The geometry of non-conformal supersymmetric non-linear sigma models in one and two dimensions are reviewed. Transformations of the Osp(1|2) subgroup of the superconformal group are derived and then used in finding geometrical constraints on the target space of an N=(1,1) sigma model reduced to an N=1 sigma model.

In high ¡Vspeed digital circuits, in order to utilize the space of printed circuit boards(PCB) efficiently, the signal via is a heavily used interconnection structure to communicate different signal layers. However, the interconnection discontinuities will result in the degradation of the signal integrity and become a crucial issue for IC designers. To analyze this problem using finite difference time domain(FDTD) method, the stair case approach of interesting structure with curved metallic surface not only introduce errors due to inaccurate approximation, but consume much simulation time and memory required . In this thesis, a conformal FDTD method of locally distorted contours is presented. By modification of Maxwell¡¦s equations in integration form, we simulate the signal via successfully and discuss several interesting issues such as resonance in power/ground plane, the simultaneous switching noise(SSN), the effect of adding ground vias in PCB, and common-mode and differential-mode drives for source, etc.

Thesis (doctoral)--Georg-Augusts-Universität zu Göttingen, 1910. / Cover title. Vita. Includes bibliographical references.

Thesis (doctoral)--Rheinischen Friedrich-Wilhelms-Universität zu Bonn, 1928. / Vita. Includes bibliographical references.

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1933. / Sonderabdruck aus den "Schriften des Mathematischen Seminars und des Instituts für angewandte Mathematik der Universität Berlin, Band 1"--T.p. verso. Vita. Includes bibliographical references.

Thesis--Universität Zürich. / Curriculum vitae.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1901. / "Reprinted from the Transactions of the Wisconsin Academy of Sciences, Arts, and Letters, Vol. 14." Includes bibliographical references.

Let f be a mapping (i.e., continuous transformation) of a topological space X onto a topological space Y. It is of interest to investigate the properties of X which are inherited by Y under the mapping f. In particular, if f is a homeomorphism, X and Y are topologically equivalent, so that Y will share all the topological properties of X. Hovever, under 1ess restricted oonditions on f , many of the properties such as connectedness, compactness, separability, local separability (i.e., first countability) and strong separability (i.e., second countability), etc., will be inherited by Y. In this work, we are interested in investigating some important classes of mappings: open mappings, closed mappings and perfect mappings, and in determining how the image space is affected under such mappings. These mappings play fundamental role in many studies, e.g., the theory of function of one or several complex variables. Work along these lines have been initiated by G. T. Whyburn, S. Stoilow, H. Grauert, B. Remmert and K. Stein.

Aspects of the Affine Superalgebra sl(2|l) at Fractional Level Ph.D. Thesis by Gavin Balfour Johnstone, April 2001 In this thesis we study the affine superalgebra sl(2|l; C) at fractional levels of the form k = l/u-l,uєN\{l}. It is for these levels that admissible representations exist, which transform into each other under modular transformations. In the second chapter we review background material on conformal field theory, particularly the Wess-Zumino-Witten model and the connection with modular transformations. The superalgebra sl(2|l;C) is introduced, as is its affine version. The next chapter studies the modular transformation properties of sl(2|l;C) characters. We derive formulae for these transformations for all levels of the form K = 1/u-1,uєN\{1}. We also investigate some modular invariant combinations of characters and find two series of modular invariants, analogous to the A- and D-series of the classification of sl{2) modular invariants. In chapter 4 we turn to the study of fusion rules. We concentrate on the case k = -1/2. By considering the decoupling of singular vectors, we are able to find consistent fusion rules for this particular level. These fusion rules correspond to a modular invariant found in chapter 3. This study suggests that one may consistently define a conformal field theory based on sl(2|l;C) at fractional level.

Thesis (M.S.)--Rochester Institute of Technology, 1990. / Typescript. Includes bibliographical references (leaves 38-39).