978 resultados para geometric morphometry


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Long-term relative sea-level cycles (0 5 to 6 Myr) have yet to be fully understood for the Cretaceous. During the Aptian, in the northern Maestrat Basin (Eastern Iberian Peninsula), fault-controlled subsidence created depositional space, but eustasy governed changes in depositional trends. Relative sea-level history was reconstructed by sequence stratigraphic analysis. Two forced regressive stages of relative sea-level were recognized within three depositional sequences. The first stage is late Early Aptian age (intra Dufrenoyia furcata Zone) and is characterized by foreshore to upper shoreface sedimentary wedges, which occur detached from a highstand carbonate platform, and were deposited above basin marls. The amplitude of relative sea-level drop was in the order of tens of metres, with a duration of <1 Myr. The second stage of relative sea-level fall occurred within the Late Aptian and is recorded by an incised valley that, when restored to its pre-contractional attitude, was >2 km wide and cut 115 m down into the underlying Aptian succession. With the subsequent transgression, the incision was back-filled with peritidal to shallow subtidal deposits. The changes in depositional trends, lithofacies evolution and geometric relation of the stratigraphic units characterized are similar to those observed in coeval rocks within the Maestrat Basin, as well as in other correlative basins elsewhere. The pace and magnitude of the two relative sea-level drops identified fall within the glacio-eustatic domain. In the Maestrat Basin, terrestrial palynological studies provide evidence that the late Early and Late Aptian climate was cooler than the earliest part of the Early Aptian and the Albian Stage, which were characterized by warmer environmental conditions. The outcrops documented here are significant because they preserve the results of Aptian long-term sea-level trends that are often only recognizable on larger scales (i.e. seismic) such as for the Arabian Plate.

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On the domain of general assignment games (with possible reservation prices) the core is axiomatized as the unique solution satisfying two consistency principles: projection consistency and derived consistency. Also, an axiomatic characterization of the nucleolus is given as the unique solution that satisfies derived consistency and equal maximum complaint between groups. As a consequence, we obtain a geometric characterization of the nucleolus. Maschler et al. (1979) provide a geometrical characterization for the intersection of the kernel and the core of a coalitional game, showing that those allocations that lie in both sets are always the midpoint of certain bargaining range between each pair of players. In the case of the assignment game, this means that the kernel can be determined as those core allocations where the maximum amount, that can be transferred without getting outside the core, from one agent to his / her optimally matched partner equals the maximum amount that he / she can receive from this partner, also remaining inside the core. We now prove that the nucleolus of the assignment game can be characterized by requiring this bisection property be satisfied not only for optimally matched pairs but also for optimally matched coalitions. Key words: cooperative games, assignment game, core, nucleolus

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Professional cleaning is a basic service occupation with a wide variety of tasks carried out in all kind of different sectors and workplaces by a large workforce. One important risk for cleaning workers is the exposure to chemical substances that are present in cleaning products.Monoethanolamine was found to be often present in cleaning products such as general purpose cleaners, bathroom cleaners, floor cleaners and kitchen cleaners. Monoethanolamine can injure the skin, and exposure to monoethanolamine was associated to asthma even when the air concentrations were low. It is a strong irritant and known to be involved in sensitizing mechanisms. It is very likely that the use of cleaning products containing monoethanolamine gives rise to respiratory and dermal exposures. Therefore there is a need to further investigate the exposures to monoethanolamine for both, respiratory and dermal exposure.The determination of monoethanolamine has traditionally been difficult and analytical methods available are little adapted for occupational exposure assessments. For monoethanolamine air concentrations, a sampling and analytical method was already available and could be used. However, a method to analyses samples for skin exposure assessments as well as samples of skin permeation experiments was missing. Therefore one main objective of this master thesis was to search an already developed and described analytical method for the measurement of monoethanolamine in water solutions, and to set it up in the laboratory. Monoethanolamine was analyzed after a derivatisation reaction with o-pthtaldialdehyde. The derivated fluorescing monoethanolamine was then separated with high performance liquid chromatography and detection took place with a fluorescent detector. The method was found to be suitable for qualitative and quantitative analysis of monoethanolamine. An exposure assessment was conducted in the cleaning sector to measure the respiratory and dermal exposures to monoethanolamine during floor cleaning. Stationary air samples (n=36) were collected in 8 companies and samples for dermal exposures (n=12) were collected in two companies. Air concentrations (Mean = 0.18 mg/m3, Standard Deviation = 0.23 mg/m3, geometric Mean = 0.09 mg/m3, Geometric Standard Deviation = 3.50) detected were mostly below 1/10 of the Swiss 8h time weighted average occupational exposure limit. Factors that influenced the measured monoethanolamine air concentrations were room size, ventilation system and the concentration of monoethanolamine in the cleaning product and amount of monoethanolamine used. Measured skin exposures ranged from 0.6 to 128.4 mg/sample. Some cleaning workers that participated in the skin exposure assessment did not use gloves and had direct contact with the solutions containing the cleaning product and monoethanolamine. During the entire sampling campaign, cleaning workers mostly did not use gloves. Cleaning workers are at risk to be regularly exposed to low air concentrations of monoethanolamine. This exposure may be problematic if a worker suffers from allergic reactions (e.g. Asthma). In that case a substitution of the cleaning product may be a good prevention measure as several different cleaning products are available for similar cleaning tasks. Currently there are no occupational exposure limits to compare the skin exposures that were found. To prevent skin exposures, adaptations of the cleaning techniques and the use of gloves should be considered. The simultaneous skin and airborne exposures might accelerate adverse health effects. Overall the risks caused by exposures to monoethanolamine are considered as low to moderate when the cleaning products are used correctly. Whenever possible, skin exposures should be avoided. Further research should consider especially the dermal exposure routes, as very high exposures might occur by skin contact with cleaning products. Dermatitis but also sensitization might be caused by skin exposures. In addition, new biomedical insights are needed to better understand the risks of the dermal exposure. Therefore skin permeability experiments should be considered.

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L'exposition aux poussières de bois est associé à un risque accru d'adénocarcinomes des fosses nasales et des sinus paranasaux (SNC, 'Sinonasal cancer') chez les travailleurs du bois. Les poussières de bois sont ainsi reconnues comme cancérogènes avérés pour l'homme par le Centre international de Recherche sur le Cancer (CIRC). Toutefois, l'agent causal spécifique et le mécanisme sous-jacent relatifs au cancer lié aux poussières de bois demeurent inconnus. Une possible explication est une co-exposition aux poussières de bois et aux Hydrocarbures Aromatiques Polycycliques (HAP), ces derniers étant potentiellement cancérogènes. Dans les faits, les travailleurs du bois sont non seulement exposés aux poussières de bois naturel, mais également à celles générées lors d'opérations effectuées à l'aide de machines (ponceuses, scies électriques, etc.) sur des finitions de bois (bois traités) ou sur des bois composites, tels que le mélaminé et les panneaux de fibres à densité moyenne (MDF, 'Medium Density Fiberboard'). Des HAP peuvent en effet être générés par la chaleur produite par l'utilisation de ces machines sur la surface du bois. Les principaux objectifs de cette thèse sont les suivants: (1) quantifier HAP qui sont présents dans les poussières générées lors de diverses opérations courantes effectuées sur différents bois (2) quantifier l'exposition individuelle aux poussières de bois et aux HAP chez les travailleurs, et (3) évaluer les effets génotoxiques (dommages au niveau de l'ADN et des chromosomes) due à l'exposition aux poussières de bois et aux HAP. Cette thèse est composée par une étude en laboratoire (objectif 1) et par une étude de terrain (objectifs 2 et 3). Pour l'étude en laboratoire, nous avons collecté des poussières de différents type de bois (sapin, MDF, hêtre, sipo, chêne, bois mélaminé) générées au cours de différentes opérations (comme le ponçage et le sciage), et ceci dans une chambre expérimentale et dans des conditions contrôlées. Ensuite, pour l'étude de terrain, nous avons suivi, dans le cadre de leur activité professionnelle, 31 travailleurs de sexe masculin (travailleurs du bois et ébenistes) exposés aux poussières de bois pendant deux jours de travail consécutifs. Nous avons également recruté, comme groupe de contrôle, 19 travailleurs non exposés. Pour effectuer une biosurveillance, nous avons collecté des échantillons de sang et des échantillons de cellules nasales et buccales pour chacun des participants. Ces derniers ont également rempli un questionnaire comprenant des données démographiques, ainsi que sur leur style de vie et sur leur exposition professionnelle. Pour les travailleurs du bois, un échantillonnage individuel de poussière a été effectué sur chaque sujet à l'aide d'une cassette fermée, puis nous avons évalué leur exposition à la poussière de bois et aux HAP, respectivement par mesure gravimétrique et par Chromatographie en phase gazeuse combinée à la spectrométrie de masse. L'évaluation des dommages induits à l'ADN et aux chromosomes (génotoxicité) a été, elle, effectuée à l'aide du test des micronoyaux (MN) sur les cellules nasales et buccales et à l'aide du test des comètes sur les échantillons de sang. Nos résultats montrent dans la poussière de la totalité des 6 types de bois étudiés la présence de HAP (dont certains sont cancérogènes). Des différences notoires dans les concentrations ont été néanmoins constatées en fonction du matériau étudié : les concentrations allant de 0,24 ppm pour la poussière de MDF à 7.95 ppm pour le mélaminé. Nos résultats montrent également que les travailleurs ont été exposés individuellement à de faibles concentrations de HAP (de 37,5 à 119,8 ng m-3) durant les opérations de travail du bois, alors que les concentrations de poussières inhalables étaient relativement élevés (moyenne géométrique de 2,8 mg m-3). En ce qui concerne la génotoxicité, les travailleurs exposés à la poussière de bois présentent une fréquence significativement plus élevée en MN dans les cellules nasales et buccales que les travailleurs du groupe témoin : un odds ratio de 3.1 a été obtenu pour les cellules nasales (IC 95% : de 1.8 à 5.1) et un odds ratio de 1,8 pour les cellules buccales (IC 95% : de 1.3 à 2.4). En outre, le test des comètes a montré que les travailleurs qui ont déclaré être exposés aux poussières de MDF et/ou de mélaminé avaient des dommages à l'ADN significativement plus élevés que les deux travailleurs exposés à la poussière de bois naturel (sapin, épicéa, hêtre, chêne) et que les travailleurs du groupe témoin (p <.01). Enfin, la fréquence des MN dans les cellules nasales et buccales augmentent avec les années d'exposition aux poussières de bois. Par contre, il n'y a pas de relation dose-réponse concernant la génotoxicité due à l'exposition journalière à la poussière et aux HAP. Cette étude montre qu'une exposition aux HAP eu bien lieu lors des opérations de travail du bois. Les travailleurs exposés aux poussières de bois, et donc aux HAP, courent un risque plus élevé (génotoxicité) par rapport au groupe témoin. Étant donné que certains des HAP détectés sont reconnus potentiellement cancérogènes, il est envisageable que les HAP générés au cours du travail sur les matériaux de bois sont un des agents responsables de la génotoxicité de la poussière de bois et du risque élevé de SNC observé chez les travailleurs du secteur. Etant donné la corrélation entre augmentation de la fréquence des MN, le test des micronoyaux dans les cellules nasales et buccales constitue sans conteste un futur outil pour la biosurveillance et pour la détection précoce du risque de SNC chez les travailleurs. - Exposures to wood dust have been associated with an elevated risk of adenocarcinomas of the Dasal cavity and the paranasal sinuses (sinonasal cancer or SNC) among wood workers. Wood dust is recognized as a human carcinogen by the International Agency for Research on Cancer. However, the specific cancer causative agent(s) and the mechanism(s) behind wood dust related carcinogenesis remains unknown. One possible explanation is a co-exposure to wood dust and polycyclic aromatic hydrocarbons (PAH), the latter being carcinogenic. In addition, wood workers are not only exposed to natural wood but also to wood finishes and composite woods such as wood melamine and medium density fiber (MDF) boards during the manipulation with power tools. The heat produced by the use of power tools can cause the generation of PAH from wood materials. The main objectives of the present thesis are to: (1) quantify possible PAH concentrations in wood dust generated during various common woodworking operations using different wood materials; (2) quantify personal wood dust concentrations and PAH exposures among wood workers; and (3) assess genotoxic effects (i.e., DNA and chromosomal damage) of wood dust and PAH exposure in wood workers. This thesis is composed by a laboratory study (objective 1) and a field study (objectives 2 and 3). In the laboratory study we collected wood dust from different wood materials (fir, MDF, beech, mahagany, oak, and wood melamine) generated during different wood operations (e.g., sanding and sawing) in an experimental chamber under controlled conditions. In the following field study, we monitored 31 male wood workers (furniture and construction workers) exposed to wood dust during their professional activity for two consecutive work shifts. Additionally, we recruited 19 non exposed workers as a control group. We collected from each participant blood samples, and nasal and buccal cell samples. They answered a questionnaire including demographic and life-style data and occupational exposure (current and past). Personal wood dust samples were collected using a closed-face cassette. We used gravimetrie analysis to determine the personal wood dust concentrations and capillary gas chromatography - mass spectrometry analysis to determine PAH concentrations. Genotoxicity was assessed with the micronucleus (MN) assay for nasal and buccal cells and with the comet assay for blood samples. Our results show that PAH (some of them carcinogenic) were present in dust from all six wood materials tested, yet at different concentrations depending on the material. The highest concentration was found in dust from wood melamine (7.95 ppm) and the lowest in MDF (0.24 ppm). Our results also show that workers were individually exposed to low concentrations of PAHs (37.5-119.8 ng m"3) during wood working operations, whereas the concentrations of inhalable dust were relatively high (geometric mean 2.8 mg m"3). Concerning the genotoxicity, wood workers had a significantly higher MN frequency in nasal and buccal cells than the workers in the control group (odds ratio for nasal cells 3.1 (95%CI 1.8-5.1) and buccal cells 1.8 (95%CI 1.3-2.4)). Furthermore, the comet assay showed that workers who reported to be exposed to dust from wooden boards (MDF and wood melamine) had significantly higher DNA damage than both the workers exposed to natural woods (fir, spruce, beech, oak) and the workers in the control group (p < 0.01). Finally, MN frequency in nasal and buccal cells increased with increasing years of exposure to wood dust. However, there was no genotoxic dose-response relationship with the per present day wood dust and PAH exposure. This study shows that PAH exposure occurred during wood working operations. Workers exposed to wood dust, and thus to PAH, had a higher risk for genotoxicity compared to the control group. Since some of the detected PAH are potentially carcinogenic, PAH generated from operations on wood materials may be one of the causative agents for the observed increased genotoxicity in wood workers. Since increased genotoxicity is manifested in an increased MN frequency, the MN assay in nasal and buccal cells may become a relevant biomonitoring tool in the future for early detection of SNC risk.

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Multi-center studies using magnetic resonance imaging facilitate studying small effect sizes, global population variance and rare diseases. The reliability and sensitivity of these multi-center studies crucially depend on the comparability of the data generated at different sites and time points. The level of inter-site comparability is still controversial for conventional anatomical T1-weighted MRI data. Quantitative multi-parameter mapping (MPM) was designed to provide MR parameter measures that are comparable across sites and time points, i.e., 1 mm high-resolution maps of the longitudinal relaxation rate (R1 = 1/T1), effective proton density (PD(*)), magnetization transfer saturation (MT) and effective transverse relaxation rate (R2(*) = 1/T2(*)). MPM was validated at 3T for use in multi-center studies by scanning five volunteers at three different sites. We determined the inter-site bias, inter-site and intra-site coefficient of variation (CoV) for typical morphometric measures [i.e., gray matter (GM) probability maps used in voxel-based morphometry] and the four quantitative parameters. The inter-site bias and CoV were smaller than 3.1 and 8%, respectively, except for the inter-site CoV of R2(*) (<20%). The GM probability maps based on the MT parameter maps had a 14% higher inter-site reproducibility than maps based on conventional T1-weighted images. The low inter-site bias and variance in the parameters and derived GM probability maps confirm the high comparability of the quantitative maps across sites and time points. The reliability, short acquisition time, high resolution and the detailed insights into the brain microstructure provided by MPM makes it an efficient tool for multi-center imaging studies.

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The objective of this work was to compare the morphometry of hatchery-reared and wild-caught mangrove crab (Ucides cordatus) megalopae. Ten U. cordatus megalopae of each group (hatchery-reared and wild-caught) were individually analyzed using a stereoscopic microscope equipped with an ocular micrometer. Length, width, and height of all megalopae were measured, and the size of body appendices was determined. The results indicate that the hatchery-reared megalopae are more robust than the wild ones. Furthermore, some significant differences in the size of certain appendices can be cues of the kind of alterations that hatchery-reared individuals experience.

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PURPOSE: Diisononyl phthalate (DiNP) is primarily used as a plasticizer in polyvinyl chloride (PVC) materials. While information is available on general population exposure to DiNP, occupational exposure data are lacking. We present DiNP metabolite urinary concentrations in PVC processing workers, estimate DiNP daily intake for these workers, and compare worker estimates to other populations. METHODS: We assessed DiNP exposure in participants from two companies that manufactured PVC materials, a PVC film manufacturer (n = 25) and a PVC custom compounder (n = 12). A mid-shift and end-shift urine sample was collected from each participant and analyzed for the DiNP metabolite mono(carboxy-isooctyl) phthalate (MCiOP). Mixed models were used to assess the effect on MCiOP concentrations of a worker being assigned to (1) a task using DiNP and (2) a shift where DiNP was used. A simple pharmacokinetic model was used to estimate DiNP daily intake from the MCiOP concentrations. RESULTS: Creatinine-adjusted MCiOP urinary concentrations ranged from 0.42-80 μg/g in PVC film and from 1.11-13.4 μg/g in PVC compounding. PVC film participants who worked on a task using DiNP (n = 7) had the highest MCiOP geometric mean (GM) end-shift concentration (25.2 μg/g), followed by participants who worked on a shift where DiNP was used (n = 11) (17.7 μg/g) as compared to participants with no task (2.92 μg/g) or shift (2.08 μg/g) exposure to DiNP. The GM end-shift MCiOP concentration in PVC compounding participants (4.80 μg/g) was comparable to PVC film participants with no task or shift exposure to DiNP. Because no PVC compounding participants were assigned to tasks using DINP on the day sampled, DiNP exposure in this company may be underestimated. The highest DiNP intake estimate was 26 μg/kg/day. CONCLUSION: Occupational exposure to DiNP associated with PVC film manufacturing tasks were substantially higher (sixfold to tenfold) than adult general population exposures; however, all daily intake estimates were less than 25% of current United States or European acceptable or tolerable daily intake estimates. Further characterization of DiNP occupational exposures in other industries is recommended.

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A comparative performance analysis of four geolocation methods in terms of their theoretical root mean square positioning errors is provided. Comparison is established in two different ways: strict and average. In the strict type, methods are examined for a particular geometric configuration of base stations(BSs) with respect to mobile position, which determines a givennoise profile affecting the respective time-of-arrival (TOA) or timedifference-of-arrival (TDOA) estimates. In the average type, methodsare evaluated in terms of the expected covariance matrix ofthe position error over an ensemble of random geometries, so thatcomparison is geometry independent. Exact semianalytical equationsand associated lower bounds (depending solely on the noiseprofile) are obtained for the average covariance matrix of the positionerror in terms of the so-called information matrix specific toeach geolocation method. Statistical channel models inferred fromfield trials are used to define realistic prior probabilities for therandom geometries. A final evaluation provides extensive resultsrelating the expected position error to channel model parametersand the number of base stations.

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This paper presents a relational positioning methodology for flexibly and intuitively specifying offline programmed robot tasks, as well as for assisting the execution of teleoperated tasks demanding precise movements.In relational positioning, the movements of an object can be restricted totally or partially by specifying its allowed positions in terms of a set of geometric constraints. These allowed positions are found by means of a 3D sequential geometric constraint solver called PMF – Positioning Mobile with respect to Fixed. PMF exploits the fact that in a set of geometric constraints, the rotational component can often be separated from the translational one and solved independently.

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The general objective of this study was to conduct astatistical analysis on the variation of the weld profiles and their influence on the fatigue strength of the joint. Weld quality with respect to its fatigue strength is of importance which is the main concept behind this thesis. The intention of this study was to establish the influence of weld geometric parameters on the weld quality and fatigue strength. The effect of local geometrical variations of non-load carrying cruciform fillet welded joint under tensile loading wasstudied in this thesis work. Linear Elastic Fracture Mechanics was used to calculate fatigue strength of the cruciform fillet welded joints in as-welded condition and under cyclic tensile loading, for a range of weld geometries. With extreme value statistical analysis and LEFM, an attempt was made to relate the variation of the cruciform weld profiles such as weld angle and weld toe radius to respective FAT classes.

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The objective of this work was to evaluate the spore density and diversity of arbuscular mycorrhizal fungi (AMF) in soil aggregates from fields of "murundus" (large mounds of soil) in areas converted and not converted to agriculture. The experiment was conducted in a completely randomized design with five replicates, in a 5x3 factorial arrangement: five areas and three aggregate classes (macro-, meso-, and microaggregates). The evaluated variables were: spore density and diversity of AMF, total glomalin, total organic carbon (TOC), total extraradical mycelium (TEM), and geometric mean diameter (GMD) of soil aggregates. A total of 21 AMF species was identified. Spore density varied from 29 to 606 spores per 50 mL of soil and was higher in microaggregates and in the area with 6 years of conversion to agriculture. Total glomalin was higher between murundus in all studied aggregate classes. The area with 6 years showed lower concentration of TOC in macroaggregates (8.6 g kg-1) and in microaggregates (10.1 g kg-1). TEM was greater at the top of the murundus in all aggregate classes. GMD increased with the conversion time to agriculture. The density and diversity of arbuscular mycorrhizal spores change with the conversion of fields of murundus into agriculture.

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Yleisesti tiedetään hitsin pintageometrian vaikuttavan rakenteen väsymislujuuteen. Nopean, edullisen ja luotettavan pintageometrian mittausmenetelmän kehittäminen on askel kohti tarkempaa ja varmempaa rakenteen väsymislujuuden tarkastelua. Tässä työssä on tutkittu hitsejä, joiden pinnan geometria on mitattu norjalaisen SINTEF -yrityksen kehittämällä rakenteellisen valon menetelmällä. Osana työtä kehitettiin MatLab -pohjainen ohjelma, jolla jälkikäsitellään mittauksesta saadut x-y-z -mittapisteet. Mittausdatan jälkikäsittelyssä saadaan mittauksesta määritettyähitsin reunan pyöristys, liittymäkulma, a-mitta, reunahaava ja kateettisuhde. Kehitettyä menetelmää käyttämällä mitattiin lähes 300 voimaakantamatontaristiliitoksen hitsiä. Mittaustuloksia verrattiin vastaavista kappaleista tehtyihin hiemittauksiin. Manuaalisen hieestä tehdyn mittauksen havaittiin olevan tarkempi ja pystyttiin havaitsemaan paikallisempia muotoja. Rakenteellisen valon mittauksissa tapahtunut heijastelu saatiin pienenemään käsittelemällä mitattava pinta mattavalkoisella maalilla. Rakenteellisen valon mittatarkkuudeksi saatiin noin 0,2 mm. Pohjautuen mitattuun hitsin reunan pyöristykseen ja liittymäkulmaan voidaan yksinkertaista kaavaa käyttämällä laskea hitsin jännityskonsentraatio ja näin saada alkuarvaus väsymislujuudelle. Myös muiden tekijöiden tiedetään vaikuttavan hitsin väsymislujuuteen, joten pyöristyksen ja liittymäkulman avulla tehdyt arviot eivät ole absoluuttisen oikeita. Tämä havaittiin väsytyskokeilla, joista yhdessä väsymisvaurio ei syntynyt suurimmankaan jännityskonsentraation alueella.

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En el presente artículo se analiza la adopción en el contexto ibérico catalán de los patrones métricos característicos de las colonias griegas del Mediterráneo occidental. La determinación de la unidad de medida constructiva empleada, así como de su aplicación, ha sido posible mediante la identificación de los principios geométricos estructurales de las torres defensivas ibéricas.

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BACKGROUND: Radiofrequency (RF) ablation is used to obtain local control of unresectable tumors in liver, kidney, prostate, and other organs. Accurate data on expected size and geometry of coagulation zones are essential for physicians to prevent collateral damage and local tumor recurrence. The aim of this study was to develop a standardized terminology to describe the size and geometry of these zones for experimental and clinical RF. METHODS: In a first step, the essential geometric parameters to accurately describe the coagulation zones and the spatial relationship between the coagulation zones and the electrodes were defined. In a second step, standard terms were assigned to each parameter. RESULTS: The proposed terms for single-electrode RF ablation include axial diameter, front margin, coagulation center, maximal and minimal radius, maximal and minimal transverse diameter, ellipticity index, and regularity index. In addition a subjective description of the general shape and regularity is recommended. CONCLUSIONS: Adoption of the proposed standardized description method may help to fill in the many gaps in our current knowledge of the size and geometry of RF coagulation zones.

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A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.