Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1926. / "Sonderabdruck aus: Zeitschrift für angewandte Mathematik und Mechanik, Bd. 6, 1926"--P. [1]. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Illinois, 1915. / Vita. "Selected bibliography": p. 117-120.

Thesis (M.S.) -- Central Connecticut State University, 1998. / Thesis advisor: Dr. Jeffrey McGowan. "...in partial fulfillment of the requirements for the degree of Master of Science." Includes bibliographical references (leaves [78-79]).

A synthetic approach to the construction of projective geometry, its methods and selected results are given in the proposed thesis. The main historical drawbacks of the original proof of Chasles's theorem for non-developable ruled surfaces and von Staudt's formalization of projective geometry are commented. The corre- sponding theoretical background is elaborated on visual demonstrations with the accent to interrelations of classical synthetic, axiomatic and analytic points of view. Synthetic methods of projective geometry and their mixture with analytic methods are described on examples including numerous alternative proofs and generalizations of some theorems. A method of four-dimensional visualization is introduced in details. Elementary constructions of images of points, lines, planes and 3-spaces are followed by models of polychora, their sections and shadows. Chasles's theorem is proven for non-developable ruled quadrics on synthetic vi- sualizations, then generalized and proven within the pure projective framework for algebraic surfaces. The synthetic classification of regular quadrics is derived from descriptive geometry constructions of sections of four-dimensional cones and analytically verified in the projective extension of the real space. An integral part of the thesis is a...

The Fontan repair is a three-stage palliative surgical procedure for single ventricle congenital heart diseases, ultimately resulting in the right heart bypass. This is accomplished by routing the systemic venous return directly to the lungs. Although this procedure reduces the mortality rate, its long-term outcome is still considered far from optimal. Over the years several modifications have been suggested, ultimately leading to the total cavopulmonary connection (TCPC), which is the current procedure of choice. A better understanding of the hemodynamics in the TCPC is critical for further optimization of the TCPC design and surgical planning, which may lead to improved surgical outcome. Recent experimental and numerical studies have focused on characterizing the fluid dynamics of the TCPC but to date no study has attempted to relate the geometry of the TCPC anatomies with their hemodynamic parameters. The present study therefore proposes to quantify the complex geometrical characteristics of patient-specific TCPC anatomies and correlate these characteristics with their hemodynamic efficiency. A technique using skeletonization approach is thus developed to achieve this goal. The centerline approximation of the TCPC geometry is used to extract main geometric parameters such as vessel area, curvature and offset. The developed methodology is then applied to characterize the shape of various TCPC templates including extra-cardiac (EC) and intra-atrial (IA) TCPCs, TCPCs with bilateral Superior Vena Cavae and geometries before the third stage. The obtained geometric parameters are then related to the TCPC hemodynamics, particularly to the power loss.