Polar foliations and isoparametric maps

A singular Riemannian foliation F on a complete Riemannian manifold M is called a polar foliation if, for each regular point p, there is an immersed submanifold Sigma, called section, that passes through p and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of M into the orbits of a polar action, i.e., an isometric action with sections. In this article we prove that the leaves of H : M -> Sigma, coincide with the level sets of a smooth map H: M -> Sigma, if M is simply connected. In particular, the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.

Secondary production of sandy beach macrofauna: An evaluation of predictive models

During the last three decades, several predictive models have been developed to estimate the somatic production of macroinvertebrates. Although the models have been evaluated for their ability to assess the production of macrobenthos in different marine ecosystems, these approaches have not been applied specifically to sandy beach macrofauna and may not be directly applicable to this transitional environment. Hence, in this study, a broad literature review of sandy beach macrofauna production was conducted and estimates obtained with cohort-based and size-based methods were collected. The performance of nine models in estimating the production of individual populations from the sandy beach environment, evaluated for all taxonomic groups combined and for individual groups separately, was assessed, comparing the production predicted by the models to the estimates obtained from the literature (observed production). Most of the models overestimated population production compared to observed production estimates, whether for all populations combined or more specific taxonomic groups. However, estimates by two models developed by Cusson and Bourget provided best fits to measured production, and thus represent the best alternatives to the cohort-based and size-based methods in this habitat. The consistent performance of one of these Cusson and Bourget models, which was developed for the macrobenthos of sandy substrate habitats (C&B-SS), shows that the performance of a model does not depend on whether it was developed for a specific taxonomic group. Moreover, since some widely used models (e.g., the Robertson model) show very different responses when applied to the macrofauna of different marine environments (e.g., sandy beaches and estuaries), prior evaluation of these models is essential.

Production of Excirolana armata (Dana, 1853) (Isopoda, Cirolanidae) on an exposed sandy beach in southeastern Brazil

The somatic and gonad productions of the cirolanid isopod Excirolana armata were analyzed by taking monthly samples from December 2003 to November 2005 on Una beach, So Paulo state (24A degrees S), southeastern Brazil. Sampling was performed along three fixed transects established from the base of the foredunes to the waterline. Weight-specific growth rate was used to estimate the E. armata somatic production for 2004 and 2005, separately. The gonad production was estimated based on the monthly reproductive potential (mean number of eggs/embryos per female x monthly abundance of ovigerous females with near-release broods) for 2004. The annual somatic production of E. armata population varied from 15.57 to 17.25 g AFDW m(-1) year(-1) and the somatic production/biomass ratio (P (s)/B) from 3.55 to 3.14 year(-1) for 2004 and 2005, respectively. The P (s)/B ratios were higher for males (4.02 and 3.19 year(-1) for 2004 and 2005) than for females (3.10 year(-1) for both years). The annual gonad production (P (g) = 1.07 g AFDW m(-1) year(-1)) contributed about 15 and 6% to the total production (P (s) + P (g)) of females and the population, respectively. The proportion of gonad to somatic production of females (P (g)/P (s)) increased with individual size (ca 90% in the 7.5 mm size class), and the annual weight-specific gonad production (P (g)/B ratio) was estimated to 0.24 year(-1). The high P (s)/B ratios estimated for E. armata derive from the fast growth of individuals and show the importance of this population to the energy flow on Una beach ecosystem. However, the low percentage of juveniles verified in this population and in other studies of populations of the genus Excirolana is discussed as an important source of underestimation of P (s)/B ratio.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

Mapeamento de solos e da produtividade de plantações de Eucalyptus grandis, com uso de sistema de informação geográfica

Detailed environmental land characterization is essential for technical and financial planning, for both the scientific point of view and technological application. This work aimed at the physiographic and pedological characterization and eucalyptus productivity mapping at Itatinga Forest Sciences Experimental Station (southeastern Brazil), using geographic information systems in order to identify possible cause-effect relationships between forest productivity and soil attributes. The digital cartographic dataset was structured as follows: as primary source of data, aerial photograph and field survey were used and, as a secondary source, topographical, geological and land use occupation maps were used. For mapping wood productivity at age six (MAI6, Mean Annual Increment), inventory data of permanent plots (same species, provenance and age) were used, which were obtained from Eucalyptus grandis plantations. Using simple linear correlation and backward stepwise multiple regression analysis, the dependent variable (MAI) was related with physical and chemical characteristics of the soils. Two standards of contour curves were identified, one with close curves, narrow and surrounding the drainage network, in the steeper and lower altitude areas; the other, with spaced contour lines, in the areas of higher altitude and with plane relief. Six types of soils were characterized as being highly related to the physiographic patterns of the area: loamy sandy to sandy clayey Typic Hapludox (LVAd, 47.5%), clayey Rhodic Hapludox (LVd1, 33.4%), sandy clay Rhodic Hapludox (LVd2, 6%), clayey Rhodic Hapludox (LVdf, 9.1%), Entisols (G, 3.4%) and Fluvents soil (RY, 0.6%). There were large variations in wood productivity in the Eucalyptus grandis plantations, characterized in six classes, ranging from 26 to 52 m(3) ha(-1) yr(-1). These productivity changes were strictly related to soil mapping units. Through multiple regression analysis, we found that clay and organic matter contents were the attributes which most strongly explained the productivity differences.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

Comparison measures of maps generated by geostatistical methods

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

Hydro-physical characterization of soils under tropical semi-deciduous forest

The study of the hydro-physical behavior in soils using toposequences is of great importance for better understanding the soil, water and vegetation relationships. This study aims to assess the hydro-physical and morphological characterization of soil from a toposequence in Galia, state of São Paulo, Brazil). The plot covers an area of 10.24 ha (320 × 320 m), located in a semi-deciduous seasonal forest. Based on ultra-detailed soil and topographic maps of the area, a representative transect from the soil in the plot was chosen. Five profiles were opened for the morphological description of the soil horizons, and hydro-physical and micromorphological analyses were performed to characterize the soil. Arenic Haplustult, Arenic Haplustalf and Aquertic Haplustalf were the soil types observed in the plot. The superficial horizons had lower density and greater hydraulic conductivity, porosity and water retention in lower tensions than the deeper horizons. In the sub-superficial horizons, greater water retention at higher tensions and lower hydraulic conductivity were observed, due to structure type and greater clay content. The differences observed in the water retention curves between the sandy E and the clay B horizons were mainly due to the size distribution, shape and type of soil pores.

Brazilian sandy beach macrofauna production: a review

The state of the art of the studies on the production of Brazilian sandy beach macrofauna was analyzed on the basis of the data available in the literature. For this purpose, the representativeness of the production dataset was examined by latitudinal distribution, degree of exposure and morphodynamic state of beaches, taxonomic groups, and methods employed. A descriptive analysis was, further, made to investigate the trends in production of the more representative taxonomic groups and species of sandy beach macrofauna. A total of 69 macrofauna annual production estimates were obtained for 38 populations from 25 studies carried out between 22º56'S and 32º20'S. Production estimates were restricted to populations on beaches located on the southern and southeastern Brazilian coast. Most of the populations in the dataset inhabit exposed dissipative sandy beaches and are mainly represented by mollusks and crustaceans, with a smaller number of polychaetes. The trends in production among taxonomic groups follow a similar pattern to that observed on beaches throughout the world, with high values for bivalves and decapods. The high turnover rate (P/B ratio) of the latter was due to the presence of several populations of the mole crab Emerita brasiliensis, which can attain high values of productivity, in the dataset. Most of the studies focus on the comparison of production and, especially, of P/B ratio according to life history traits in populations of the same species/taxonomic group. Despite the importance of life history-production studies, other approaches, such as the effect of man-induce disturbances on the macrofauna, should be undertaken in these threatened environments.