Let M be a Riemannian manifold with metric g, and let P be a principal G-bundle over M having connection one-form a. One can define a modified version of the Ricci flow on P by fixing the size of the fiber. These equations are called the Ricci Yang-Mills flow, due to their coupling of the Ricci flow and the Yang-Mills heat flow. In this thesis, we derive the Ricci Yang-Mills flow and show that solutions exist for a short time and are unique. We study obstructions to the long-time existence of the flow and prove a compactness theorem for pointed solutions. We represent the Ricci Yang-Mills flow as a gradient flow and derive monotonicity formulas that can be used to study breather and soliton solutions. Finally, we use maximal regularity theory and ideas of Simonett concerning the asymptotic behavior of abstract quasilinear parabolic partial differential equations to study the stability of the Ricci Yang-Mills flow in dimension 2 at Einstein Yang-Mills metrics. / text

Arabidopsis thaliana contains two genes annotated as methylthioadenosine nucleosidases (MTN): MTN1, At4g38800 and MTN2, At4g34840. This enzyme activity hydrolyzes the methylthioadenosine (MTA) produced by nicotianamine (NA), polyamine (PA), and ethylene biosynthesis to methylthioribose (MTR) within the Yang cycle. Comprehensive analysis of the mtn1-1mtn2-1 mutant line with 14 % residual MTN activity revealed a complex phenotype that includes male and female infertility and abnormal vascular development. Based on metabolite profiling, mtn1-1mtn2-1 has a reduced NA content, altered PA profiles with higher putrescine (Put) and lower spermidine (Spd) and spermine (Spm) levels, disrupted metal ion profiles, and abnormal auxin distribution. The modeling of Arabidopsis PA synthases developed by comparison with the crystal structures of human Spd and spermine synthases complexed with MTA suggests that Arabidopsis PA synthases are product inhibited by MTA. Thus, these pleiotropic mutant phenotypes possibly are the result of one metabolite directly inhibiting numerous pathways. By creating and analyzing a series of mutants and transgenic lines with moderate levels of MTN activity the complex phenotype of mtn1-1mtn2-1 was dissected in order to determine the fundamental trait associated with MTN deficiency. Two double mutants were identified by crossing single T-DNA mutants, and an artificial micro RNA (amiRNA) line was generated by transforming mtn1-1 with amiRNA specific to MTN2. The T-DNA double mutants, mtn1 4mtn2-1, and mtn1-1mtn2-5 had 98 % and 28 % MTN activity, respectively, whereas the amiRNA line has 16 % MTN activity. The growth, development, and metabolite analysis of these mutants revealed that their delayed bolting, correlated with an increased number of leaves, was the common trait observed across all lines. Xylem proliferation defects and increased number of vascular bundles per unit area were shared in all lines except mtn1 4mtn2-1. Based on these results, auxin distribution is proposed as the key target of the accumulated MTA that results from MTN deficiency. The infertility related to MTN-deficiency was restored by supplying 100 ??M of Spd to the mtn1-1mtn2-1 seedlings over 14 days. The data presented in this thesis reveals two potential links that work synergistically to recover fertility in this mtn1-1mtn2-1 line. Based on a detailed analysis of the female gynoecia morphology, transcript, hormone and metabolite profiles, it is proposed that the Spd partially reverses the mutant phenotypes through the recovery of auxin distribution and /or vascular development. Interestingly, the Spd effect seems to be transgenerational: they give rise to plants that are genotypically mtn1-1mtn2-1 but phenotypically WT over generations. Taken together, all of the results suggest that MTN-deficient mutants provide the potential for unraveling the molecular mechanism associated with nicotianamine, polyamines, auxin, and vascular development with respect to enhancing the efficiency of nutrient use and yields in plants.

Quantum Field Theory (QFT) provides the essential background for formulating the standard model of elementary particles and, moreover, practically all other theories attempting to explore the physical laws of nature at the sub-atomic level. One of the main observables in QFT are the scattering amplitudes, physical quantities which encode the information of the scattering process of particles. Accordingly, having authentic, well-defined and feasible prescriptions for the calculations of amplitudes is of huge importance to theoretical physicists. Actual calculations show that the text-book prescription, the Feynman method, besides in general being very cumbersome also hides some of the beautiful mathematical features of amplitudes. The last decade has seen tremendous efforts and achievements to improve such calculations, particularly in supersymmetric gauge theories, which have also led to better understanding of QFT itself. Among the known physically and mathematically interesting quantum field theories is perturbative gravity and its supersymmetric version, N=8 supergravity- much less understood than gauge theory. Following the developments in gauge theory, this dissertation mainly aims at exploring scattering amplitudes in gravity as a quantum field theory, using the modern approaches to QFT. The goal is not only to improve our understanding of gravity amplitudes by applying part of the known modern methods of calculations to it but also to introduce and develop new ones.

The one-loop effective action for N = 2 and N = 4 supersymmetric Yang-Mills theories are computed to order F5; and F6 respectively by the use of heat kernel techniques in N = 1 superspace. The computations are carried out via the introduction of a new method for computing DeWitt-Seeley coefficients in the coincidence limit. To order F5, the bosonic components of both N = 2 and N = 4 supersymmetric Yang-Mills theories are extracted and compared with the existing literature. For N = 4 super Yang-Mills theories the F5 terms are found to be consistent with the non-Abelian Born-Infeld action computed to this order by superstring methods and various other means of computing deformations of supersymmetric Yang-Mills theory. The result proved to be the final piece of a puzzle, leaving little doubt that there exists a unique deformation of maximally symmetric super Yang-Mills theories at this order. The F6 terms will be of importance for comparison with superstring calculations, including direct tests of the AdS/CFT conjecture. The bosonic components of N = 2 supersymmetric Yang-Mills are also shown to be consistent with existing literature, and will be of importance for testing of generalizations of the AdS/CFT conjecture.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (M.A.)--Guo li zheng zhi da xue, 1972. / On double leaves. Includes bibliographical references (leaf 56).

Thesis (Ph. D.)--Duke University, 2007. / Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains x, 94 p.; also includes graphics Includes bibliographical references (p. 52-54). Available online via OhioLINK's ETD Center

Thesis (Ph.D.) - University of Queensland, 2005. / Includes bibliography.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 65-70).