ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Coexistence of forest and savanna in an Amazonian area from a geological perspective

Question: How can the coexistence of savanna and forest in Amazonian areas with relatively uniform climates be explained? Location: Eastern Marajo Island, northeast Amazonia, Brazil. Methods: The study integrated floristic analysis, terrain morphology, sedimentology and delta(13)C of soil organic matter. Floristic analysis involved rapid ecological assessment of 33 sites, determination of occurrence, specific richness, hierarchical distribution and matrix of floristic similarity between paired vegetation types. Terrain characterization was based on analysis of Landsat images using 4(R), 5(G) and 7(B) composition and digital elevation model (DEM). Sedimentology involved field descriptions of surface and core sediments. Finally, radiocarbon dating and analysis of delta(13)C of soil profile organic matter and natural ecotone forest-savanna was undertaken. Results: Slight tectonic subsidence in eastern Marajo Island favours seasonal flooding, making it unsuitable for forest growth. However, this area displays slightly convex-up, sinuous morphologies related to paleochannels, covered by forest. Terra-firme lowland forests are expanding from west to east, preferentially occupying paleochannels and replacing savanna. Slack, running water during channel abandonment leads to disappearance of varzea/gallery forest at channel margins. Long-abandoned channels sustain continuous terra-firme forests, because of longer times for more species to establish. Recently abandoned channels have had less time to become sites for widespread tree development, and are either not vegetated or covered by savanna. Conclusion: Landforms in eastern Marajo Island reflect changes in the physical environment due to reactivation of tectonic faults during the latest Quaternary. This promoted a dynamic history of channel abandonment, which controlled a set of interrelated parameters (soil type, topography, hydrology) that determined species location. Inclusion of a geological perspective for paleoenvironmental reconstruction can increase understanding of plant distribution in Amazonia.

Woodgrain defect on tinned steel Flandres foil

Tin electrocoated steel strip, also referred to as Flandres foil, is largely used for manufacturing food containers. Tinplates must have good corrosion resistance, workability, weldability, as well as a bright appearance. The woodgrain defect, a not yet fully understood defect that occurs on tinplates and accounts for their high scrap rate, consists of alternate bands of bright/dull reflectivity and resembles longitudinally cut wood. Observations of the woodgrain defect by scanning electron microscopy showed that the molten tin spreads irregularly during both the melting and solidification stages. X-ray diffraction analyses showed that the metallic tin tended to crystallize in the (200) direction for coupons with and without the woodgrain defect. Nevertheless, the preferential orientation degree decreased for coupons with the woodgrain defect. The rocking curves, also known as omega-scan, showed that the tin grains were uniformly aligned parallel to the strip surface for coupons with no defects, whereas for tinplates with woodgrain, the tin grains were not uniformly oriented, probably due to the misalignment of the grains in relation to the surface. (C) 2011 Elsevier Inc. All rights reserved.

An algorithm for computerized automatic tuning of power system stabilizers

The main objective of this paper is to relieve the power system engineers from the burden of the complex and time-consuming process of power system stabilizer (PSS) tuning. To achieve this goal, the paper proposes an automatic process for computerized tuning of PSSs, which is based on an iterative process that uses a linear matrix inequality (LMI) solver to find the PSS parameters. It is shown in the paper that PSS tuning can be written as a search problem over a non-convex feasible set. The proposed algorithm solves this feasibility problem using an iterative LMI approach and a suitable initial condition, corresponding to a PSS designed for nominal operating conditions only (which is a quite simple task, since the required phase compensation is uniquely defined). Some knowledge about the PSS tuning is also incorporated in the algorithm through the specification of bounds defining the allowable PSS parameters. The application of the proposed algorithm to a benchmark test system and the nonlinear simulation of the resulting closed-loop models demonstrate the efficiency of this algorithm. (C) 2009 Elsevier Ltd. All rights reserved.

Simulated annealing applied to the irregular rotational placement of shapes over containers with fixed dimensions

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular two dimensional polygons inside a two dimensional container. This problem is approached with an heuristic based on simulated annealing. Traditional 14 external penalization"" techniques are avoided through the application of the no-fit polygon, that determinates the collision free area for each polygon before its placement. The simulated annealing controls: the rotation applied, the placement and the sequence of placement of the polygons. For each non placed polygon, a limited depth binary search is performed to find a scale factor that when applied to the polygon, would allow it to be fitted in the container. It is proposed a crystallization heuristic, in order to increase the number of accepted solutions. The bottom left and larger first deterministic heuristics were also studied. The proposed process is suited for non convex polygons and containers, the containers can have holes inside. (C) 2009 Elsevier Ltd. All rights reserved.

Adaptive Carrier Tracking for Mars to Earth Communications During Entry, Descent, and Landing

We propose a robust and low complexity scheme to estimate and track carrier frequency from signals traveling under low signal-to-noise ratio (SNR) conditions in highly nonstationary channels. These scenarios arise in planetary exploration missions subject to high dynamics, such as the Mars exploration rover missions. The method comprises a bank of adaptive linear predictors (ALP) supervised by a convex combiner that dynamically aggregates the individual predictors. The adaptive combination is able to outperform the best individual estimator in the set, which leads to a universal scheme for frequency estimation and tracking. A simple technique for bias compensation considerably improves the ALP performance. It is also shown that retrieval of frequency content by a fast Fourier transform (FFT)-search method, instead of only inspecting the angle of a particular root of the error predictor filter, enhances performance, particularly at very low SNR levels. Simple techniques that enforce frequency continuity improve further the overall performance. In summary we illustrate by extensive simulations that adaptive linear prediction methods render a robust and competitive frequency tracking technique.

Transient and Steady-State Analysis of the Affine Combination of Two Adaptive Filters

In this paper, we propose an approach to the transient and steady-state analysis of the affine combination of one fast and one slow adaptive filters. The theoretical models are based on expressions for the excess mean-square error (EMSE) and cross-EMSE of the component filters, which allows their application to different combinations of algorithms, such as least mean-squares (LMS), normalized LMS (NLMS), and constant modulus algorithm (CMA), considering white or colored inputs and stationary or nonstationary environments. Since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant, its adaptation is also taken into account in the transient analysis. Furthermore, we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance. Good agreement between analysis and simulation results is always observed.

Measuring complexity in three-trophic level systems

This essay is a trial on measuring complexity in a three-trophic level system by using a convex function of the informational entropy. The complexity measure defined here is compatible with the fact that real complexity lies between ordered and disordered states. Applying this measure to the data collected for two three-trophic level systems some hints about their organization are obtained. (C) 2008 Elsevier B.V. All rights reserved.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

Spatio-temporal variability behavior of land surface soil water content in shrub- and grass-land

The knowledge of the relationship between spatial variability of the surface soil water content (theta) and its mean across a spatial domain (theta(m)) is crucial for hydrological modeling and understanding soil water dynamics at different scales. With the aim to compare the soil moisture dynamics and variability between the two land uses and to explore the relationship between the spatial variability of theta and theta(m), this study analyzed sets of surface theta measurements performed with an impedance soil moisture probe, collected 136 times during a period of one year in two transects covering different land uses, i.e., korshinsk peashrub transect (KPT) and bunge needlegrass transect (BNT), in a watershed of the Loess Plateau, China. Results showed that the temporal pattern of theta behaved similarly for the two land uses, with both relative wetter soils during wet period and relative drier soils during dry period recognized in BNT. Soil moisture tended to be temporally stable among different dates, and more stable patterns could be observed for dates with more similar soil water conditions. The magnitude of the spatial variation of theta in KPT was greater than that in ENT. For both land uses, the standard deviation (SD) of theta in general increased as theta(m) increased, a behavior that could be well described with a natural logarithmic function. Convex relationship of CV and theta(m) and the maximum CV for both land uses (43.5% in KPT and 41.0% in BNT) can, therefore, be ascertained. Geostatistical analysis showed that the range in KPT (9.1 m) was shorter than that in BNT (15.1 m). The nugget effects, the structured variability, hence the total variability increased as theta(m) increased. For both land uses, the spatial dependency in general increased with increasing theta(m). 2011 Elsevier B.V. All rights reserved.

How rare is too rare to harvest? Management challenges posed by timber species occurring at low densities in the Brazilian Amazon

Tropical forests are characterized by diverse assemblages of plant and animal species compared to temperate forests. Corollary to this general rule is that most tree species, whether valued for timber or not, occur at low densities (<1 adult tree ha(-1)) or may be locally rare. In the Brazilian Amazon, many of the most highly valued timber species occur at extremely low densities yet are intensively harvested with little regard for impacts on population structures and dynamics. These include big-leaf mahogany (Swietenia macrophylla), ipe (Tabebuia serratifolia and Tabebuia impetiginosa), jatoba (Hymenaea courbaril), and freijo cinza (Cordia goeldiana). Brazilian forest regulations prohibit harvests of species that meet the legal definition of rare - fewer than three trees per 100 ha - but treat all species populations exceeding this density threshold equally. In this paper we simulate logging impacts on a group of timber species occurring at low densities that are widely distributed across eastern and southern Amazonia, based on field data collected at four research sites since 1997, asking: under current Brazilian forest legislation, what are the prospects for second harvests on 30-year cutting cycles given observed population structures, growth, and mortality rates? Ecologically `rare` species constitute majorities in commercial species assemblages in all but one of the seven large-scale inventories we analyzed from sites spanning the Amazon (range 49-100% of total commercial species). Although densities of only six of 37 study species populations met the Brazilian legal definition of a rare species, timber stocks of five of the six timber species declined substantially at all sites between first and second harvests in simulations based on legally allowable harvest intensities. Reducing species-level harvest intensity by increasing minimum felling diameters or increasing seed tree retention levels improved prospects for second harvests of those populations with a relatively high proportion of submerchantable stems, but did not dramatically improve projections for populations with relatively flat diameter distributions. We argue that restrictions on logging very low-density timber tree populations, such as the current Brazilian standard, provide inadequate minimum protection for vulnerable species. Population declines, even if reduced-impact logging (RIL) is eventually adopted uniformly, can be anticipated for a large pool of high-value timber species unless harvest intensities are adapted to timber species population ecology, and silvicultural treatments are adopted to remedy poor natural stocking in logged stands. (C) 2008 Elsevier B.V. All rights reserved.

Forest certification in Amazonia: standards matter

Forest Stewardship Council (FSC) certification promises international consumers that `green-label` timber has been logged sustainably. However, recent research indicates that this is not true for ipe (Tabebuia spp.), currently flooding the US residential decking market, much of it logged in Brazil. Uneven or non-application of minimum technical standards for certification could undermine added value and eventually the certification process itself. We examine public summary reports by third-party certifiers describing the evaluation process for certified companies in the Brazilian Amazon to determine the extent to which standards are uniformly applied and the degree to which third-party certifier requirements for compliance are consistent among properties. Current best-practice harvest systems, combined with Brazilian legal norms for harvest levels, guarantee that no certified company or community complies with FSC criteria and indicators specifying species-level management. No guidelines indicate which criteria and indicators must be enforced, or to what degree, for certification to be conferred by third-party assessors; nor do objective guidelines exist for evaluating compliance for criteria and indicators for which adequate scientific information is not yet available to identify acceptable levels. Meanwhile, certified companies are expected to monitor the long-term impacts of logging on biodiversity in addition to conducting best-practice forest management. This burden should reside elsewhere. We recommend a clarification of `sustained timber yield` that reflects current state of knowledge and practice in Amazonia. Quantifiable verifiers for best-practice forest management must be developed and consistently employed. These will need to be flexible to reflect the diversity in forest structure and dynamics that prevails across this vast region. We offer suggestions for how to achieve these goals.

Modeling of transpiration reduction in van Genuchten-Mualem type soils

We derive an analytic expression for the matric flux potential (M) for van Genuchten-Mualem (VGM) type soils which can also be written in terms of a converging infinite series. Considering the first four terms of this series, the accuracy of the approximation was verified by comparing it to values of M estimated by numerical finite difference integration. Using values of the parameters for three soils from different texture classes, the proposed four-term approximation showed an almost perfect match with the numerical solution, except for effective saturations higher than 0.9. Including more terms reduced the discrepancy but also increased the complexity of the equation. The four-term equation can be used for most applications. Cases with special interest in nearly saturated soils should include more terms from the infinite series. A transpiration reduction function for use with the VGM equations is derived by combining the derived expression for M with a root water extraction model. The shape of the resulting reduction function and its dependency on the derivative of the soil hydraulic diffusivity D with respect to the soil water content theta is discussed. Positive and negative values of dD/d theta yield concave and convex or S-shaped reduction functions, respectively. On the basis of three data sets, the hydraulic properties of virtually all soils yield concave reduction curves. Such curves based solely on soil hydraulic properties do not account for the complex interactions between shoot growth, root growth, and water availability.

A Fibred Tableau Calculus for Modal Logics of Agents

In previous works we showed how to combine propositional multimodal logics using Gabbay's \emph{fibring} methodology. In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/fibred logics. To achieve this end we first make a comparison between two types of tableau proof systems, (\emph{graph} $\&$ \emph{path}), with the help of a scenario (The Friend's Puzzle). Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system \KEM. We conclude with a discussion on \KEM's features.