Thesis (Ph. D.)--University of Wisconsin--Madison, 1930. / Typescript with manuscript equations. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Inaug.-Diss.--Georg-Augusts-Universität zu Göttingen.

Thesis (Ph. D.)--Princeton University, 1914. / "Reprinted from Annals of mathematics, vol. XVI., no. 4, June, 1915."

Thesis (Ph. D.)--University of Wisconsin--Madison, 1931. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

No description available.

No description available.

In this thesis we consider new approaches to the numerical solution of a class of Volterra integral equations, which contain a kernel with singularity of non-standard type. The kernel is singular in both arguments at the origin, resulting in multiple solutions, one of which is differentiable at the origin. We consider numerical methods to approximate any of the (infinitely many) solutions of the equation. We go on to show that the use of product integration over a short primary interval, combined with the careful use of extrapolation to improve the order, may be linked to any suitable standard method away from the origin. The resulting split-interval algorithm is shown to be reliable and flexible, capable of achieving good accuracy, with convergence to the one particular smooth solution.

by Wing-Fai Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 7-8). / Abstract --- p.1-2 / Introduction --- p.3-6 / References --- p.7-8 / Paper I --- p.9-32 / Paper II --- p.33-60

La theorie c1assique de la fonctionnelle de la densite est appliquee a l'etude de la solvatation de molecules dans des solvants polaires. Une forme approximative de la fonctionnelle est obtenue en calculant par simulation la fonction de correlation directe du solvant pur. Cette fonctionnelle est ensuite minirnisee en presence d'un solute pour obtenir son energie libre de solvatation et la denslte d'equi'ibre du solvant. La fonctionnelle est d'abord timitee a un developpernent dipolaire et exprimee en fonction de la densite de nombre et de la polarisation. Elle est appliquee a la solvatation dans Ie liquide de Stockmayer, avec de tres bons resuitats, et dans un modele dipolaire d'eau, avec des resultats raisonnables hors des especes charqees. Enfin une representation de la fonctionnelle sur une grille de position et d'orientation est introduite. Elle conduit a une description precise de la solvatation de differents solutes rnoleculaires dans I'acetonitrile. / Classical density functional theory is applied to the study of the solvation of molecules in polar solvents. For a given solvent, an approximate form of the functional is obtained by computing by numerical simulations the direct correlation function of the pure solvent. This functional can then be jninirnized in the presence of a solute to yield its solvation free energy and the equilibrium solvent density. The functional is first limited to a dipolar expansion and expressed in terms of the number and polarisation density. The approach is applied to solvation in the Stockmayer liquid, with good results, and in a dipolar water model, with reasonable results except for charged species. At last a complete representation of the functional on a position and angular grid is introduced which leads to a precise description of the solvation of different molecular solutes in acetonitrile.

Thesis (Ph. D.)--Oregon State University, 1970. / Typescript (photocopy). Includes bibliographical references (leaves 81-82). Also available on the World Wide Web.