The Minimum Number of Points Taking Part in k-Sets in Sets of Unaligned Points

En este trabajo se da un ejemplo de un conjunto de n puntos situados en posición general, en el que se alcanza el mínimo número de puntos que pueden formar parte de algún k-set para todo k con 1menor que=kmenor quen/2. Se generaliza también, a puntos en posición no general, el resultado de Erdõs et al., 1973, sobre el mínimo número de puntos que pueden formar parte de algún k-set. The study of k- sets is a very relevant topic in the research area of computational geometry. The study of the maximum and minimum number of k-sets in sets of points of the plane in general position, specifically, has been developed at great length in the literature. With respect to the maximum number of k-sets, lower bounds for this maximum have been provided by Erdõs et al., Edelsbrunner and Welzl, and later by Toth. Dey also stated an upper bound for this maximum number of k-sets. With respect to the minimum number of k-set, this has been stated by Erdos el al. and, independently, by Lovasz et al. In this paper the authors give an example of a set of n points in the plane in general position (no three collinear), in which the minimum number of points that can take part in, at least, a k-set is attained for every k with 1 ≤ k < n/2. The authors also extend Erdos’s result about the minimum number of points in general position which can take part in a k-set to a set of n points not necessarily in general position. That is why this work complements the classic works we have mentioned before.

Use of calculus of variations to determine the shape of hovering rotors of minimum power and its application to micro air vehicles

In this paper, calculus of variations and combined blade element and momentum theory (BEMT) are used to demonstrate that, in hover, when neither root nor tip losses are considered; the rotor, which minimizes the total power (MPR), generates an induced velocity that varies linearly along the blade span. The angle of attack of every blade element is constant and equal to its optimum value. The traditional ideal twist (ITR) and optimum (OR) rotors are revisited in the context of this variational framework. Two more optimum rotors are obtained considering root and tip losses, the ORL, and the MPRL. A comparison between these five rotors is presented and discussed. The MPR and MPRL present a remarkable saving of power for low values of both thrust coefficient and maximum aerodynamic efficiency. The result obtained can be exploited to improve the aerodynamic behaviour of rotary wing micro air vehicles (MAV). A comparison with experimental results obtained from the literature is presented.

Solving the minimum vertex floodlight problem with hybrid metaheuristics

In this paper we propose four approximation algorithms (metaheuristic based), for the Minimum Vertex Floodlight Set problem. Urrutia et al. [9] solved the combinatorial problem, although it is strongly believed that the algorithmic problem is NP-hard. We conclude that, on average, the minimum number of vertex floodlights needed to illuminate a orthogonal polygon with n vertices is n/4,29.

Approaching minimum area polygonization

The problem of finding a minimum area polygonization for a given set of points in the plane, Minimum Area Polygonization (MAP) is NP-hard. Due to the complexity of the problem we aim at the development of algorithms to obtain approximate solutions. In this work, we suggest di?erent strategies in order to minimize the polygonization area.We propose algorithms to search for approximate solutions for MAP problem. We present an experimental study for a set of instances for MAP problem.

Approximations on minimum weight pseudo-triangulation problem using ant colony optimization

In this work, we consider the Minimum Weight Pseudo-Triangulation (MWPT) problem of a given set of n points in the plane. Globally optimal pseudo-triangulations with respect to the weight, as optimization criteria, are difficult to be found by deterministic methods, since no polynomial algorithm is known. We show how the Ant Colony Optimization (ACO) metaheuristic can be used to find high quality pseudo-triangulations of minimum weight. We present the experimental and statistical study based on our own set of instances since no reference to benchmarks for these problems were found in the literature. Throughout the experimental evaluation, we appraise the ACO metaheuristic performance for MWPT problem.

Simulating improved combinations tillage-rotation under dryland conditions.

The adequate combination of reduced tillage and crop rotation could increase the viability of dry land agriculture in Mediterrenean zones. Crop simulation models can support to examine various tillage-rotation combinations and explore management scenarios. The decision support system for agrotechnology transfer (DSSAT) (Hoogenboom et al., 2010) provides a suite of crop models suitable for this task. The objective of this work was to simulate the effects of two tillage systems, conventional tillage (ConvT) and no tillage (NoT), and three crop rotations, continuous cereal (CC), fallow-cereal (FallowC) and legume-cereal (LegumeC), under dry conditions, on the cereal yield, soil organic carbon (SOC) and nitrogen (SON) in a 15-year experiment, comparing these simulations with field observations.

Influence of tillage on soil surface roughness structure andsurface porosity.

Soil erosion is a complex phenomenon involving the detachment and transport of soil particles, storage and runoff of rainwater, and infiltration. The relative magnitude and importance of these processes depends on several factors being one of them surface microtopography, usually quantified trough soil surface roughness (SSR). Surface soil porosity and SSR can be altered by tillage operation. Even though the surface porosity is an important parameter of a tilled field, however, no practical technique for rapid and non-contact measurement of surface porosity has been developed yet.

Effect of reservoir tillage on rainwater harvesting and soil erosion control under a developed rainfall simulator.

Soil erosion is a serious environmental threat in the Mediterranean region due to torrential rainfalls, and it contributes to the degradation of agricultural land. Techniques such as rainwater harvesting may improve soil water storage and increase agricultural productivity, which could result in more effective land usage. Reservoir tillage is an effective system of harvesting rainwater, but it has not been scientifically evaluated like other tillage systems. Its suitability for the conditions in Spain has not been determined. To investigate and quantify water storage from reservoir tillage and how it could be adapted to improve infiltration of harvested rainwater, a laboratory-scale rainfall simulator was developed. Rainfall characteristics, including rainfall intensity, spatial uniformity and raindrop size, confirm that natural rainfall conditions are simulated with sufficient accuracy. The simulator was auto-controlled by a solenoid valve and three pressure nozzles were used to spray water corresponding to five rainfall intensities ranging from 36 to 112 mm h-1 for 3 to 101-year return period with uniformity coefficients between 83 and 94%. In order to assess the reservoir tillage method under surface slopes of 0, 5, and 10%, three soil scooping devices with identical volume were used to make depressions in the following forms: a) truncated square pyramid, b) triangular prism, and c) truncated cone. These depressions were compared to a control soil surface with no depression. For the loam soil used in this study, results show that reservoir tillage was able to reduce soil erosion and surface runoff and significantly increase infiltration. There was significant difference between the depressions and the control. Compared to the control, depression (a) reduced surface runoff by about 61% and the sediment yield concentration by about 79%.

Minimum time control for multiphase buck converter: analysis and application

The combination of minimum time control and multiphase converter is a favorable option for dc-dc converters in applications where output voltage variation is required, such as RF amplifiers and dynamic voltage scaling in microprocessors, due to their advantage of fast dynamic response. In this paper, an improved minimum time control approach for multiphase buck converter that is based on charge balance technique, aiming at fast output voltage transition is presented. Compared with the traditional method, the proposed control takes into account the phase delay and current ripple in each phase. Therefore, by investigating the behavior of multiphase converter during voltage transition, it resolves the problem of current unbalance after the transient, which can lead to long settling time of the output voltage. The restriction of this control is that the output voltage that the converter can provide is related to the number of the phases, because only the duty cycles at which the multiphase converter has total ripple cancellation are used in this approach. The model of the proposed control is introduced, and the design constraints of the buck converters filter for this control are discussed. In order to prove the concept, a four-phase buck converter is implemented and the experimental results that validate the proposed control method are presented. The application of this control to RF envelope tracking is also presented in this paper.

N2O emissions and N efficiency due to tillage systems and crop rotation under a rainfed Mediterranean agroecosystem

Application of nitrogen (N) fertilizers in agricultural soils increases the risk of N loss to the atmosphere in the form of ammonia (NH3), nitrous oxide (N2O) and nitric oxide (NO)and the water bodies as nitrate (NO3-). The implementation of agricultural management practices can affect these losses. In Mediterranean irrigation systems, the greatest losses of NO3-through leaching occur within the irrigation and the intercropperiod. One way to abate these losses during the intercrop period is the use of cover crops that absorb part of the residual N from the root zone (Gabriel and Quemada, 2011). Moreover, during the following crop, these species could be applied as amendments to the soil, providing both C and N to the soil. This effect of cover and catch crops on decreasing the pool of N potentially lost has focused primarily on NO3-leaching. The aim of this work was to evaluate the effect of cover crops on N2O emission during the in tercrop period in a maize system and its subsequent incorporation into the soil in the following maize crop.

Spatial variability of seed depth placement of maize under no tillage.

Among the various factors that contribute towards producing a successful maize crop, seed depth placement is a key determinant, especially in a no-tillage system. The main objective of this work was to evaluate the spatial variability of seed depth placement and crop establishment in a maize crop under no-tillage conditions, using precision farming technologies. The obtained results indicate that seed depth placement was significantly affected by soil moisture content, while a very high coefficient of variation of 39% was found for seed depth. Seeding depth had a significant impact on mean emergence time and percentage of emerged plants. Shallow average depth values and the high coefficient of variation suggest a need for improvement in controlling the seeder sowing depth.

Simulating improved combinations tillage-rotation under dryland conditions.

Crop simulation models allow analyzing various tillage-rotation combinations and exploring management scenarios. This study was conducted to test the DSSAT (Decision Support System for Agrotechnology Transfer) modelling system in rainfed semiarid central Spain. The focus is on the combined effect of tillage system and winter cereal-based rotations (cereal/legume/fallow) on the crop yield and soil quality. The observed data come from a 16-year field experiment. The CERES and CROPGRO models, included in DSSAT v4.5, were used to simulate crop growth and yield, and DSSAT- CENTURY was used in the soil organic carbon (SOC) and soil nitrogen (SN) simulations. Genetic coefficients were calibrated using part of the observed data. Field observations showed that barley grain yield was lower for continuous cereal (BB) than for vetch (VB) and fallow (FB) rotations for both tillage systems. The CERES-Barley model also reflected this trend. The model predicted higher yield in the conventional tillage (CT) than in the no tillage (NT) probably due to the higher nitrogen availability in the CT, shown in the simulations. The SOC and SN in the top layer only, were higher in NT than in CT, and decreased with depth in both simulated and observed values. These results suggest that CT-VB and CT-FB were the best combinations for the dry land conditions studied. However, CT presented lower SN and SOC content than NT. This study shows how models can be a useful tool for assessing and predicting crop growth and yield, under different management systems and under specific edapho-climatic conditions. Additional key words: CENTURY model; CERES-Barley; crop simulation models; DSSAT; sequential simula- tion; soil organic carbon.

Planar point sets with large minimum convex decompositions

We show the existence of sets with n points (n ? 4) for which every convex decomposition contains more than (35/32)n?(3/2) polygons,which refutes the conjecture that for every set of n points there is a convex decomposition with at most n+C polygons. For sets having exactly three extreme pointswe show that more than n+sqr(2(n ? 3))?4 polygons may be necessary to form a convex decomposition.

Influence of Tillage and Liming on N2O emission from a rainfed crop

Nitrous oxide (N2O) is the main greenhouse gas (GHG) produced by agricultural soils due to microbial processes. The application of N fertilizers is associated with an increase of N2O losses. However, it is possible to mitigate these emissions by the introduction of adequate management practices (Snyder et al., 2009). Soil conservation practices (i.e.no tillage, NT) have recently become widespread because they promote several positive effects (increases in soil organic carbonand soil fertility, reduction of soil erosion, etc). In terms of GHG emissions, there is no consensus in the literature on the effects of tillage on N2O. Several studies found that NT can produce greater (Baggs et al., 2003), lower (Malhi et al., 2006) or similar (Grandey et al., 2006) N2O emissions compared to traditional tillage (TT). This large uncertainty is associated with the duration of tillage practices and climatic variability. Liming is widely use to solve problems of soil acidity (Al toxicity, yield penalties, etc). Several studies show a decrease in N2O emissions with liming (Barton et al., 2013) whereas no significant effects or increases were observed in others (Galbally et al., 2010). The aim of this work was to evaluate the effects of tillage (NT vs TT) and liming application or not of Ca-amendment) on N2O emissions from an acid soil during a rainfed crop.

Volume, Surface, Connectivity and Size Distribution of Soil Pore Space in CT Images: Comparison of Samples at Different Depths from Nearby Natural and Tillage Areas

The study of soil structure, i.e., the pores, is of vital importance in different fields of science and technology. Total pore volume (porosity), pore surface, pore connectivity and pore size distribution are some (probably the most important) of the geometric measurements of pore space. The technology of X-ray computed tomography allows us to obtain 3D images of the inside of a soil sample enabling study of the pores without disturbing the samples. In this work we performed a set of geometrical measures, some of them from mathematical morphology, to assess and quantify any possible difference that tillage may have caused on the soil. We compared samples from tilled soil with samples from a soil with natural vegetation taken in a very close area. Our results show that the main differences between these two groups of samples are total surface area and pore connectivity per unit pore volume.