Robustness and perturbations of minimal bases II: The case with given row degrees

This paper studies generic and perturbation properties inside the linear space of $m\times (m+n)$ polynomial matrices whose rows have degrees bounded by a given list $d_1, \ldots, d_m$ of natural numbers, which in the particular case $d_1 = \cdots = d_m = d$ is just the set of $m\times (m+n)$ polynomial matrices with degree at most $d$. Thus, the results in this paper extend to a much more general setting the results recently obtained in [Van Dooren & Dopico, Linear Algebra Appl. (2017), http://dx.doi.org/10.1016/j.laa.2017.05.011] only for polynomial matrices with degree at most $d$. Surprisingly, most of the properties proved in [Van Dooren & Dopico, Linear Algebra Appl. (2017)], as well as their proofs, remain to a large extent unchanged in this general setting of row degrees bounded by a list that can be arbitrarily inhomogeneous provided the well-known Sylvester matrices of polynomial matrices are replaced by the new trimmed Sylvester matrices introduced in this paper. The following results are presented, among many others, in this work: (1) generically the polynomial matrices in the considered set are minimal bases with their row degrees exactly equal to $d_1, \ldots , d_m$, and with right minimal indices differing at most by one and having a sum equal to $\sum_{i=1}^{m} d_i$, and (2), under perturbations, these generic minimal bases are robust and their dual minimal bases can be chosen to vary smoothly.Comment: arXiv admin note: text overlap with arXiv:1612.0379

Adaptive neurofuzzy ANFIS modeling of laser surface treatments

This paper introduces a new ANFIS adaptive neurofuzzy inference model for laser surface heat treatments based on the Green’s function. Due to its high versatility, efficiency and low simulation time, this model is suitable not only for the analysis and design of control systems, but also for the development of an expert real time supervision system that would allow detecting and preventing any failure during the treatment

Ek tou Homerou ad Homerum: A Survey of the Roman Imperial Iconography of Homer

This thesis evaluates the imagery of Homer in Roman imperial mosaics stemming from the 2nd century AD to the 5th century AD. In doing so, it will show that the Romans perhaps transformed the image of Homer in order that the patron may identify himself as an erudite and intellectual elite. This practice might have strong parallels with literary treatments with Homer during the Second Sophistic, especially among the Platonic philosophical tradition in the imperial period. As a tool for those wishing to do a systematic analysis of figures in Roman art, mosaics contain some advantages that other forms of art do not. The first of which is their high degree of uniformity despite regional differences across the Empire. For example, the Iberian peninsula, the North African provinces, and Greece contain examples of black-and-white mosaics of an Italic style dating to the first two centuries AD such as a black-and-white mosaic found in the baths of Isthmia near Corinth. Furthermore, these three regions begin to employ classicizing polychromatic mosaics beginning by the second century and well into the 4th and 5th centuries. A notable example is a gladiatorial scene depicted on a mosaic found in the House of Silenus Mosaic in Kos, Greece. A second advantage is that mosaics generally share motifs throughout the Empire. Some examples include hunt, bucolic, circus, and some mythological scenes with the most popular being Dionysiac (e.g. mosaic of Dionysus and Ariadne in Thessalonica). A third advantage is that mosaics are more numerous than other art forms, display regional variations within common repertoires, and generally are found in situ in comparison to other art forms. My thesis will present three case studies which include an examination of the portrayals of the Muses, Homer, and finally Orpheus during both the Hellenistic and Roman imperial periods. During the Hellenistic period, Homer and the Muses are typically portrayed either as divine figures or with divine figures. However, then during the Roman Empire, the images of Homer and Muses undergo some transformations in which both figures are shown alongside intellectual figures such as politicians or philosophers. The third chapter on Orpheus will demonstrate a counter example in which the Late Hellenistic portrayals of Orpheus as a charmer of animals are simply absorbed without changed by the Romans. This shows that Hellenistic and Greek archetypal patterns did not always need iconographic changes and could be consonant with Roman values. As a result, there is the possibility that the changes in the depictions of Homer and the Muses during the Roman Empire might possibly have occurred in order to be more in line with the social and cultural attitudes of the Romans. Roman preoccupation with self-image perhaps drives the change in depiction of Homer from a divine figure of the gods into a philosophical teacher. Just as imperial iconography of hunting is used to display virtus during the Hadrianic period, likewise, for the learned Roman, Homer becomes a symbol of virtus for the intellect. The implications of this would ask a small re-evaluation on the “Hellenization” of Roman society during the Second Sophistic with special attention to Roman art. It would suggest that cultural reception is never a one way street. Although the Second Sophistic was a revival of Greek culture throughout the Roman Empire, we may begin to ask what was form and shape of the Greek cultural revival in regards to art. We may also ask to what extent was Homer “Romanized” and to what extent the Middle Platonists and Neoplatonist engage with the larger cultural attitudes of Homer