Solving Kepler’s equation via Smale’s \alpha -theory

We obtain an approximate solution $\tilde{E}=\tilde{E}(e,M)$ of Kepler’s equation $E-e\sin (E)=M$ for any $e\in [0,1)$ and $M\in [0,\pi ]$ . Our solution is guaranteed, via Smale’s $\alpha $ -theory, to converge to the actual solution $E$ through Newton’s method at quadratic speed, i.e. the $n$ -th iteration produces a value $E_n$ such that $|E_n-E|\le (\frac{1}{2})^{2^n-1}|\tilde{E}-E|$ . The formula provided for $\tilde{E}$ is a piecewise rational function with conditions defined by polynomial inequalities, except for a small region near $e=1$ and $M=0$ , where a single cubic root is used. We also show that the root operation is unavoidable, by proving that no approximate solution can be computed in the entire region $[0,1)\times [0,\pi ]$ if only rational functions are allowed in each branch.     

Larval growth,size, stage duration and recruitment success of a temperate reef fish

Understanding the causes of variation in recruitment of marine fishes has been a central goal for marine ecologists, fishery scientists and resource managers over the last century. Although the idea that recruitment variability is linked to the pelagic environmental conditions that enhance larval growth, survival, and/or delivery is consensual, such relationship is poorly known for most species. In this study we analyzed patterns of recruitment and early life history of a temperate reef fish, Coris julis from the Azores archipelago to test the relationships between early life history and recruitment success over two consecutive years. Growth from hatch to larval age 30 d was the best predictor of recruitment, implying that fast growing larger-at-age larvae have a survival advantage and contribute more to high recruitment, supporting the “bigger-is-better” hypothesis. The “stage-duration” hypothesis and the predictions regarding the relationships between size at age (SAA), size at settlement (SAS) and recruit abundance were also partially supported. The results presented in this study highlight the importance of understanding the early life traits that determine recruitment and larval-survivorship patterns, especially early larval growth, as this may provide a basis for prediction of recruitment and thus management of resources.     

Influence of sieving time on the efficiency and accuracy of grain‐size analysis of beach and dune sands

Grain size is a fundamental property of sediments and is commonly used to describe sedimentary facies and classify sedimentary environments. Among the various conventional techniques utilized to determine grain‐size frequency distributions, sieving is the most widely applied procedure. The accuracy of such analyses is, among other factors, strongly dependent on the sieving time. However, despite a substantial amount of research in this field, optimal sieving times for different types of sediments have, to date, not been established. In this article, the influence of sieving time on grain‐size analyses of medium‐grained microtidal and mesotidal beach and dune sands has been determined. To assess the precision of important textural parameters, such as median grain size, sorting, skewness and kurtosis, an error analysis was carried out for different sieving times (2, 5, 10, 15 and 20 minutes). After calibrating the analytical and sampling methodologies, significant deviations were registered when sieving time was less than 10 minutes. However, such deviations were very small and grain‐size distributions remained almost identical for sieving times of 10 minutes and longer, relative errors being as low as 0% in some cases.     

Bioerosion by the sea urchin Diadema mexicanum along Eastern Tropical Pacific coral reefs

Bioerosion is a natural process in coral reefs. It is fundamental to the health of these ecosystems. In the Eastern Tropical Pacific (ETP) coral reefs, the most important bioeroders are sponges, bivalves, sea urchins and the fish Arothron meleagris. In the 1980s, El Niño caused high coral mortality and an increase in macroalgal growth. As a result, greater sea urchin bioerosion occurred. This weakened the reef framework. Considering the high vulnerability of the ETP coral reefs, the goal of this study was to determine the current bioerosion impact of the sea urchin Diadema mexicanum along the western coasts of Mexico, El Salvador, Costa Rica and Panamá. The balance between coral bioaccretion and sea urchin bioerosion was also calculated. Between 2009 and 2010, in 12 coral reefs localities, D. mexicanum density, bottom cover and rugosity were quantified along band transects. The daily bioerosion rate was obtained from the amount of carbonates evacuated by sea urchins per unit time. The rate of coral accretion was calculated by multiplying the coral growth rate of the dominant genus by the density of their skeleton and by their specific coral cover. The localities were dissimilar (R = 0.765, P < 0.001) in terms of live coral cover, crustose calcareous algae, turf cover, rugosity index, and density and size of D. mexicanum. At all sites, with the exception of Bahía Culebra (Costa Rica), coral bioerosion was less than coral bioaccretion. Diadema mexicanum plays a dominant role in the balance of carbonates in the ETP, but this depends on reef condition (protection, overfishing, eutrophication) and so the impacts can be either positive or negative.     

Fluid flow through the sedimentary cover in northern Switzerland recorded by calcite–celestite veins (Oftringen borehole,Olten)

Abundant veins filled by calcite, celestite and pyrite were found in the core of a 719 m deep borehole drilled in Oftringen near Olten, located in the north-western Molasse basin, close to the thrust of the Folded Jura. Host rocks are calcareous marl, argillaceous limestone and limestone of the Dogger and Malm. The δ¹⁸O values of vein calcite are lower than in host rock carbonate and, together with microthermometric data from fluid inclusions in vein calcite, indicate precipitation from a seawater-dominated fluid at average temperatures of 56–68°C. Such temperatures were reached at the time of maximum burial of the sedimentary pile in the late Miocene. The depth profile of δ¹³C and ⁸⁷Sr/⁸⁶Sr values and Sr content of both whole-rock carbonate and vein calcite show marked trends towards negative δ¹³C, high ⁸⁷Sr/⁸⁶Sr, and low Sr content in the uppermost 50–150 m of the Jurassic profile (upper Oxfordian). The ⁸⁷Sr/⁸⁶Sr of vein minerals is generally higher than that of host rock carbonate, up to very high values corresponding to Burdigalian seawater (Upper Marine Molasse, Miocene), which represents the last marine incursion in the region. No evidence for internally derived radiogenic Sr (clay minerals) has been found and so an external source is required. S and O isotope composition of vein celestite and pyrite can be explained by bacterial reduction of Miocene seawater sulphate. The available data set suggests the vein mineralization precipitated from descending Burdigalian seawater and not from a fluid originating in the underlying Triassic evaporites.     

Seismic reliability functions for multistorey frame and wall‐frame systems

Seismic reliability functions of multistorey frame systems are expressed as values of Cornell's βindex in terms of two alternative measures of the earthquake intensity, normalized with respect to the yield displacement or to the deformation capacity of a simplified model of the global behaviour of the system obtained by pushover analysis. The safety margin is defined as the difference of the natural logarithms of the intensity that leads to collapse and that assumed to act on the system. The problem of defining a deformation capacity for a multistorey system is circumvented in this manner. The method proposed is illustrated through its application to several reinforced concrete rigid frames, including both column‐and‐beam and wall‐frame systems. Ground motion excitations are representative of those recorded at soft soil sites in the Valley of Mexico. A comparison is made of the reliability functions obtained on the basis of the gross section or the cracked section of reinforced concrete members. The results show that the reliability functions do not only depend on the expected values of the normalized intensity, but also on its dispersion, which is sensitive to the ratio of the fundamental period of the system to the dominant period of the ground motion. Some comments are presented about the establishment of reliability‐based seismic design criteria for generic systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Phytoplankton response to pH rise in a N-limited floodplain lake: relevance of N2-fixing heterocystous cyanobacteria

Phosphorus has been traditionally regarded as the controlling nutrient for phytoplankton growth, however, N-limitation is likely to occur in several environments. For example, nitrogen is considered the main nutrient limiting phytoplankton in floodplain lakes of the Paraná River basin. However, N₂-fixing heterocystous cyanobacteria (N₂-cyano) are usually absent in these water bodies. The low pH values frequently found may limit the development of these algae. We hypothesise that long-term lake isolation allows conspicuous phytoplankton growth during summer, resulting in high photosynthetic rates and pH. This scenario combined with low DIN (dissolved inorganic nitrogen) would favour the development of N₂-cyano. Phytoplankton composition was studied during 16 months in a vegetated and isolated floodplain lake in the Paraná basin. Additionally, pH was artificially increased in in situ mesocosms to test effects on phytoplankton structure. Lake phytoplankton was dominated by flagellates (cryptophytes and euglenophytes) and small coccoid algae (chlorophytes and colonial cyanobacteria). Algal biomass was highest during warm periods. Although pH increased up to 8.8 during the second summer period, N₂-cyano remained rare, most likely because of the high DIN concentration recorded. The alkalophilic diatom Cyclotella meneghiniana dominated and was positively correlated with pH. Conversely, PO₄⁼ concentrations in the mesocosm experiment were high and DIN remained relatively low. pH enhancement in the treated mesocosms (avg. pH = 8.2) promoted the development of N₂-cyano (Anabaena spp.) and C. meneghiniana, which after 1 month of incubation accounted together for 50% of the biomass in contrast to less than 1.6% in control containers. Our results support the hypothesis that during the warm season and under low DIN concentration, high pH favours N₂-cyano growth in these lakes. We provide new evidence supporting the idea that even under optimal nutrient conditions, N₂-cyano do not thrive unless other requirements are satisfied.     

Third world cities and the environment of poverty

This paper examines environmental problems associated with Third World cities. It concentrates on environmental problems as they relate to health and living conditions, especially for lower income groups. After an outline of urban growth trends, these problems are discussed on three different geographic scales. At the regional level, the paper discusses how cities draw on a wider area for natural resources (and usually for labour) and have environmental impacts which stretch far beyond their boundaries, although the most pressing impacts tend to be on their immediate hinterland. At the city-wide level there are problems of disposing of household, human and industrial wastes and of associated problems of air and water pollution. At the level of the home or workplace there are problems of inadequate space and ventilation, inadequate infrastructure and basic services, and lack of provision for the safeguarding of human health. The final section discusses how governments might tackle the causes of these environmental problems on each of these scales.