Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory

This paper deals with the problem of estimating the level sets of an unknown distribution function $F$. A plug-in approach is followed. That is, given a consistent estimator $F_n$ of $F$, we estimate the level sets of $F$ by the level sets of $F_n$. In our setting no compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by applications in multivariate risk theory. In this sense we also present simulated and real examples which illustrate our theoretical results.Level sets ; Distribution function ; Plug-in estimation ; Hausdorff distance ; Conditional Tail Expectation

Characterisation of electrospray properties in high vacuum with a view to application in colloid thruster technology

PhDThe operational environment of colloid thrusters is high vacuum (10-3 _ 10-6 mbar) however, much of the experimental data collected to date to identify parameter relationships in cone jet mode electrosprays (ES), such as current-volumetric flow rate scaling laws, has been conducted in atmospheric conditions. This highlights a need for electrospray data under high vacuum conditions. Electrospray experimental data was collected using medium conductivity solutions (0.0025 -0.0160 S/m) of TEG doped with sodium iodide in high vacuum. These sprays were obtained from a stainless steel capillary and a disk counter electrode with central aperture. An online flow measurement system is described, which has been developed during this research to measure the fluid volumetric flow rate, concurrently with applied voltage and spray properties such as spray current and cone, jet and spray geometry. This automated flow measurement system was used to measure flow rates as low as InUs with an absolute accuracy of 0.3nUs and a resolution of 0.03nus. It is identified that this system may be easily adapted for lower flow rates and higher resolutions. The ES data collected demonstrates, for the first time, the detailed dependence of volumetric flow rate upon the applied voltage. The sensitivity of nominal flow rate to applied voltage was found to be higher for lower nominal flow rates. For a volumetric flow rate -4nLIs a 25% a change in flow rate per kV was recorded over a cone-jet mode stability range spanning -1.5kV. This volumetric flow rate voltage sensitivity holds particular significance for colloid thruster systems, which operate at or near minimum flow rate conditions. The current was found to have a power law dependence on flow rate similar to the current scaling laws of F. de la Mora and Gahan-Calvo however the exponent of this power law differs significantly from these scaling laws. A study considering the effect of charge carrier mobility in simple 1: 1 electrolytes shows that the exponent of the power law current-flow rate scaling increased with increasing charge carrier mobility. Contrary to the various scaling laws the spray current was found to be dependent on electrostatic conditions. The sensitivity of the emitted current to the applied voltage was also found to increase with increasing nominal volumetric flow rate. The geometrical parameters of cone angle, spray angle and jet length were measured for varying TEG/Nal solution conductivity. Cone geometry was found to be relatively independent of conductivity in the range tested. Jet length was found to have an inverse relationship with solution conductivity

The calculus according to S. F. Lacroix (1765-1843)

Silvestre François Lacroix (Paris. 1765 - ibid., 1843) was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous book is a monumental Traité du calcul différentiel et du calcul intégral (three large volumes, 1797-1800; a second edition appeared in 1810-1819) - an encyclopaedic appraisal of 18th-century calculus. He also published many textbooks, one of which is closely associated to this large Traité: the Traité élémentaire du calcul différentiel et du calcul intégral (first edition in 1802; four more editions in Lacroix's lifetime; four posthumous editions). Although most historians acknowledge the great influence of Lacroix's large Traité in early 19th-century mathematics it has not been thoroughly studied. This thesis is a contribution for correcting this omission. The focus is on its first edition, but the second edition and the Traité élémentaire, are also addressed. The thesis starts with a short biography of Lacroix, followed by an overview of the first edition of the large Traité. Next corne five chapters where particular aspects are analyzed in detail: the foundations of the calculus, analytic and differential geometry, approximate integration and conceptions of the integral, types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions), and three aspects related to finite differences and series (the use of subscript indices, types of solutions of finite difference equations, and mixed difference equations); for all these aspects Lacroix's treatment is compared to the 18th-century background, and to his likely sources. Then we examine how the large Traité was adapted to a textbook - the Traité élémentaire, we take a look at the second edition of the large Traité, and conclude the body of the thesis with some final remarks

The mathematical works of Bernard Bolzano published between 1804 and 1817

The purpose of the thesis is to assess the mathematical achievements of Bernard Bolzano on the basis of the five early published works. The material is divided into the areas of the foundations of mathematics, geometry and analysis. In making this assessment there have been two principal considerations. Firstly, any judgement of the significance of Bolzano's work should be made in the light of the historical context, so considerable space is devoted to the relevant 18th century sources. Secondly, as a general framework to the thesis there is the question of how Bolzano's general views about mathematical proofs and concepts are related to his achievements. The main claim and conclusion of the thesis is that this relationship was unusually clear and significant in the case of Bolzano's work. There is an Appendix containing the first English translation of all five of Bolzano's works as well as the German texts of their first editions

Fourth Decade of Hydraulics at the State University of Iowa, 1960

In order to make available the results of all research conducted at the Iowa Institute of Hydraulic Research, a series of bulletins containing abstracts of graduate theses, reviews of Institute research and lists of staff publications has been published at irregular intervals. Previous titles in this series, a part of the Iowa Studies in Engineering, have been Bulletin 19, Two Decades of Hydraulics at the University of Iowa ( 1939); Bulletin 26, Investigations of the Iowa Institute of Hydraulic Research, 1939-1940; Bulletin 30, The Iowa Institute of Hydraulic Research, 1946; and Bulletin 33, Third Decade of Hydraulics at the State University of Iowa ( 1949) with Supplement ( 1952). This series is being brought up to date with the current publication

The argument of Ulysses

(print) 485 p. ; 24 cmIntroduction 3 -- Ch. One 31 -- 1 The Tower 33 -- 2 The School 42 -- 3 The Strand (Stephen) 51 -- In Search Of Stephen 62 -- Ch. Two 89 -- 4 The Kitchen 89 -- 5 The Post Office 93 -- 6 The Cemetery 98 -- Mr. Leopold Paula Bloom 104 -- Ch. Three 108 -- 7 The Newspaper Office 109 -- About "Episodes" And Correspondences 118 -- Ch. Four 123 -- 8 Davy Byrne's 123 -- Style In Ulysses 138 -- Ch. Five 149 -- 9 The Library 149 -- Joyce's Dublin And Dublin's Joyce 181 -- Ch. Six 205 -- 10 The City 205 -- Ch. Seven 220 -- 11 The Ormond Hotel 220 -- 12 Barney Kiernan's 232 -- Ch. Eight 263 -- 13 The Strand (Bloom) 263 -- 14 The Hospital 277 -- Ch. Nine 302 -- 15 Nighttown 302 -- Ch. Ten 362 -- 16 The Cabmen's Shelter 363 -- 17 The House (To Stephen's Departure) 382 -- Ch. Eleven 395 -- 17 The House (From Stephen's Departure) 400 -- 18 The Bed 415 -- Conclusion 451 -- Index 46