Teorema de Pitágoras: algumas extensões/generalizações e atividades com o Software GeoGebra

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sobre pavimentações do plano euclidiano

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Collision free region determination by modified polygonal Boolean operations

Cutting and packing problems are found in numerous industries such as garment, wood and shipbuilding. The collision free region concept is presented, as it represents all the translations possible for an item to be inserted into a container with already placed items. The often adopted nofit polygon concept and its analogous concept inner fit polygon are used to determine the collision free region. Boolean operations involving nofit polygons and inner fit polygons are used to determine the collision free region. New robust non-regularized Boolean operations algorithm is proposed to determine the collision free region. The algorithm is capable of dealing with degenerated boundaries. This capability is important because degenerated boundaries often represent local optimal placements. A parallelized version of the algorithm is also proposed and tests are performed in order to determine the execution times of both the serial and parallel versions of the algorithm.

The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Patterned-ground plant communities along a bioclimate gradient in the High Arctic, Canada

Non-sorted circles, non-sorted polygons, and earth hummocks are common ground-surface features ill arctic regions. The), are caused by a variety of physical processes that Occur in permafrost regions including contraction cracking and frost heave. Here we describe the vegetation of patterned-ground forms on zonal sites at three location!: along an N-S transect through the High Arctic of Canada. We made 75 releves on patterned-ground features (circles, polygons, earth hummocks) and adjacent tundra (Interpolygon, intercircle, interhummock areas) and identified and classified the vegetation according to the Braun-Blanquet Method. Environmental factors were correlated with the vegetation data using a nonmetric multidimensional scaling ordination (NMDS). We identified eleven commnunities: (1) Puccinellia angustata-Papaver radicalum community in xeromesic non-sorted polygons of subzone A of the Circumpolar Arctic Vegetation Map; (2) Saxifraga-Parmelia omphalodes ssp. glacialis community in hydromesic interpolygon areas of subzone A; (3) Hypogymnia subobscura-Lecanora epibryon community In xeromesic non-sorted polygons of subzone B; (4) Orthotrichum speciosum-Salix arctica community In xeromesic interpolygon areas of subzone B; (5) Cochlearia groenlandica-Luzula nivalis community in hydromesic earth Mocks Of subzone B; (6) Salix arctica-Eriophorum angustifolium ssp. triste community in hygric earth hummocks of subzone 13; (7) Puccinellia angustata-Potentilla vahliana community in xeromesic non-sorted circles and bare patches of subzone Q (8) Dryas integrifolia-Carex rupestris community in xeromesic intercircle areas and vegetated patches of subzone C; (9) Braya glabella ssp. purpurascens-Dryas integrifolia community In hydromesic non-sorted circles of subzone Q (10) Dryas integrifolia-Carex aquatilis community in hydromesic intercircle areas of subzone C; and (11) Eriophorum angustifolium ssp. triste-Carex aquatilis community ill hygric intercircle areas of subzone C. The NMDS ordination displayed the vegetation types with respect to complex environmental gradients. The first axis of the ordination corresponds to a complex soil moisture gradient and the second axis corresponds to a complex geology/elevation/climate gradient. The tundra plots have a greater moss and graminoid cover than the adjacent frost-heave communities. In general, frost-heave features have greater thaw depths, more bare ground, thinner organic horizons, and lower soil moisture than the surrounding tundra. The morphology of the investigated patterned ground forms changes along the climatic gradient, with non-sorted pollygons dominating in the northernmost sites and non-sorted circles dominating, in the southern sites.

Some notes on the spatial representations

There are conventional methods to calculate the centroid of spatial units and distance among them with using Geographical Information Systems (GIS). The paper points out potential measurement errors of this calculation. By taking Indian district data as an example, systematic errors concealed in such variables are shown. Two comparisons are examined; firstly, we compare the centroid obtained from the spatial units, polygons, and the centre of each city where its district headquarters locates. Secondly, between the centres represented in the above, we calculate the direct distances and road distances obtained from each pair of two districts. From the comparison between the direct distances of centroid of spatial units and the road distances of centre of district headquarters, we show the distribution of errors and list some caveats for the use of conventional variables obtained from GIS.

The integration of multi-source data to improve the classification of remotely sensed images

The number of remote sensing platforms and sensors rises almost every year, yet much work on the interpretation of land cover is still carried out using either single images or images from the same source taken at different dates. Two questions could be asked of this proliferation of images: can the information contained in different scenes be used to improve the classification accuracy and, what is the best way to combine the different imagery? Two of these multiple image sources are MODIS on the Terra platform and ETM+ on board Landsat7, which are suitably complementary. Daily MODIS images with 36 spectral bands in 250-1000 m spatial resolution and seven spectral bands of ETM+ with 30m and 16 days spatial and temporal resolution respectively are available. In the UK, cloud cover may mean that only a few ETM+ scenes may be available for any particular year and these may not be at the time of year of most interest. The MODIS data may provide information on land cover over the growing season, such as harvest dates, that is not present in the ETM+ data. Therefore, the primary objective of this work is to develop a methodology for the integration of medium spatial resolution Landsat ETM+ image, with multi-temporal, multi-spectral, low-resolution MODIS \Terra images, with the aim of improving the classification of agricultural land. Additionally other data may also be incorporated such as field boundaries from existing maps. When classifying agricultural land cover of the type seen in the UK, where crops are largely sown in homogenous fields with clear and often mapped boundaries, the classification is greatly improved using the mapped polygons and utilising the classification of the polygon as a whole as an apriori probability in classifying each individual pixel using a Bayesian approach. When dealing with multiple images from different platforms and dates it is highly unlikely that the pixels will be exactly co-registered and these pixels will contain a mixture of different real world land covers. Similarly the different atmospheric conditions prevailing during the different days will mean that the same emission from the ground will give rise to different sensor reception. Therefore, a method is presented with a model of the instantaneous field of view and atmospheric effects to enable different remote sensed data sources to be integrated.

Characteristics of samples obtained during Pokhodsk 2012-2013 campaigns in the joint Russian-German POLYGON Project

Polygonal tundra, thermokarst basins and pingos are common and characteristic periglacial features of arctic lowlands underlain by permafrost in Northeast Siberia. Modern polygonal mires are in the focus of biogeochemical, biological, pedological, and cryolithological research with special attention to their carbon stocks and greenhouse-gas fluxes, their biodiversity and their dynamics and functioning under past, present and future climate scenarios. Within the frame of the joint German-Russian DFG-RFBR project Polygons in tundra wetlands: state and dynamics under climate variability in Polar Regions (POLYGON) field studies of recent and of late Quaternary environmental dynamics were carried out in the Indigirka lowland and in the Kolyma River Delta in summer 2012 and summer 2013. Using a multidisciplinary approach, several types of polygons and thermokarst lakes were studied in different landscapes units in the Kolyma Delta in 2012 around the small fishing settlement Pokhodsk. The floral and faunal associations of polygonal tundra were described during the fieldwork. Ecological, hydrological, meteorological, limnological, pedological and cryological features were studied in order to evaluate modern and past environmental conditions and their essential controlling parameters. The ecological monitoring and collection program of polygonal ponds were undertaken as in 2011 in the Indigirka lowland by a former POLYGON expedition (Schirrmeister et al. [eds.] 2012). Exposures, pits and drill cores in the Kolyma Delta were studied to understand the cryolithological structures of frozen ground and to collect samples for detailed paleoenvironmental research of the late Quaternary past. Dendrochronological and ecological studies were carried out in the tree line zone south of the Kolyma Delta. Based on previous work in the Indigirka lowland in 2011 (Schirrmeister et al. [eds.] 2012), the environmental monitoring around the Kytalyk research station was continued until the end of August 2012. In addition, a classical exposure of the late Pleistocene permafrost at the Achchaygy Allaikha River near Chokurdakh was studied. The ecological studies near Pokhodsk were continued in 2013 (chapter 13). Other fieldwork took place at the Pokhodsk-Yedoma-Island in the northwestern part of the Kolyma Delta.

Multivariate analysis of regional-scale geochemical data for environmental monitoring

A compositional multivariate approach is used to analyse regional scale soil geochemical data obtained as part of the Tellus Project generated by the Geological Survey Northern Ireland (GSNI). The multi-element total concentration data presented comprise XRF analyses of 6862 rural soil samples collected at 20cm depths on a non-aligned grid at one site per 2 km2. Censored data were imputed using published detection limits. Using these imputed values for 46 elements (including LOI), each soil sample site was assigned to the regional geology map provided by GSNI initially using the dominant lithology for the map polygon. Northern Ireland includes a diversity of geology representing a stratigraphic record from the Mesoproterozoic, up to and including the Palaeogene. However, the advance of ice sheets and their meltwaters over the last 100,000 years has left at least 80% of the bedrock covered by superficial deposits, including glacial till and post-glacial alluvium and peat. The question is to what extent the soil geochemistry reflects the underlying geology or superficial deposits. To address this, the geochemical data were transformed using centered log ratios (clr) to observe the requirements of compositional data analysis and avoid closure issues. Following this, compositional multivariate techniques including compositional Principal Component Analysis (PCA) and minimum/maximum autocorrelation factor (MAF) analysis method were used to determine the influence of underlying geology on the soil geochemistry signature. PCA showed that 72% of the variation was determined by the first four principal components (PC’s) implying “significant” structure in the data. Analysis of variance showed that only 10 PC’s were necessary to classify the soil geochemical data. To consider an improvement over PCA that uses the spatial relationships of the data, a classification based on MAF analysis was undertaken using the first 6 dominant factors. Understanding the relationship between soil geochemistry and superficial deposits is important for environmental monitoring of fragile ecosystems such as peat. To explore whether peat cover could be predicted from the classification, the lithology designation was adapted to include the presence of peat, based on GSNI superficial deposit polygons and linear discriminant analysis (LDA) undertaken. Prediction accuracy for LDA classification improved from 60.98% based on PCA using 10 principal components to 64.73% using MAF based on the 6 most dominant factors. The misclassification of peat may reflect degradation of peat covered areas since the creation of superficial deposit classification. Further work will examine the influence of underlying lithologies on elemental concentrations in peat composition and the effect of this in classification analysis.

Zooplankton and chlorophyll in upper water layers within research polygons in the Atlantic Ocean, June-September 2001

During Cruise 46 of R/V Akademik Mstislav Keldysh (from June to September 2001), vertical distributions of Radiolaria (Acantharia - Bac and Euradiolaria - Beur), mesozooplankton (from 0.2 to 3.0 mm size, Bm), and chlorophyll a (Cchl) in the epipelagic zone of the North Atlantic were studied. To examine the above-listed characteristics, samples were taken by Niskin 30 l bottles from 12-16 depth levels within the upper 100 to 200 m layer in the subarctic (48°11'N, 16°06'W) and subtropical (27°31'N, 75°51'W) waters, as well as in the transitional zone (41°44'N, 49°57'W). The latter proved to be characterized by the highest values of all averaged parameters examined by us within the upper 100 m layer (Bm - 365mg/m**3, Bac - 140 mg/m**3, Beur - 0.37 mg/m**3, and Cchl - 0.32 mg/m**3). For subarctic and subtropical waters corresponding characteristics were as follows: Bm - 123 and 53 mg/m**3, Bac - 0 and 0.06 mg/m**3, Beur - 0.17 and 0.19 mg/m**3, and Cchl - 0.27 and 0.05 mg/m**3, respectively. Percentage of Acantharia in total biomass of Radiolaria and zooplankton ranged from 0 to 39%, whereas that of Euradiolaria varied from 0.01 to 0.36%. Depth levels with maximum abundance of Acantharia were located above maxima of zooplankton and chlorophyll a or coincided with them. As for Euradiolaria, vertical profiles of their biomass were more diverse as compared with Acantharia. The latter group preferred more illuminated depth levels for its maximum development (10-100% of surface irradiance, E0) with respect to Euradiolaria (1-60% of E0). Possible reasons for this difference are discussed.