraneum) were grown in a moderate P, sterilized field soil, either with (+AMF) or without (−AMF) addition of unsterilized field soil. After 9–10 weeks, half the pots received 15 mg P kg−1 of soil. One week later, we measured: shoot and root dry weights; percentage of root length colonized by AMF; plant P, nitrogen and manganese (Mn) concentrations; and rhizosphere carboxylates, pH and plant-available P. The P pulse raised root P concentration by a similar amount in uncolonized and colonized plants, but shoot P concentration increased by 143% in uncolonized plants and 53% in colonized plants. Inoculation with AMF decreased the amount of rhizosphere carboxylates by 52%, raised rhizosphere pH by ∼0.2–0.7 pH units and lowered shoot Mn concentration by 38%. We conclude that AMF are not simply a means for plants to enhance P uptake when P is limiting, but also act to maintain shoot P within narrow boundaries and can affect nutrient uptake through their influence on rhizosphere chemistry.

Controle químico de nematoides em canaviais implantados com Tecnologia Plene

Pós-graduação em Agronomia (Produção Vegetal) - FCAV

Aspectos nutricionais do baru (Dipteryx alata Vog.) em casa de vegetação e em campo

With the objective of evaluating the response of baru (Dipteryx alata Vog.) to nutrient limitation and to the different levels of fertilization, seven experiments were conducted. Experiment 1: Nutritional limitation in greenhouse. We employed 12 treatments in a completely randomized design with eight replicates. Experiment 2: Levels of liming and P in greenhouse. The experimental design was completely randomized in a factorial scheme with four levels of liming (V23.2% (natural soil), V45%, V65% and V85%) and four doses of P (0, 100, 300 and 500 mg kg -1 of P). Experiment 3: Doses of N in greenhouse. We used seven treatments (0, 75, 150, 225, 300, 375 and 450 mg kg -1 of N) in a completely randomized design. Experiment 4: Doses of K in greenhouse. We used seven treatments (0, 75, 150, 225, 300, 375 and 450 mg kg -1 ) in a completely randomized design. Experiment 5: Levels of liming under field conditions. We used four treatments (V6.7% (natural soil), V35%, V55% and V75%) in a randomized blocks design. Experiment 6: doses of P under field conditions. We used five treatments (0, 23.67, 53.34, 106.67 and 213.36 kg ha -1 of P 2O5) in a randomized blocks design. Experiment 7: Doses of N under field conditions. We used five treatments (0, 30, 60, 120 and 240 kg ha -1 of N) in Latin square. In greenhouse, the evaluations were conducted at eight months (for experiments 1 and 2) and 12 months (for experiments 3 and 4) after seeding, when the measurements of height and root collar diameter of the seedlings. Subsequently, the plants were harvested and separated into shoot and root system, for weighing and evaluating dry biomass gain. In the field, the evaluations were conducted at six, 12, 18, 24 and 30 months (for experiments 5 and 6) and at six, 12 and 18 months (for experiment 7). In these experiments, we evaluated the survival of the seedlings, height of the plants and diameter of the stem at soil height. The data obtained were submitted to analysis of variance, mean tests and regression analysis. In conclusion, during the phase of seedling formation, the species is little demanding in S and B, negatively responds to liming, positively responds to phosphate fertilization and does not respond to nitrogen and potassium fertilization. In the field, in general, the species does not respond to the application of P or to liming, and is negatively influenced by the application of elevated doses of nitrogen.

Eutrophication and macroalgal blooms in temperate and tropical coastal waters: nutrient enrichment experiments with Ulva spp.

Receiving coastal waters and estuaries are among the most nutrient-enriched environments on earth, and one of the symptoms of the resulting eutrophication is the proliferation of opportunistic, fast-growing marine seaweeds. Here, we used a widespread macroalga often involved in blooms, Ulva spp., to investigate how supply of nitrogen (N) and phosphorus (P), the two main potential growth-limiting nutrients, influence macroalgal growth in temperate and tropical coastal waters ranging from low- to high-nutrient supplies. We carried out N and P enrichment field experiments on Ulva spp. in seven coastal systems, with one of these systems represented by three different subestuaries, for a total of nine sites. We showed that rate of growth of Ulva spp. was directly correlated to annual dissolved inorganic nitrogen (DIN) concentrations, where growth increased with increasing DIN concentration. Internal N pools of macroalgal fronds were also linked to increased DIN supply, and algal growth rates were tightly coupled to these internal N pools. The increases in DIN appeared to be related to greater inputs of wastewater to these coastal waters as indicated by high delta 15N signatures of the algae as DIN increased. N and P enrichment experiments showed that rate of macroalgal growth was controlled by supply of DIN where ambient DIN concentrations were low, and by P where DIN concentrations were higher, regardless of latitude or geographic setting. These results suggest that understanding the basis for macroalgal blooms, and management of these harmful phenomena, will require information as to nutrient sources, and actions to reduce supply of N and P in coastal waters concerned.

Natural antibody response to Plasmodium falciparum merozoite antigens MSP5, MSP9 and EBA175 is associated to clinical protection in the Brazilian Amazon

BACKGROUND: Antibodies have an essential role in the acquired immune response against blood stage P. falciparum infection. Although several antigens have been identified as important antibody targets, it is still elusive which antigens have to be recognized for clinical protection. Herein, we analyzed antibodies from plasmas from symptomatic or asymptomatic individuals living in the same geographic area in the Western Amazon, measuring their recognition of multiple merozoite antigens. METHODS: Specific fragments of genes encoding merozoite proteins AMA1 and members of MSP and EBL families from circulating P. falciparum field isolates present in asymptomatic and symptomatic patients were amplified by PCR. After cloning and expression of different versions of the antigens as recombinant GST-fusion peptides, we tested the reactivity of patients' plasmas by ELISA and the presence of IgG subclasses in the most reactive plasmas. RESULTS: 11 out of 24 recombinant antigens were recognized by plasmas from either symptomatic or asymptomatic infections. Antibodies to MSP9 (X2(DF=1) = 9.26/p = 0.0047) and MSP5 (X2(DF=1) = 8.29/p = 0.0069) were more prevalent in asymptomatic individuals whereas the opposite was observed for MSP1 block 2-MAD20 (X2(DF=1) = 6.41/p = 0.0206, Fisher's exact test). Plasmas from asymptomatic individuals reacted more intensely against MSP4 (U = 210.5, p < 0.03), MSP5 (U = 212, p < 0.004), MSP9 (U = 189.5, p < 0.002) and EBA175 (U = 197, p < 0.014, Mann-Whitney's U test). IgG1 and IgG3 were predominant for all antigens, but some patients also presented with IgG2 and IgG4. The recognition of MSP5 (OR = 0.112, IC95% = 0.021-0.585) and MSP9 (OR = 0.125, IC95% = 0.030-0.529, cross tab analysis) predicted 8.9 and 8 times less chances, respectively, to present symptoms. Higher antibody levels against MSP5 and EBA175 were associated by odds ratios of 9.4 (IC95% = 1.29-69.25) and 5.7 (IC95% = 1.12-29.62, logistic regression), respectively, with an asymptomatic status. CONCLUSIONS: Merozoite antigens were targets of cytophilic antibodies and antibodies against MSP5, MSP9 and EBA175 were independently associated with decreased symptoms.