A note on the integral trace form in cyclotomic fields

Let m >= 3 be an integer, zeta(m) is an element of C a primitive mth root of unity, and K-m the cyclotomic field Q(zeta(m)). An explicit description of the integral trace form Tr-Km/Q(x (x) over bar)vertical bar Z[zeta(m)] where (x) over bar is the complex conjugate of x is presented. In the case where m is prime, a procedure for finding the minimum of the form subject to x being a nonzero element of a certain Z- module in Z[zeta(m)] is presented.

Representação geométrica em Q(zeta_pq)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Forma traço sobre algumas extensões galoisianas de corpos p-Ádicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cúbicas galoisianas

Pós-graduação em Matemática - IBILCE

Corpos cujo condutor é potência de primo: caracterização e reticulados ideais associados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Torres de extensões abelianas de grau primo ímpar não ramificado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The effect of trace elements on the sintering of an Al-Zn-Mg-Cu alloy

Trace elements can have a significant effect on the processing and properties of aluminium alloys, including sintered alloys. As little as 0.07 wt% (100 ppm) lead, tin or indium promotes sintering in an Al-Zn-Mg-Cu alloy produced from mixed elemental powders. This is a liquid phase sintering system and thin liquid films form uniformly throughout the alloy in the presence of the trace elements, but liquid pools develop in their absence. Analytical transmission electron microscopy indicates that the trace elements are confined to the interparticle and grain boundary regions. The sintering enhancement is attributed to the segregation of the microalloying addition to the liquid-vapour interface. Because the microalloying elements have a low surface tension, they lower the effective surface tension of the liquid. This reduces the wetting angle and extends the spreading of the liquid through the matrix. An improvement in sintering results. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Fluid-mobile trace element constraints on the role of slab melting and implications for Archaean crustal growth models

We use published and new trace element data to identify element ratios which discriminate between arc magmas from the supra-subduction zone mantle wedge and those formed by direct melting of subducted crust (i.e. adakites). The clearest distinction is obtained with those element ratios which are strongly fractionated during refertilisation of the depleted mantle wedge, ultimately reflecting slab dehydration. Hence, adakites have significantly lower Pb/Nd and B/Be but higher Nb/Ta than typical arc magmas and continental crust as a whole. Although Li and Be are also overenriched in continental crust, behaviour of Li/Yb and Be/Nd is more complex and these ratios do not provide unique signatures of slab melting. Archaean tonalite-trondhjemite-granodiorites (TTGs) strongly resemble ordinary mantle wedge-derived arc magmas in terms of fluid-mobile trace element content, implying that they-did not form by slab melting but that they originated from mantle which was hydrated and enriched in elements lost from slabs during prograde dehydration. We suggest that Archaean TTGs formed by extensive fractional crystallisation from a mafic precursor. It is widely claimed that the time between the creation and subduction of oceanic lithosphere was significantly shorter in the Archaean (i.e. 20 Ma) than it is today. This difference was seen as an attractive explanation for the presumed preponderance of adakitic magmas during the first half of Earth's history. However, when we consider the effects of a higher potential mantle temperature on the thickness of oceanic crust, it follows that the mean age of oceanic lithosphere has remained virtually constant. Formation of adakites has therefore always depended on local plate geometry and not on potential mantle temperature.

A methodology to event reconstruction from trace images

The widespread use of digital imaging devices for surveillance (CCTV) and entertainment (e.g., mobile phones, compact cameras) has increased the number of images recorded and opportunities to consider the images as traces or documentation of criminal activity. The forensic science literature focuses almost exclusively on technical issues and evidence assessment [1]. Earlier steps in the investigation phase have been neglected and must be considered. This article is the first comprehensive description of a methodology to event reconstruction using images. This formal methodology was conceptualised from practical experiences and applied to different contexts and case studies to test and refine it. Based on this practical analysis, we propose a systematic approach that includes a preliminary analysis followed by four main steps. These steps form a sequence for which the results from each step rely on the previous step. However, the methodology is not linear, but it is a cyclic, iterative progression for obtaining knowledge about an event. The preliminary analysis is a pre-evaluation phase, wherein potential relevance of images is assessed. In the first step, images are detected and collected as pertinent trace material; the second step involves organising and assessing their quality and informative potential. The third step includes reconstruction using clues about space, time and actions. Finally, in the fourth step, the images are evaluated and selected as evidence. These steps are described and illustrated using practical examples. The paper outlines how images elicit information about persons, objects, space, time and actions throughout the investigation process to reconstruct an event step by step. We emphasise the hypothetico-deductive reasoning framework, which demonstrates the contribution of images to generating, refining or eliminating propositions or hypotheses. This methodology provides a sound basis for extending image use as evidence and, more generally, as clues in investigation and crime reconstruction processes.

Chemical Evaluation of Selected Organics and Trace Metals in the Mangrove Macroflora Of Cochin

Mangroves are considered to play a significant role in global carbon cycling. Themangrove forests would fix CO2 by photosynthesis into mangrove lumber and thus decrease the possibility of a catastrophic series of events - global warming by atmospheric CO2, melting of the polar ice caps, and inundation of the great coastal cities of the world. The leaf litter and roots are the main contributors to mangrove sediments, though algal production and allochthonous detritus can also be trapped (Kristensen et al, 2008) by mangroves due to their high organic matter content and reducing nature are excellent metal retainers. Environmental pollution due to metals is of major concern. This is due to the basic fact that metals are not biodegradable or perishable the way most organic pollutants are. While most organic toxicants can be destroyed by combustion and converted into compounds such as C0, C02, SOX, NOX, metals can't be destroyed. At the most the valance and physical form of metals may change. Concentration of metals present naturally in air, water and soil is very low. Metals released into the environment through anthropogenic activities such as burning of fossils fuels, discharge of industrial effluents, mining, dumping of sewage etc leads to the development of higher than tolerable or toxic levels of metals in the environment leading to metal pollution. Of course, a large number of heavy metals such as Fe, Mn, Cu, Ni, Zn, Co, Cr, Mo, and V are essential to plants and animals and deficiency of these metals may lead to diseases, but at higher levels, it would lead to metal toxicity. Almost all industrial processes and urban activities involve release of at least trace quantities of half a dozen metals in different forms. Heavy metal pollution in the environment can remain dormant for a long time and surface with a vengeance. Once an area gets toxified with metals, it is almost impossible to detoxify it. The symptoms of metal toxicity are often quite similar to the symptoms of other common diseases such as respiratory problems, digestive disorders, skin diseases, hypertension, diabetes, jaundice etc making it all the more difficult to diagnose metal poisoning. For example the Minamata disease caused by mercury pollution in addition to affecting the nervous system can disturb liver function and cause diabetes and hypertension. The damage caused by heavy metals does not end up with the affected person. The harmful effects can be transferred to the person's progenies. Ironically heavy metal pollution is a direct offshoot of our increasing ability to mass produce metals and use them in all spheres of existence. Along with conventional physico- chemical methods, biosystem approachment is also being constantly used for combating metal pollution

Mineralogy and trace-element geochemistry of the high-grade iron ores of the Aguas Claras Mine and comparison with the Capao Xavier and Tamandua iron ore deposits, Quadrilahero Ferrifero, Brazil

Several major iron deposits occur in the Quadrilatero Ferrifero (QF), southeastern region of Brazil, where metamorphosed and heterogeneously deformed banded iron formation (BIF) of the Caue Formation, regionally called itabirite, was transformed into high- (Fe >64%) and lowgrade (30%trace elements. The high-grade ores at the Aguas Claras Mine have at least a dual origin, involving hypogene and supergene processes. The occurrence of the hard, massive high-grade ore within ""fresh"" dolomitic itabirite is evidence of its hypogene origin. Despite the contention about the origin of the dolomitic itabirite (if this rock is a carbonate-rich facies of the Caue Formation or a hematite-carbonate precursor of the soft high-grade ore), mineralogical and geochemical features of the soft high-grade ore indicate that it was formed by leaching of dolomite from the dolomitic itabirite by meteoric water. The comparison of the Aguas Claras, Capao Xavier and Tamandua orebodies shows that the original composition of the itabiritic protore plays a major role in the genesis of high- and low-grade soft ores in the QF. Under the same weathering and structural conditions, the dolomitic itabirite is the more favorable to form high-grade deposits than siliceous itabirite. Field relations at the Aguas Claras and Capao Xavier deposits suggest that it is not possible to form huge soft high-grade supergene deposits from siliceous itabirite, unless another control, such as impermeable barriers, had played an important role. The occurrence in the Tamandua Mine of a large, soft, high-grade orebody formed from siliceous itabirite and closely associated with hypogene hard ore suggests that large, soft, high-grade orebodies of the Quadrilatero Ferrifero, which occur within siliceous itabirite, have a hypogene contribution in their formation.

Morphological ripening of fluid inclusions and coupled zone-refining in quartz crystals revealed by cathodoluminescence imaging: Implications for CL-petrography, fluid inclusion analysis and trace-element geothermometry

Cathodoluminescence (CL) studies have previously shown that some secondary fluid inclusions in luminescent quartz are surrounded by dark, non-luminescent patches, resulting from fracture-sealing by late, trace-element-poor quartz. This finding has led to the tacit generalization that all dark CL patches indicate influx of low temperature, late-stage fluids. In this study we have examined natural and synthetic hydrothermal quartz crystals using CL imaging supplemented by in-situ elemental analysis. The results lead us to propose that all natural, liquid-water-bearing inclusions in quartz, whether trapped on former crystal growth surfaces (i.e., of primary origin) or in healed fractures (i.e., of pseudosecondary or secondary origin), are surrounded by three-dimensional, non-luminescent patches. Cross-cutting relations show that the patches form after entrapment of the fluid inclusions and therefore they are not diagnostic of the timing of fluid entrapment. Instead, the dark patches reveal the mechanism by which fluid inclusions spontaneously approach morphological equilibrium and purify their host quartz over geological time. Fluid inclusions that contain solvent water perpetually dissolve and reprecipitate their walls, gradually adopting low-energy euhedral and equant shapes. Defects in the host quartz constitute solubility gradients that drive physical migration of the inclusions over distances of tens of μm (commonly) up to several mm (rarely). Inclusions thus sequester from their walls any trace elements (e.g., Li, Al, Na, Ti) present in excess of equilibrium concentrations, thereby chemically purifying their host crystals in a process analogous to industrial zone refining. Non-luminescent patches of quartz are left in their wake. Fluid inclusions that contain no liquid water as solvent (e.g., inclusions of low-density H2O vapor or other non-aqueous volatiles) do not undergo this process and therefore do not migrate, do not modify their shapes with time, and are not associated with dark-CL zone-refined patches. This new understanding has implications for the interpretation of solids within fluid inclusions (e.g., Ti- and Al-minerals) and for the elemental analysis of hydrothermal and metamorphic quartz and its fluid inclusions by microbeam methods such as LA-ICPMS and SIMS. As Ti is a common trace element in quartz, its sequestration by fluid inclusions and its depletion in zone-refined patches impacts on applications of the Ti-in-quartz geothermometer.

The Interplay between Melting, Refertilization and Carbonatite Metasomatism in Off-Cratonic Lithospheric Mantle under Zealandia: an Integrated Major, Trace and Platinum Group Element Study

It is widely accepted that stabilization of the continental crust requires the presence of sub-continental lithospheric mantle. However, the degree of melt depletion required to stabilize the lithosphere and whether widespread refertilization is a significant process remain unresolved. Here, major and trace element, including platinum group elements (PGE), characterization of 40 mantle xenoliths from 13 localities is used to constrain the melt depletion, refertilization and metasomatic history of lithospheric mantle underneath the micro-continent Zealandia. Our previously published Re–Os isotopic data for a subset of these xenoliths indicate Phanerozoic to Paleoproterozoic ages and, reinterpreted with the new major and trace element data presented here, demonstrate that a large volume (>2 million km3) of lithospheric mantle with an age of 1·99 ± 0·21 Ga is present below the much younger crust of Zealandia. A peritectic melting model using moderately incompatible trace elements (e.g. Yb) in bulk-rocks demonstrates that these peridotites experienced a significant range of degrees of partial melting, between 3 and 28%. During subsolidus equilibration clinopyroxene gains significant rare earth elements (REE), which then leads to the underestimation of the degree of partial melting by ≤12% in fertile xenoliths. A new approach taking into account the effects of subsolidus re-equilibration on clinopyroxene composition effectively removes discrepancies in the calculated degree of melting and provides consistent estimates of between 4 and 29%. The estimated amount of melting is independent of the Re–Os model ages of the samples. The PGE patterns record simple melt depletion histories and the retention of primary base metal sulfides in the majority of the xenoliths. A rapid decrease in Pt/IrN observed at c. 1·0 wt % Al2O3 is a direct result of the exhaustion of sulfide in the mantle residue at c. 20–25% partial melting and the inability of Pt to form a stable alloy phase. Major elements preserve evidence for refertilization by a basaltic component that resulted in the formation of secondary clinopyroxene and low-forsterite olivine. The majority of xenoliths show the effects of cryptic metasomatic overprinting, ranging from minor to strong light REE enrichments in bulk-rocks (La/YbN = 0·16–15·9). Metasomatism is heterogeneous, with samples varying from those with weak REE enrichment and notable positive Sr and U–Th anomalies and negative Nb–Ta anomalies in clinopyroxene to those that have extremely high concentrations of REE, Th–U and Nb. Chemical compositions are consistent with a carbonatitic component contributing to the metasomatism of the lithosphere under Zealandia. Notably, the intense metasomatism of the samples did not affect the PGE budget of the peridotites as this was controlled by residual sulfides.

Forebrain-cerebellum interactions revealed by trace eyelid conditioning

While it is commonly assumed that brain systems receive and process information from other brain systems, there are few examples of tractable behaviors that allow such interactions to be studied. With the experiments presented in this dissertation we provide evidence that trace eyelid conditioning, a simple form of associative learning, is mediated by cerebellar learning in response to the output of persistent neural activity in the prefrontal cortex (PFC) and thus may be useful in analyses of PFC-cerebellar interactions. In a series of stimulation and reversible inactivation experiments we provide evidence that trace eyelid conditioning is mediated by cerebellar learning in response to a learned forebrain-driven input. Specifically, we provide evidence that this input is driven by the medial PFC and persists through the stimulus free trace interval of trace eyelid conditioning. In the next set of experiments we show that directly presenting the cerebellum with a pattern of input that mimics the classic persistent activity of PFC neurons reconstitutes trace eyelid conditioning, as assessed by a number of stringent tests. Finally, in set of reversible inactivation experiments, we provide evidence that bidirectional learning during trace eyelid conditioning involves the omission of the persistent, PFC-driven input that the cerebellum learns and responds to during trace eyelid conditioning. Given that persistent activity in PFC is often associated with working memory, these experiments suggest that trace eyelid conditioning may be useful in analyses of working memory mechanisms, cerebellar information processing and their interaction. To facilitate future analyses, we conclude with a working hypothesis of forebrain-cerebellum interactions during trace eyelid conditioning that addresses how persistent activity in PFC is induced and how the cerebellum decodes and uses PFC-driven input. ^

(Table 1) Isotopic and trace-element composition of ODP Leg 127/128 basalts

The western Pacific includes many volcanic island arc and backarc complexes, yet multi-isotopic studies of them are rare. Basement rocks of the Sea of Japan backarc basin were encountered at Sites 794,795, and 797, and consisted of basaltic sills and lava flows. These rocks exhibit a broad range in isotopic composition, broader than that seen in any other western Pacific arc or backarc system: 87Sr/86Sr = 0.70369 to 0.70499, 143Nd/144Nd = 0.51267 to 0.51317, 206Pb/204Pb = 17.64 to 18.36. The samples form highly correlated arrays between very depleted mid-ocean ridge basalt (MORB) and the Pacific pelagic sediment fields on Pb-Pb plots. Similarly, on plots of Sr-Pb and Nd-Pb, the Sea of Japan samples lie on mixing curves between depleted mantle and enriched mantle ("EM II"), which is interpreted to be of average crustal or pelagic sediment composition. The source of these backarc rocks appears to be a MORB-like mantle source, contaminated by pelagic sediments. Unlike the Mariana and Izu arc/backarc systems, Japanese arc and backarc rocks are indistinguishable from each other in a Sr-Nd isotope plot, and have similar trends in Pb-Pb plots. Thus, sediment contamination of the mantle wedge appears to control the isotopic compositions of both the arc and backarc magmas. Two-component mixing calculations suggest that the percentage of sediments in the magma source varies from 0.5% to 2.5%.