1942-1943 Xavier University College of Liberal Arts Course Catalog

https://www.exhibit.xavier.edu/coursecatalog/1245/thumbnail.jp

Randomized approximation algorithms : facility location, phylogenetic networks, Nash equilibria

Despite a great effort, researchers are unable to find efficient algorithms for a number of natural computational problems. Typically, it is possible to emphasize the hardness of such problems by proving that they are at least as hard as a number of other problems. In the language of computational complexity it means proving that the problem is complete for a certain class of problems. For optimization problems, we may consider to relax the requirement of the outcome to be optimal and accept an approximate (i.e., close to optimal) solution. For many of the problems that are hard to solve optimally, it is actually possible to efficiently find close to optimal solutions. In this thesis, we study algorithms for computing such approximate solutions

The Blackholic energy and the canonical Gamma-Ray Burst

We outline the main results of our GRB model, based on the three interpretation paradigms we proposed in July 2001, comparing and contrasting them with the ones in the current literature. Thanks to the observations by Swift and by VLT, this analysis points to a "canonical GRB" originating from markedly different astrophysical scenarios. The communality is that they are all emitted in the formation of a black hole with small or null angular momentum. The following sequence appears to be canonical: the vacuum polarization process creating an optically thick self accelerating electron-positron plasma; the engulfment of baryonic mass during the plasma expansion; the adiabatic expansion of the optically thick "fireshell" up to the transparency; the interaction of the remaining accelerated baryons with the interstellar medium (ISM). This leads to the canonical GRB composed of a proper GRB (P-GRB), emitted at the moment of transparency, followed by an extended afterglow. The parameters are the plasma total energy, the fireshell baryon loading and the ISM filamentary distribution around the source. In the limit of no baryon loading the total energy is radiated in the P-GRB. In this limit, the canonical GRBs explain as well the short GRBs.Comment: 163 pages, 89 figures, to appear on the "Proceedings of the XIIth Brazilian School of Cosmology and Gravitation", M. Novello, S.E. Perez-Bergliaffa (editors), AIP, in pres

Attempted reconstruction of design procedures and concepts during the reign of Sultan Qaytbay (872/1468-901/1496) in Jerusalem and Cairo: with special reference to the Madrasa Al-Ashrafiyya and the Minbar in the Khanaqah of Farag Ibn Barquq

Scholars in all areas of Islamic study are fascinated by and are often at pains to underline the unity inherent in Islam. This can be manifested in a multitude of ways, it can be demonstrated against the theological background established by the ,ur'an, or, it may be seen as transcending the barriers enclosing the various arts and sciences of Islam.If it is seen in terms of art and architecture, it can be explained on the grand scale by trading connections built up in times of peace and stability or by forced population movements in the face of conflict, both forces that can transfer from one geographical location to another the artistic traditions, expertise, and techniques previously reserved to the former location but which through their transference are unified with other Islamic traditions.I can see that the nature of unity can be visually expressed by, and is found within, the three broad categories noted by Grabar; but there are others in the field of Islamic art who maintain that a meaning can be attached to a specific design and that this meaning can be verbalised_. I find that I cannot accept that a verbalised meaning can be conveyed by each and every decorative composition, but I find I cannot deny the likeliehood of a visualised one. In fact my hypothesis is that in the notable examples of high cuality iriamluk architecture a visualised meaning does exist. But, just as the expression cf the nuances and form of a piece of music have a greater clarity when in an expos use is main of a musical instrument to illustrate them, rather than an excessive reliance on words to provide the meaning, I believe that architectural experiences are often best expressed in visual terms. For example, later in this Dissertation the stone mi.nbar presented by Sultan tb.y to the Khanaq h of Farag b. Barqúq is analysed in great detail, to my eyes it offers a statement not only on its own symmetry, which is normal for a minbar, but much more it concerns itself with a statement about the symmetry of the Iihtinagah; orally to present my findings and the reasons behind them takes tens of pages compared to a graphical presentation of only five figures.In one sense I admit to this being a final statement, but in another sense it should be the beginning of Islamic architectural appreciation and investigation leading into areas where it may be possible theoretically to reconstitute Islamic works of art from criteria deduced from other known and existing works of art. Those of us who are fortunate enough to work on the evidence at first hand as a job, or, those who have time from other interests for such diversions, must strive to understand and show precisely what was in the minds of the craftsmen and how they detailed their architectural contributions to make a statement. An efficacious route is to choose a high period in the architectural arts sustained either by one bowerful patron or by one atelier over a reasonable ueriod of years. Having thoroughly investigated the period it would then be advantageous to use this fund of knowledge by applying it to the periods immediately before and after the chosen one. However, in my case the first stage has still years of basic cataloguing to do and so I have not embarked on the second stage, nor have I had the opportunity to trace the antecedents of the many decorative elements current at the time of Sultan jytbay.The methods I have used to reach my conclusions are, for the architecture accurate surveys drawn-up at a scale not smaller than 1:50, and for the architectural decoration paper squeezes. (See Appendix A). But I have also consciously developed my own natural visual sequence into a chronology of 'Appreciation Levels'.The method using Appreciation Level is n attempt at recording the precise order in which an initiate assimilates the numerous elements of a design +. design with continual reference back to previous visual exrperiences and mental stimuli. I suggest that in the elements a natural order can be found which, in general terms, assists the efforts of the uninitiated as well as those initiates who can apperceive the visual compatibilities and conflicts reflected in the desin. iith these activities in mind I originally chose the term '?ecognition Levels' before discarding it on the grounds that it implied the item is 'known again' or 'identified as known before', thus I saw the term to be restrictive. On the other hand the word 'Appreciation' is apposite, it may be defined as: estimation; judgement; percebtion; critique. o value; adequate recognition; rise in o each of the words chosen to qualify and define the word 'Appreciation' can be ascribed a function to be attempted by a person when confronted by an object for the first time. This, therefore, is a more accurate term to apply to the ordering of elements.There is, I think, a general thought process connected to :appreciation Levels regardless of the size and type of artifact. The first level is the recognition of the material(s) used in the artifact's construction, assuming that there does exist between the observer and the observed a satisfactory proximity. The second level in this chronology can involve an appreciation of size, of scale and of the architectonic qualities and purposes of the object, leading on perhaps to an appreciation of the over -all shape, and then on to the substructures or repetitious elements which may then lead back to a fuller appreciation of the over -all shape by emphasising it. At this stage in the chronological ordering of the Appreciation Levels a slight change can occur in the type of information perceived, the object's main visual elements come into focus allowing the component parts to be determined and classified, e.g. a geometric skeleton with nodes or the softer curving lines of vegetal patterns.This last Appreciation Level is likely to be the final level attained by the observer and thus it is here that the judgements concerning the beauty and the interest of the artifact are made based on the design content seen in this and the preceding levels. I like to think that as the medieval craftsmen realised the limited visual abilities of the average casual observer so he strived to present the major design elements with the strength, clarity, and meaning which might be com- prehended without excessive mental exertions. _'he prizes await those with more developed powers of observation and perce_,tion in the guise of further appreciation Levels hidden in the subtle End complex relationships of the smaller repetitive elements and whose exploration creates new rythms and harmonies