Directional discrepancy in two dimensions

In the present paper, we study the geometric discrepancy with respect to families of rotated rectangles. The well-known extremal cases are the axis-parallel rectangles (logarithmic discrepancy) and rectangles rotated in all possible directions (polynomial discrepancy). We study several intermediate situations: lacunary sequences of directions, lacunary sets of finite order, and sets with small Minkowski dimension. In each of these cases, extensions of a lemma due to Davenport allow us to construct appropriate rotations of the integer lattice which yield small discrepancy.

Shape complexity based on mutual information

Shape complexity has recently received attention from different fields, such as computer vision and psychology. In this paper, integral geometry and information theory tools are applied to quantify the shape complexity from two different perspectives: from the inside of the object, we evaluate its degree of structure or correlation between its surfaces (inner complexity), and from the outside, we compute its degree of interaction with the circumscribing sphere (outer complexity). Our shape complexity measures are based on the following two facts: uniformly distributed global lines crossing an object define a continuous information channel and the continuous mutual information of this channel is independent of the object discretisation and invariant to translations, rotations, and changes of scale. The measures introduced in this paper can be potentially used as shape descriptors for object recognition, image retrieval, object localisation, tumour analysis, and protein docking, among others

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of Cl O2 and C4 H4 O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies

The effect of counterpoise correction and relaxation energy term to the internal rotation barriers: application to the BF3 ...NH3 and C2H4 ...SO2 dimers

The relevance of the fragment relaxation energy term and the effect of the basis set superposition error on the geometry of the BF3⋯NH3 and C2H4⋯SO2 van der Waals dimers have been analyzed. Second-order Møller-Plesset perturbation theory calculations with the d95(d,p) basis set have been used to calculate the counterpoise-corrected barrier height for the internal rotations. These barriers have been obtained by relocating the stationary points on the counterpoise-corrected potential energy surface of the processes involved. The fragment relaxation energy can have a large influence on both the intermolecular parameters and barrier height. The counterpoise correction has proved to be important for these systems

Costly search and design

Firms compete by choosing both a price and a design from a family of designs thatcan be represented as demand rotations. Consumers engage in costly sequential searchamong firms. Each time a consumer pays a search cost he observes a new offering. Anoffering consists of a price quote and a new good, where goods might vary in the extentto which they are good matches for the consumer. In equilibrium, only two design-styles arise: either the most niche where consumers are likely to either love or loathethe product, or the broadest where consumers are likely to have similar valuations. Inequilibrium, different firms may simultaneously offer both design-styles. We performcomparative statics on the equilibrium and show that a fall in search costs can lead tohigher industry prices and profits and lower consumer surplus. Our analysis is relatedto discussions of how the internet has led to the prevalence of niche goods and the"long tail" phenomenon.

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

Influence of the dipolar interactions in the magnetization reversal asymmetry of hard-soft magnetic ribbons

Partial crystallization of the metallic glass Co66Si16B12Fe4Mo2 was performed by annealing at temperatures between 500 and 540°C for 10-20 min, resulting in crystallite volume fractions of (0.7-5)×10¿3 and sizes of 50-100 nm. This two-phase alloy presents a remarkable feature: a hysteresis loop shift that can be tailored by simply premagnetizing the sample in the adequate magnetic field. Shifts as large as five times the coercive field have been obtained which make them interesting for application as magnetic cores in dc pulse transformers. The asymetrical magnetic reversal is explained in terms of the magnetic dipolar field interaction and the observed hysteresis loops have been satisfactorily simulated by a modification of Stoner-Wohlfarth¿s model of coherent rotations.

Loop bifurcation and magnetization rotation in exchange-biased Ni/FeF2

Exchange-biased Ni/FeF2 films have been investigated using vector coil vibrating-sample magnetometry as a function of the cooling field strength HFC . In films with epitaxial FeF2 , a loop bifurcation develops with increasing HFC as it divides into two sub-loops shifted oppositely from zero field by the same amount. The positively biased sub-loop grows in size with HFC until only a single positively shifted loop is found. Throughout this process, the negative and positive (sub)loop shifts maintain the same discrete value. This is in sharp contrast to films with twinned FeF2 where the exchange field gradually changes with increasing HFC . The transverse magnetization shows clear correlations with the longitudinal subloops. Interestingly, over 85% of the Ni reverses its magnetization by rotation, either in one step or through two successive rotations. These results are due to the single-crystal nature of the antiferromagnetic FeF2 , which breaks down into two opposite regions of large domains.

Inclusion of soil erosion impacts in life cycle assessment on a global scale: application to energy crops in Spain

Purpose: Despite the fundamental role of ecosystem goods and services in sustaining human activities, there is no harmonized and internationally agreed method for including them in life cycle assessment (LCA). The main goal of this study was to develop a globally applicable and spatially resolved method for assessing land-use impacts on the erosion regulation ecosystem service.Methods: Soil erosion depends much on location. Thus, unlike conventional LCA, the endpoint method was regionalized at the grid-cell level (5 arc-minutes, approximately 10×10 km2) to reflect the spatial conditions of the site. Spatially explicit characterization factors were not further aggregated at broader spatial scales. Results and discussion: Life cycle inventory data of topsoil and topsoil organic carbon (SOC) losses were interpreted at the endpoint level in terms of the ultimate damage to soil resources and ecosystem quality. Human health damages were excluded from the assessment. The method was tested on a case study of five three-year agricultural rotations, two of them with energy crops, grown in several locations in Spain. A large variation in soil and SOC losses was recorded in the inventory step, depending on climatic and edaphic conditions. The importance of using a spatially explicit model and characterization factors is shown in the case study.Conclusions and outlook: The regionalized assessment takes into account the differences in soil erosion-related environmental impacts caused by the great variability of soils. Taking this regionalized framework as the starting point, further research should focus on testing the applicability of the method trough the complete life cycle of a product and on determining an appropriate spatial scale at which to aggregate characterization factors, in order to deal with data gaps on location of processes, especially in the background system. Additional research should also focus on improving reliability of the method by quantifying and, insofar as it is possible, reducing uncertainty.

Assessing the environmental impact of water consumption by energy crops grown in Spain

The environmental impact of the water consumption of four typical crop rotations grown in Spain, including energy crops, was analyzed and compared against Spanish agricultural and natural reference situations. The life cycle assessment (LCA) methodology was used for the assessment of the potential environmental impact of blue water (withdrawal from water bodies) and green water (uptake of soil moisture) consumption. The latter has so far been disregarded in LCA. To account for green water, two approaches have been applied: the first accounts for the difference in green water demand of the crops and a reference situation. The second is a green water scarcity index, which measures the fraction of the soil-water plant consumption to the available green water. Our results show that, if the aim is to minimize the environmental impacts of water consumption, the energy crop rotations assessed in this study were most suitable in basins in the northeast of Spain. In contrast, the energy crops grown in basins in the southeast of Spain were associated with the greatest environmental impacts. Further research into the integration of quantitative green water assessment in LCA is crucial in studies of systems with a high dependence on green water resources.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Comparison between land suitability and actual crop distribution in an irrigation district of the Ebro valley (Spain)

El objetivo de la presente investigación fue analizar la correspondencia entre los resultados de una evaluación de tierras con la distribución real de los cultivos. Para ello la aptitud biofísica de las tierras se comparó con diferentes tipologías de frecuencia de ocurrencia de los cultivos y rotaciones derivadas de mapas de cultivos multitemporales. La investigación fue llevada a cabo en el distrito de riego de Flumen (33.000 ha), localizado en el valle del Ebro (NE España). La evaluación de tierras se basó en una cartografía de suelos 1:100.000, según el esquema FAO, para los principales cultivos presentes en el área de estudio (alfalfa, cereales de invierno, maíz, arroz y girasol). Se utilizaron tres mapas de frecuencia de cultivos y un mapa de rotaciones, derivado de una serie temporal de imágenes Landsat TM y ETM+ del periodo 1993-2000, y se compararon con los mapas de aptitud de tierras para los diferentes cultivos. Se analizó estadísticamente (Pearson χ2, Cramer V, Gamma y Somers D) la relación entre los dos tipos de variables. Los resultados muestran la existencia de una relación significativa (P=0,001) entre la localización de los cultivos y la idoneidad de las tierras, excepto de cultivos oportunistas como el girasol, muy influenciado por las subvenciones en el periodo estudiado. Las rotaciones basadas en la alfalfa muestran los mayores porcentajes (52%) de ocupación en las tierras más aptas para la agricultura en el área de estudio. El presente enfoque multitemporal de análisis de la información ofrece una visión más real que la comparación entre un mapa de evaluación de tierras y un mapa de cultivos de una fecha determinada, cuando se valora el grado de acuerdo entre las recomendaciones sobre la aptitud de las tierras y los cultivos realmente cultivados por los agricultores.

Nitrogen replacement value of alfalfa to corn and wheat under irrigated Mediterranean conditions

In crop rotations that include alfalfa (Medicago sativa L.), agronomic and environmental concerns mean that it is important to determine the N fertilizer contribution of this legume for subsequent crops in order to help to increase the sustainability of cropping systems. To determine the N fertilizer replacement value (FRV) of a 2-yr alfalfa crop on subsequent crops of corn (Zea mays L.) followed by wheat (Triticum aestivum L.) under irrigated Mediterranean conditions, two 4-yr rotations (alfalfa-corn-wheat and corn-corn-corn-wheat) were conducted from 2001 to 2004 in a Typic Xerofluvent soil. Corn yields were compared after two years of alfalfa and a third year of corn under monoculture and wheat yields were also compared after both rotations. Corn production after alfalfa outyielded monoculture corn at all four rates of N fertilizer application analyzed (0, 100, 200 and 300 kg N/ha). The FRV of 2-yr alfalfa for corn was about 160 kg N/ha. Wheat grown after the alfalfa-corn rotation outyielded that grown after corn under monoculture at both the rates of N studied (0 and 100 kg N/ha). The FRV of alfalfa for wheat following alfalfa-corn was about 76 kg N/ha. Soil NO3 -N content after alfalfa was greater than with the corn monoculture at all rates of N fertilizer application and this higher value persisted during the second crop after alfalfa. This was probably one of the reasons for the better yields associated with the alfalfa rotation. These results make a valuable contribution to irrigated agriculture under mediterranean conditions, show reasons for interest in rotating alfalfa with corn, and explain how it is possible to make savings when applying N fertilizer.

Minimum-uncertaity states and pseudoclassical dynamics. II

The set of initial conditions for which the pseudoclassical evolution algorithm (and minimality conservation) is verified for Hamiltonians of degrees N (N>2) is explicitly determined through a class of restrictions for the corresponding classical trajectories, and it is proved to be at most denumerable. Thus these algorithms are verified if and only if the system is quadratic except for a set of measure zero. The possibility of time-dependent a-equivalence classes is studied and its physical interpretation is presented. The implied equivalence of the pseudoclassical and Ehrenfest algorithms and their relationship with minimality conservation is discussed in detail. Also, the explicit derivation of the general unitary operator which linearly transforms minimum-uncertainty states leads to the derivation, among others, of operators with a general geometrical interpretation in phase space, such as rotations (parity, Fourier).