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This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their Cartesian parts, their numerical radii, the numerical radius of the product of two operators, and the Aluthge transform.

The weighted numerical radius of a Hilbert space operator has been defined recently. This article explores other properties and uses this newly defined numerical radius to obtain several new interesting inequalities for the weighted numerical radius and the numerical radius. In particular, new identities for the numerical radius, further comparisons between the numerical radius and the real and imaginary parts, and some inequalities for sectorial operators will be presented.

The main goal of this work is to present new matrix inequalities of the Cauchy-Schwarz type. In particular, we investigate the so-called Lieb functions, whose definition came as an umbrella of Cauchy-Schwarz-like inequalities, then we consider the mixed Cauchy-Schwarz inequality. This latter inequality has been influential in obtaining several other matrix inequalities, including numerical radius and norm results. Among many other results, we show that \[\left\| T \right\|\le \frac{1}{4}\left( \left\| \left| T \right|+\left| {{T}^{*}} \right|+2\mathfrak RT \right\|+\left\| \left| T \right|+\left| {{T}^{*}} \right|-2\mathfrak RT \right\| \right),\] where $\mathfrak RT$ is the real part of $T$., Comment: to appear in Oper. Matrices

Detall d'una implementació d'un sistema de computació al núvol a baixa escala i a nivell corporatiu. Detalle de la implementación de un sistema de computación en nube a baja escala y a nivel corporativo. Details for implementation of a small corporative cloud computing system.

Thisproject focuses on object detection and tracking in video sequences. In particular the goal is to detect fishes in coastal areas. State-of-art methods based on deep learning will be adapted to this problem. This research work in done in collaboration with IMEDEA (Advanced Mediterranean Studies) to support biologist in their research. This project is a computer vision work with underwater images with seabed images, with the purpose of locate fishes. The main purpose of this thesis is to develop an algorithm capable of get the largest amount of background possible in underwater imageswhile keeping all foreground elements, in our case, fish. This project is considered as part of a bigger module, that serves the purpose of helping research laboratories to catalog biodiversity. We have faced the problem using two different strategies. The first one is to produce a model of the background, to detect outsiders, using an anomaly detection algorithm. The other strategy is to detect the elements of the foreground,eliminating all the other regions, for this strategy we have used object detection and image segmentation algorithms. The tests have achieved promising results with the image segmentation algorithm. Este proyecto es un trabajo de visión por computador con imágenes del fondo marino con el objetivo de localizar peces. Para ello el principal objetivo de nuestro trabajo es desarrollar un algoritmo capaz de extraer la mayor cantidad posible de fondo de imágenes subacuáticas, manteniendo todos los elementos que no pertenezcan al fondo,en este caso, peces. Se considera que el trabajo realizado en este proyecto como un módulo de uno mayor, que sigue el objetivo de ayudar a laboratorios de investigación a catalogar mejor la biodiversidad. Hemos afrontado el problema usando dos estrategias distintas. La primera, producir un modelo del fondo, para así detectar aquellos elementos que no forman parte de el, usando un algoritmo de detección de anomalías. La otra estrategia consiste en detectar los peces, eliminando todos los otros elementos, para esta estrategia hemos usado algoritmos de detección de objetos y segmentación de imagen. Las pruebas realizadas han conseguido resultados prometedores con el algoritmo de segmentación de imagen. Aquest projecte és un treball de visió per computador amb imatges del fons marí, amb l?objectiu de localitzar peixos. Per aquest propòsit, el nostre principal objectiu és desenvolupar un algoritme capaç d?extreure la quantitat més gran possible de fons d?imatges subaquàtiques, conservant tots els elements del fons, en aquest cas, peixos. Es considera el treball realitzat en aquest projecte com un mòdul d?un més gran, que persegueix l?objectiu d?ajudar a laboratoris d?investigació a catalogar la biodiversitat. Hem afrontat el problema fent servir dues estratègies distintes. La primera, creant un model del fons, per així detectar aquells elements que no en formen part. L?altra estratègia, consisteix a detectar els peixos, eliminant tots els altres elements, per aquest plantejament hem fet servir algoritmes de localització d?objectes i de segmentació d?imatge. Les proves realitzades han aconseguit resultats prometedors amb els algoritmes de segmentació d?imatge.

The edge-connectivity of a graph is the minimum number of edges whose deletion disconnects the graph. Let $��(G)$ the maximum degree of a graph $G$ and let $��(G)$ be the spectral radius of $G$. In this article we present a lower bound for $��(G)-��(G)$ in terms of the edge connectivity of $G$, where $G$ is a nonregular distance-hereditary graph. We also prove that $��(G)$ reaches the maximum at a unique graph in $\mathcal G$, when $\vert V(G)\vert = n$, and $\mathcal G$ either is in the class of graphs with bounded tree-width or is in the class of block graphs with prescribed independence number.

In [P. Renaud, "A matrix formulation of Gr��ss inequality", Linear Algebra Appl. 335 (2001), 95--100] it was proved an operator inequality involving the usual trace functional. In this article, we give a refinement of such result and we answer positively the Renaud's open problem.

Detall d'una implementació d'un sistema de computació al núvol a baixa escala i a nivell corporatiu. Detalle de la implementación de un sistema de computación en nube a baja escala y a nivel corporativo. Details for implementation of a small corporative cloud computing system.

We prove some refinements of an inequality due to X. Zhan in an arbitrary complex Hilbert space by using some results on the Heinz inequality. We present several related inequalities as well as new variants of the Corach--Porta--Recht inequality. We also characterize the class of operators satisfying $\left\Vert SXS^{-1}+S^{-1}XS+kX\right\Vert \geq (k+2)\left\Vert X\right\Vert$ under certain conditions., Comment: 12 Pages, to appear in Linear Algebra Appl. (LAA)

The objective of this project is to study new techniques in the use of Binary Partition Tree to improve the classification of objects in PolSAR images. Different techniques will be developed and the results will be compared with the state of the art. Finally, some conclusions are presented and some possible lines of future work are discussed. Binary Partition Tree (BPT) es una herramienta que permite una representación multiescala de imágenes basada en la fusión de regiones de la imagen, en la que cada nodo del BPT, representa una región. Hoy en día, se está aplicando esta herramienta en los sistemas de teledetección conocidos como PolSAR, con el objetivo representar elementos de la imagen PolSAR con diferentes niveles de detalle. L'objectiu d'aquest projecte és estudiar noves tècniques en l'ús de Binary Partition Tree's per millorar la classificació d'objectes en imatges PolSAR. Es desenvolupen diferents tècniques i es comparen els resultats obtinguts amb l'estudi de l'art. Per acabar, s'exposen algunes conclusions i es presenten i comenten algunes possibles línies de treball futures.