Ein Algorithmus zur numerischen Verifikation der äquivarianten Tamagawazahlvermutung für eine Familie von Zahlkörpererweiterungen

Sei $N/K$ eine galoissche Zahlkörpererweiterung mit Galoisgruppe $G$, so dass es in $N$ eine Stelle mit voller Zerlegungsgruppe gibt. Die vorliegende Arbeit beschäftigt sich mit Algorithmen, die für das gegebene Fallbeispiel $N/K$, die äquivariante Tamagawazahlvermutung von Burns und Flach für das Paar $(h^0(Spec(N), \mathbb{Z}[G]))$ (numerisch) verifizieren. Grob gesprochen stellt die äquivariante Tamagawazahlvermutung (im Folgenden ETNC) in diesem Spezialfall einen Zusammenhang her zwischen Werten von Artinschen $L$-Reihen zu den absolut irreduziblen Charakteren von $G$ und einer Eulercharakteristik, die man in diesem Fall mit Hilfe einer sogenannten Tatesequenz konstruieren kann. Unter den Voraussetzungen 1. es gibt eine Stelle $v$ von $N$ mit voller Zerlegungsgruppe, 2. jeder irreduzible Charakter $\chi$ von $G$ erfüllt eine der folgenden Bedingungen 2a) $\chi$ ist abelsch, 2b) $\chi(G) \subset \mathbb{Q}$ und $\chi$ ist eine ganzzahlige Linearkombination von induzierten trivialen Charakteren; wird ein Algorithmus entwickelt, der ETNC für jedes Fallbeispiel $N/\mathbb{Q}$ vollständig beweist. Voraussetzung 1. erlaubt es eine Idee von Chinburg ([Chi89]) umzusetzen zur algorithmischen Berechnung von Tatesequenzen. Dabei war es u.a. auch notwendig lokale Fundamentalklassen zu berechnen. Im höchsten zahm verzweigten Fall haben wir hierfür einen Algorithmus entwickelt, der ebenfalls auf den Ideen von Chinburg ([Chi85]) beruht, die auf Arbeiten von Serre [Ser] zurück gehen. Für nicht zahm verzweigte Erweiterungen benutzen wir den von Debeerst ([Deb11]) entwickelten Algorithmus, der ebenfalls auf Serre's Arbeiten beruht. Voraussetzung 2. wird benötigt, um Quotienten aus den $L$-Werten und Regulatoren exakt zu berechnen. Dies gelingt, da wir im Fall von abelschen Charakteren auf die Theorie der zyklotomischen Einheiten zurückgreifen können und im Fall (b) auf die analytische Klassenzahlformel von Zwischenkörpern. Ohne die Voraussetzung 2. liefern die Algorithmen für jedes Fallbeispiel $N/K$ immer noch eine numerische Verifikation bis auf Rechengenauigkeit. Den Algorithmus zur numerischen Verifikation haben wir für $A_4$-Erweiterungen über $\mathbb{Q}$ in das Computeralgebrasystem MAGMA implementiert und für 27 Erweiterungen die äquivariante Tamagawazahlvermutung numerisch verifiziert.

Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces.

Bias or rationality? The case of UK commercial real estate investment

Purpose – The purpose of this paper is to test the hypothesis that investment decision making in the UK direct property market does not conform to the assumption of economic rationality underpinning portfolio theory. Design/methodology/approach – The developing behavioural real estate paradigm is used to challenge the idea that investor “man” is able to perform with economic rationality, specifically with reference to the analysis of the spatial dispersion of the entire UK “investible stock” and “investible locations” against observed spatial patterns of institutional investment. Location quotients are derived, combining different data sets. Findings – Considerably greater variation in institutional property holdings is found across the UK than would be expected given the economic and stock characteristics of local areas. This appears to provide evidence of irrationality (in the strict traditional economic sense) in the behaviour of institutional investors, with possible herding underpinning levels of investment that cannot be explained otherwise. Research limitations/implications – Over time a lack of distinction has developed between the cause and effect of comparatively low levels of development and institutional property investment across the regions. A critical examination of decision making and behaviour in practice could break this cycle, and could in turn promote regional economic growth. Originality/value – The entire “population” of observations is used to demonstrate the relationships between economic theory and investor performance exploring, for the first time, stock and local area characteristics.

Incorporating toxicokinetics into an individual-based model for more realistic pesticide exposure estimates: A case study of the wood mouse

The potential risk of agricultural pesticides to mammals typically depends on internal concentrations within individuals, and these are determined by the amount ingested and by absorption, distribution, metabolism, and excretion (ADME). Pesticide residues ingested depend, amongst other things, on individual spatial choices which determine how much and when feeding sites and areas of pesticide application overlap, and can be calculated using individual-based models (IBMs). Internal concentrations can be calculated using toxicokinetic (TK) models, which are quantitative representations of ADME processes. Here we provide a population model for the wood mouse (Apodemus sylvaticus) in which TK submodels were incorporated into an IBM representation of individuals making choices about where to feed. This allows us to estimate the contribution of individual spatial choice and TK processes to risk. We compared the risk predicted by four IBMs: (i) “AllExposed-NonTK”: assuming no spatial choice so all mice have 100% exposure, no TK, (ii) “AllExposed-TK”: identical to (i) except that the TK processes are included where individuals vary because they have different temporal patterns of ingestion in the IBM, (iii) “Spatial-NonTK”: individual spatial choice, no TK, and (iv) “Spatial-TK”: individual spatial choice and with TK. The TK parameters for hypothetical pesticides used in this study were selected such that a conventional risk assessment would fail. Exposures were standardised using risk quotients (RQ; exposure divided by LD50 or LC50). We found that for the exposed sub-population including either spatial choice or TK reduced the RQ by 37–85%, and for the total population the reduction was 37–94%. However spatial choice and TK together had little further effect in reducing RQ. The reasons for this are that when the proportion of time spent in treated crop (PT) approaches 1, TK processes dominate and spatial choice has very little effect, and conversely if PT is small spatial choice dominates and TK makes little contribution to exposure reduction. The latter situation means that a short time spent in the pesticide-treated field mimics exposure from a small gavage dose, but TK only makes a substantial difference when the dose was consumed over a longer period. We concluded that a combined TK-IBM is most likely to bring added value to the risk assessment process when the temporal pattern of feeding, time spent in exposed area and TK parameters are at an intermediate level; for instance wood mice in foliar spray scenarios spending more time in crop fields because of better plant cover.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

Automorphism Groups of Generalized (Binary) Icosahedral, Tetrahedral and Octahedral Groups

Let G be any of the (binary) icosahedral, generalized octahedral (tetrahedral) groups or their quotients by the center. We calculate the automorphism group Aut(G).

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Brazilian regional development distribution, evidences for socio-economic policy

As to many Latin american countries, the impacts of the recent economic globalization on the Brazilian economy have revealed a diversified tendency in spatial development when regional economic indicators are observed. This is due to the specificities or each region, as regard their sector structure, the availability of human resources and the degree of technological innovation undertaken by local enterprises. From a situation of regional inequalities observed in lhe socio-economic levels of development at the beginning of the eighties the dynamics of the Brazilian regional evolution has presented different speeds and intensities in the several spaees. This paper aims to evaluate the dynamics of Brazilian regional development during the 1985-95 period and the impacts over the working population and regional disparities in order to offer some elements to assist social and economic policy. For this purpose Dispersion Quotients and Dispersion lntensity Coefficients were calculated based on two variables, the Regional Gross Domestic Product anel the Working Population. The results of the analysis confirm the existence of considerable regional disparities and it was observed that thc sector and regional redistribution of the GDP indicate that in a general way, no remarkable changes occurred in the regional development in the period. The results show that although the economic policies did stimulate a global convergence process of the per capita product among regions, those policies did not attenuate economic dynamism concentration to the desired extent.

Productive restructuring: effects on Brazilian regional development distribution

This paper aims to evaluate the dynamics of Brazilian regional development during the 1985-95 period. First, regional inequalities indexes were calculated for the whole country’s economy based on the per capita regional income (Williamson Inequality Index), in order to test the convergence or divergence. After this, the analysis aimed to verify the sector and regional dynamics in a more detailed exam, and for this purpose Dispersion Quotients and Dispersion Intensity Coefficients were calculated based on two variables, the Regional Gross Domestic Product and the Working Population. The results of the analysis confirm the existence of considerable regional disparities and it was verified that the sector and regional redistribution of the GDP indicate that, in a general way, no remarkable changes occurred in the regional productive structures in the period. It is also inferred that the economic policy at that period, in spite of resulting in a global regional convergence process of the per capita product, did not avoid the continuation of the concentration of greater economic dynamism in the most advanced regions, nor did it diminish in any considerable way the difference in the degree of development of the Northeast region.

Electroglottographic analysis of actresses and nonactresses' voices in different levels of intensity

Background: Previous studies with long-term average spectrum (LTAS) showed the importance of the glottal source for understanding the projected voices of actresses. In this study, electroglottographic (EGG) analysis was used to investigate the contribution of the glottal source to the projected voice, comparing actresses and nonactresses' voices, in different levels of intensity. Method: Thirty actresses and 30 nonactresses sustained vowels in habitual, moderate, and loud intensity levels. The EGG variables were contact quotient (CQ), closing quotient (QCQ), and opening quotient (QOQ). Other variables were sound pressure level (SPL) and fundamental frequency (F0). A KayPENTAX EGG was used. Variables were inputted in a general linear model. Results/Discussion: Actresses showed significantly higher values for SPL, in all levels, and both groups increased SPL significantly while changing from habitual to moderate and further to loud. There were no significant differences between groups for EGG quotients. There were significant differences between the levels only for F0 and CQ for both groups. Conclusion: SPL was significantly higher among actresses in all intensity levels, but in the EGG analysis, no differences were found. This apparently weak contribution of the glottal source in the supposedly projected voices of actresses, contrary to previous LTAS studies, might be because of a higher subglottal pressure or perhaps greater vocal tract contribution in SPL. Results from the present study suggest that trained subjects did not produce a significant higher SPL than untrained individuals by increasing the cost in terms of higher vocal fold collision and hence more impact stress. Future researches should explore the difference between trained and nontrained voices by aerodynamic measurements to evaluate the relationship between physiologic findings and the acoustic and EGG data. Moreover, further studies should consider both types of vocal tasks, sustained vowel and running speech, for both EGG and LTAS analysis. © 2013 The Voice Foundation.

Alterações microbianas do solo sob sistema de semeadura direta e rotação de culturas

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

Seleção do tamanho e da forma dos dentes anteriores superiores de próteses totais em quatro grupos raciais da população brasileira

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

RAMSY: Ratio Analysis of Mass Spectrometry to Improve Compound Identification

The complexity of biological samples poses a major challenge for reliable compound identification in mass spectrometry (MS). The presence of interfering compounds that cause additional peaks in the spectrum can make interpretation and assignment difficult. To overcome this issue, new approaches are needed to reduce complexity and simplify spectral interpretation. Recently, focused on unknown metabolite identification, we presented a new approach, RANSY (ratio analysis of nuclear magnetic resonance spectroscopy; Anal. Chem. 2011, 83, 7616-7623), which extracts the signals related to the same metabolite based on peak intensity ratios. On the basis of this concept, we present the ratio analysis of mass spectrometry (RAMSY) method, which facilitates improved compound identification in complex MS spectra. RAMSY works on the principle that, under a given set of experimental conditions, the abundance/intensity ratios between the mass fragments from the same metabolite are relatively constant. Therefore, the quotients of average peak ratios and their standard deviations, generated using a small set of MS spectra from the same ion chromatogram, efficiently allow the statistical recovery of the metabolite peaks and facilitate reliable identification. RAMSY was applied to both gas chromatography/MS and liquid chromatography tandem MS (LC-MS/MS) data to demonstrate its utility. The performance of RAMSY is typically better than the results from correlation methods. RAMSY promises to improve unknown metabolite identification for MS users in metabolomics or other fields.

Risk assessment of PM2.5 to child residents in Brazilian Amazon region with biofuel production

Background: Exposure to fine fractions of particulate matter (PM2.5) is associated with increased hospital admissions and mortality for respiratory and cardiovascular disease in children and the elderly. This study aims to estimate the toxicological risk of PM2.5 from biomass burning in children and adolescents between the age of 6 and 14 in Tangara da Serra, a municipality of Subequatorial Brazilian Amazon. Methods: Risk assessment methodology was applied to estimate the risk quotient in two scenarios of exposure according to local seasonality. The potential dose of PM2.5 was estimated using the Monte Carlo simulation, stratifying the population by age, gender, asthma and Body Mass Index (BMI). Results: Male asthmatic children under the age of 8 at normal body rate had the highest risk quotient among the subgroups. The general potential average dose of PM2.5 was 1.95 mu g/kg.day (95% CI: 1.62 - 2.27) during the dry scenario and 0.32 mu g/kg. day (95% CI: 0.29 - 0.34) in the rainy scenario. During the dry season, children and adolescents showed a toxicological risk to PM2.5 of 2.07 mu g/kg. day (95% CI: 1.85 - 2.30). Conclusions: Children and adolescents living in the Subequatorial Brazilian Amazon region were exposed to high levels of PM2.5 resulting in toxicological risk for this multi-pollutant. The toxicological risk quotients of children in this region were comparable or higher to children living in metropolitan regions with PM2.5 air pollution above the recommended limits to human health.

Resonance frequency analysis of overdenture retainer implants with immediate loading

Objective: To evaluate 16 patients of both sexes with lower overdenture and upper complete dentures, by analysing the resonance frequency of the initial and late stability of implants used to retain the overdenture under immediate loading. Background: Oral rehabilitation treatment with complete dentures using implants has been increasingly more common among the specialists in the oral rehabilitation area. This is an alternative for obtaining retention and stability in treatments involving conventional complete dentures, where two implants are enough to retain the overdenture satisfactorily. Materials and methods: The Osstell (TM) Mentor device was used for the analysis in the initial period (primary stability), 3 and 15 months after the installation of the lower overdenture (secondary stability). The statistical analysis was performed with the repeated measures model (p < 0.01). Results: The implant stability quotients were observed to increase after 15 months of the rehabilitating treatment. Conclusion: The use of overdentures over two lower implants should become the treatment of choice for individuals who have a fully edentulous mandible.