A main contribution of this paper is the explicit construction of comparison morphisms between the standard bar resolution and Bardzell's minimal resolution for truncated quiver algebras over arbitrary fields (TQA's). As a direct application we describe explicitly the Yoneda product and derive several results on the structure of the cohomology ring of TQA's over a field of characteristic zero. For instance, we show that the product of odd degree cohomology classes is always zero. We prove that TQA's associated with quivers with no cycles or with neither sinks nor sources have trivial cohomology rings. On the other side we exhibit a fundamental example of a TQA with nontrivial cohomology ring. Finally, for truncated polynomial algebras in one variable, we construct explicit cohomology classes in the bar resolution and give a full description of their cohomology ring.

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Este documento tiene el objetivo de describir el potencial de una interfaz visual básica en un Autocolimador del tipo Nikon 6B/6D, para reemplazar al operario en una medición de calidad metrológica. La interfaz visual implementada consta de una cámara con sensor CMOS adosada al ocular del autocolimador, partes posicionales, y un sistema de procesamiento digital de imágenes propio, escrito en lenguaje Matlab R , que analiza la imagen de la retícula para detectar la escala y la cruz de medición a nivel sub-píxel. Mediante un experimento controlado, realizado con un nivel electrónico trazable internacionalmente, se obtuvieron, con este sistema,ángulos de cabeceo (α y) con una resolución tres veces mejor que la del instrumento sin interfaz. Este ejemplo sugiere que el valor de 0.06 píxeles para la incertidumbre asociada con la posición sub-píxel de las diferentes líneas que conforman la retícula de medición es realista, y permite seguir trabajando en una interfaz robusta para todos los parámetros angulares posibles de ser medidos por el autocolimador.

The goal of this paper is to describe the potential of a visual interface applied to a Nikon 6B/6D autocollimator in order to replace human operator within a "laboratory grade" measurement. The optical interface implemented consists of a Basler HD camera attached to the autocollimator's eyepiece, camera positioning devices, and a proprietary digital image processing package, built around Matlab environment. The whole system is used to analyze the reticle image to detect both the scale and the measuring crosshair lines at sub-pixel level. The system performance was compared in a controlled experiment against an electronic level with internationally traceable certification. The resolution of the pitch angles obtained was 10 times better than that originally obtained with the instrument. This example shows that the value of 0.02 pixels for the uncertainty associated with sub-pixel position of reticle lines is realistic, allowing for continue working on a robust interface for all angle parameters that can be measured using autocollimators.