Proper motions of the HH1 jet

We describe a new method for determining proper motions of extended objects, and a pipeline developed for the application of this method. We then apply this method to an analysis of four epochs of [S~II] HST images of the HH~1 jet (covering a period of $\sim 20$~yr). We determine the proper motions of the knots along the jet, and make a reconstruction of the past ejection velocity time-variability (assuming ballistic knot motions). This reconstruction shows an "acceleration" of the ejection velocities of the jet knots, with higher velocities at more recent times. This acceleration will result in an eventual merging of the knots in $\sim 450$~yr and at a distance of $\sim 80"$ from the outflow source, close to the present-day position of HH~1.Comment: 12 pages, 8 figure

The Simultaneous Local Metric Dimension of Graph Families

In a graph G = ( V , E ) , a vertex v ∈ V is said to distinguish two vertices x and y if d G ( v , x ) ≠ d G ( v , y ) . A set S ⊆ V is said to be a local metric generator for G if any pair of adjacent vertices of G is distinguished by some element of S. A minimum local metric generator is called a local metric basis and its cardinality the local metric dimension of G. A set S ⊆ V is said to be a simultaneous local metric generator for a graph family G = { G 1 , G 2 , … , G k } , defined on a common vertex set, if it is a local metric generator for every graph of the family. A minimum simultaneous local metric generator is called a simultaneous local metric basis and its cardinality the simultaneous local metric dimension of G . We study the properties of simultaneous local metric generators and bases, obtain closed formulae or tight bounds for the simultaneous local metric dimension of several graph families and analyze the complexity of computing this parameter

Condition monitoring strategy based on spectral energy estimation and linear discriminant analysis applied to electric machines

Condition-based maintenance plays an important role to ensure the working condition and to increase the availability of the machinery. The feature calculation and feature extraction are critical signal processing that allow to obtain a high-performance characterization of the available physical magnitudes related to specific working conditions of machines. Aiming to overcome this issue, this research proposes a novel condition monitoring strategy based on the spectral energy estimation and Linear Discriminant Analysis for diagnose and identify different operating conditions in an induction motor-based electromechanical system. The proposed method involves the acquisition of vibration signals from which the frequency spectrum is computed through the Fast Fourier Transform. Subsequently, such frequency spectrum is segmented to estimate a feature matrix in terms of its spectral energy. Finally, the feature matrix is subjected to a transformation into a 2-dimentional base by means of the Linear Discriminant Analysis and the final diagnosis outcome is performed by a NN-based classifier. The proposed strategy is validated under a complete experimentally dataset acquired from a laboratory electromechanical system.Peer ReviewedPostprint (published version