Auslander-Buchweitz approximation theory for triangulated categories

We introduce and develop an analogous of the Auslander-Buchweitz approximation theory (see \cite{AB}) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results concerning relative homological algebra in a triangulated category \T, which are based on the behavior of certain subcategories under finiteness of resolutions and vanishing of Hom-spaces. For example: we establish the existence of preenvelopes (and precovers) in certain triangulated subcategories of \T. The results resemble various constructions and results of Auslander and Buchweitz, and are concentrated in exploring the structure of a triangulated category \T equipped with a pair (\X,\omega), where \X is closed under extensions and $\omega$ is a weak-cogenerator in \X, usually under additional conditions. This reduces, among other things, to the existence of distinguished triangles enjoying special properties, and the behavior of (suitably defined) (co)resolutions, projective or injective dimension of objects of \T and the formation of orthogonal subcategories. Finally, some relationships with the Rouquier's dimension in triangulated categories is discussed.Comment: To appear at: Appl. Categor. Struct. (2011); 22 page

Estrategias operativas en la resolución de problemas matemáticos en el ciclo medio de la E.G.B.

Este trabajo es el resultado de una investigación sobre cómo los niños realmente resuelven problemas matemáticos. Se han identificado doce estrategias en problemas de naturaleza muy diferente

Estudio y evaluación de organismos plagas y sus enemigos naturales del cultivo de amarantos en Argentina

Con el nombre de Amaranto se designa a numerosas especies del género Amaranthus, Familia Amarantaceae. Las especies cultivadas son herbáceas anuales de uso tanto hortícola como granífera. En la provincia de La Pampa al igual que en el resto del país, son escasos los antecedentes sobre organismos asociados al cultivo de amaranto, por tal motivo los objetivos de este trabajo fueron estudiar la entomofauna asociada a dicho cultivo. El trabajo se llevó a cabo durante la campaña 2006 - 07, en un lote del campo experimental de la Facultad de Agronomía de la UNLPam., ubicada sobre la Ruta Nacional W 35 en el Km. 334,10 km al norte de Santa Rosa (La Pampa). El ensayo siguió un diseño de bloques (N=4) con 18 tratamientos (variedades) por bloque. En cada tratamiento se seleccionaron 6 plantas al azar y se revisó mediante observación directa la planta completa. Los muestreos se realizaron semanalmente durante todo el ciclo del cultivo. La entomofauna fue variando en densidad en los diferentes estadios fenológicos del cultivo. Los ejemplares identificados se agruparon en diez órdenes que comprenden 21 familias y 23 géneros Los órdenes con el mayor número de familias fueron Coleóptera (6) y Hemiptera (4). Dentro del Orden Coleóptera las familias más representadas fueron Curculionidae y Coccinelidae; en Hemiptera la familia Pentatomidae. En estado de plántula la especie fitófaga con mayor densidad poblacional fue Acromyrmex striatus (Roger) (Hymenoptera: Formicidae). Durante los estados vegetativos las más abundantes fueron Epicauta adspersa (Klujj (Coleóptera: Meloidae), Nezara viridula (L) y Edessa meditabunda (F.) (Hemiptera: Pentatomidae), mientras que en los estados reproductivos predominó la población de arañuela roja Tetranychus urticae (Kochj (Acari: Tetranychidae).Nota: resultados parciales obtenidos en esta tesis fueron publicados como: Estudio de la entomofauna asociada al cultivo de Amaranthus en la provincia de La Pampa, Argentina. Niveyro, S., C.A. Saenz, L.O. Falkenstein y E.M. Baudino. 30° Congreso Argentino de Horticultura. 1° Simposio Internacional sobre Cultivos Protegidos. 25 al 28 de septiembre de 2007. La Plata. Buenos Aires. Argentina. Pag 378

Statistical Scattering of Waves in Disordered Waveguides: from Microscopic Potentials to Limiting Macroscopic Statistics

We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length (delta)L are derived from a potential model and used to find the evolution with length of the expectation value of physical quantities. In the potential model the scattering units consist of thin potential slices, idealized as delta slices, perpendicular to the longitudinal direction of the waveguide; the variation of the potential in the transverse direction may be arbitrary. The sets of parameters defining a given slice are taken to be statistically independent from those of any other slice and identically distributed. In the dense-weak-scattering limit, in which the potential slices are very weak and their linear density is very large, so that the resulting mean free paths are fixed, the corresponding statistical properties of the full waveguide depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem. Our final result is a diffusion equation in the space of transfer matrices of our system, which describes the evolution with the length L of the disordered waveguide of the transport properties of interest. In contrast to earlier publications, in the present analysis the energy of the incident particle is fully taken into account.Comment: 75 pages, 10 figures, submitted to Phys. Rev

Smart operator for the human liver automatic segmentation, present in medical images

The segmentation of the human body organ called liver is a highly challenging problem due to the noise, artifacts and the low contrast exhibited by the anatomical structures located around the liver and that are present in digital images, generated by any modality of medical images. The main modalities are: ultrasound, nuclear emission, magnetic resonance and the gold standard called multi-slice computed tomography. In this paper, with the objective of to address this problem, we consider multi-slice computed tomography images and we propose an automatic strategy based on two phases. In the first phase, a digital filtering bank is used for diminishing the noise effect and the artifacts impact in the quality of images. In the second phase, called liver detection, we use a smart operator based on least squares support vector machines for generating both the morphology and the volume of liver. The application of this strategy allows generating the morphology of the liver in a precise and efficient manner as it was demonstrated by the metrics used to assess its performance. These results are very important in clinical-surgical processes where both the shape and volume of liver are vital for monitoring some liver diseases that can affect the normal liver physiology