It Falls to Us: Linking The Waste Land to Dante’s Divine Comedy

Be it as a completed work or as individual sections, the ambiguity of T.S. Eliot’s most famous poem has always been the subject of scholarly debate. Though concrete conclusions are seldom reached in any of these discussions, the mere exchange of readers\u27 ideas is often the most rewarding aspect of the dialogue surrounding the poem. The presented paper attempts to join that conversation through an analysis of the fifth section of The Waste Land and how it may be related to Dante Alighieri’s Divine Comedy. Through the interpretation of a number of allusions, I propose that there is a journey of sorts depicted in the final section of The Waste Land, and that this journey is rather similar to that seen in the first two thirds of Dante’s epic voyage through the afterlife. In exploring such a connection, new lines of interdisciplinary thought may be inspired in other members of the community, be it in a theological, philosophical, or perhaps even psychological sense. If nothing else, however, the proposed subject matter will draw attention to a potential narrative within the organized choas of The Waste Land

Asymptotic independence for unimodal densities

Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (dfs). Dfs are rarely available in an explicit form, especially in the multivariate case. Often we are given the form of the density or, via the shape of the data clouds, one can obtain a good geometric image of the asymptotic shape of the level sets of the density. This paper establishes a simple sufficient condition for asymptotic independence for light-tailed densities in terms of this asymptotic shape. This condition extends Sibuya's classic result on asymptotic independence for Gaussian densities.Comment: 33 pages, 4 figure

Sensitivity of the limit shape of sample clouds from meta densities

The paper focuses on a class of light-tailed multivariate probability distributions. These are obtained via a transformation of the margins from a heavy-tailed original distribution. This class was introduced in Balkema et al. (J. Multivariate Anal. 101 (2010) 1738-1754). As shown there, for the light-tailed meta distribution the sample clouds, properly scaled, converge onto a deterministic set. The shape of the limit set gives a good description of the relation between extreme observations in different directions. This paper investigates how sensitive the limit shape is to changes in the underlying heavy-tailed distribution. Copulas fit in well with multivariate extremes. By Galambos's theorem, existence of directional derivatives in the upper endpoint of the copula is necessary and sufficient for convergence of the multivariate extremes provided the marginal maxima converge. The copula of the max-stable limit distribution does not depend on the margins. So margins seem to play a subsidiary role in multivariate extremes. The theory and examples presented in this paper cast a different light on the significance of margins. For light-tailed meta distributions, the asymptotic behaviour is very sensitive to perturbations of the underlying heavy-tailed original distribution, it may change drastically even when the asymptotic behaviour of the heavy-tailed density is not affected.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ370 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.For a sequence of independent observations Zn = (Xn, Yn) from the bivariate standard normal density there are at least three asymptotic descriptions of the sample clouds. This paper looks at sample clouds from light-tailed unimodal densities with spherical level sets. What conditions will give the asymptotic behaviour above? We do not assume that the level sets are concentric

It Falls to Us: Linking The Waste Land to Dante’s Divine Comedy

Be it as a completed work or as individual sections, the ambiguity of T.S. Eliot’s most famous poem has always been the subject of scholarly debate. Though concrete conclusions are seldom reached in any of these discussions, the mere exchange of readers\u27 ideas is often the most rewarding aspect of the dialogue surrounding the poem. The presented paper attempts to join that conversation through an analysis of the fifth section of The Waste Land and how it may be related to Dante Alighieri’s Divine Comedy. Through the interpretation of a number of allusions, I propose that there is a journey of sorts depicted in the final section of The Waste Land, and that this journey is rather similar to that seen in the first two thirds of Dante’s epic voyage through the afterlife. In exploring such a connection, new lines of interdisciplinary thought may be inspired in other members of the community, be it in a theological, philosophical, or perhaps even psychological sense. If nothing else, however, the proposed subject matter will draw attention to a potential narrative within the organized choas of The Waste Land

Design and Analysis of Constrained Layer Damping Treatments for Bending and Torsion

In this dissertation, different aspects of constrained layer damping treatments on beams of various geometries are studied. First, the optimal length of a constrained layer damping treatment mounted on a surface in linear strain is identified as a function of the relative stiffnesses of the damping layers and the non-uniformity of the surface stain. The analysis extends previous work that considered the case of uniform surface strain. Sixth order sandwich beam theory is then modified for use with a rectangular beam covered with a segmented constrained layer damping treatment. Non-dimensional variables are used to simplify the form of the problem. Also, equations are developed for a beam of circular cross section with thin narrow constrained layer strips placed parallel to the beam centerline, and it is shown the equations have the same form as the sixth order theory for the rectangular beam. A new approximation method, the Complex Rayleigh Quotient , is proposed to estimate the complex natural frequency and damping of structures. Complex mode shapes are used in a ratio similar in spirit to Rayleigh\u27s Quotient to obtain an estimate for the complex frequency of the system. The method is defined for both discrete and continuous systems, and illustrated using a rectangular beam with a segmented damping treatment. The estimates of loss factor developed from the Complex Rayleigh Quotient were much closer to the exact solutions than those developed using the Modal Strain Energy method. A new constrained layer configuration, the barberpole , is presented for beams of circular cross section. An analysis is developed which show that the barberpole configuration can damp both bending and torsional vibrations. The barberpole also provides more damping than unsegmented strips for a beam in bending. An experiment was performed to gain confidence in the bending portion of the barberpole analysis