The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge instantons on Minkowski space. Since these discoveries, a generalised theory of instantons has been emerging for manifolds with special holonomy. Beginning with connections and curvature on complex vector bundles, this thesis provides some of the essential background for studying moduli spaces of instantons. Manifolds with exceptional holonomy are special types of seven and eight dimensional manifolds whose holonomy group is contained in G2 and Spin(7), respectively. Focusing on the G2 case, instantons on G2 manifolds are defined to be solutions to an analogue of the four dimensional anti-self-dual equations. These connections are known as Donaldson-Thomas connections and a couple of examples are noted.

The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge instantons on Minkowski space. Since these discoveries, a generalised theory of instantons has been emerging for manifolds with special holonomy. Beginning with connections and curvature on complex vector bundles, this thesis provides some of the essential background for studying moduli spaces of instantons. Manifolds with exceptional holonomy are special types of seven and eight dimensional manifolds whose holonomy group is contained in G2 and Spin(7), respectively. Focusing on the G2 case, instantons on G2 manifolds are defined to be solutions to an analogue of the four dimensional anti-self-dual equations. These connections are known as Donaldson-Thomas connections and a couple of examples are noted.

This research focuses on training bundles, nonstandard work arrangement and their relationship in high-tech industry, and the conclusions are listed as follows, 1. Training bundles and training effectiveness Training practicability has a positive impact on employee productivity, company profitability, innovation and reduction of employee turnover rates. Training institutionalization has a positive impact on employee productivity and company profitability. Rather than reducing employee turnover rates, training has the greater positive impact on employee productivity. Furthermore, larger organizations have higher level of training practicability. 2. Nonstandard work arrangement in high-tech industry As the data showed, over 80% companies ever had nonstandard work arrangement in 2002, and in the companies that had such arrangement, fixed-term hires and subcontractors were mostly used. To adjust for business fluctuations and reduce administrative workload are first two reasons why companies use nonstandard work arrangement. Limited head count and personnel cost saving are also important factors to hire nonstandard workers. In particular, cost saving is the most important factor for companies to use subcontractors. About the occupational structure, most nonstandard workers are either present in the position of administration or production. Only subcontractors are most present in the service occupations such as janitors, cleaners or caterers. With regard to personnel cost saving, compare to using dispatched workers, part-time workers and fixed-term hires are more helpful to reduce the personnel cost. 3. Training bundles and nonstandard work arrangement The result indicates that the level of training bundles can not be the determinant of using nonstandard work arrangement. Besides, we found that organization size has a positive effect on using nonstandard work arrangement, fixed-term hires, dispatched workers and subcontractors.

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

The Hilbert scheme of \(n\) points in the projective plane parameterizes degree \(n\) zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying interpolation, restriction, and stability properties of certain vector bundles on the plane we fully determine these cones for just over three fourths of all values of \(n\). A general Steiner bundle on \(\mathbb{P}^N\) is a vector bundle \(E\) admitting a resolution of the form \(0 \rightarrow \mathcal{O}_{\mathbb{P}^N} (−1)^s {M \atop \rightarrow} \mathcal{O}^{s+r}_{\mathbb{P}^N} \rightarrow E \rightarrow 0\), where the map \(M\) is general. We complete the classification of slopes of semistable Steiner bundles on \(\mathbb{P}^N\) by showing every admissible slope is realized by a bundle which restricts to a balanced bundle on a rational curve. The proof involves a basic question about multiplication of polynomials on \(\mathbb{P}^1\) which is interesting in its own right. / Mathematics

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 1999. / Includes bibliographical references. Also available on the Internet.

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

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 1999. / Includes bibliographical references. Also available on the Internet.

This thesis describes the development of the two-frequency Planar Doppler Velocimetry (2n-PDV) flow measurement technique. This is modification of the Planar Doppler Velocimetry (PDV) technique that allows the measurement of up to three components of the flow velocity across a plane defined by a laser light sheet. The 2n-PDV technique reduces the number of components required to a single CCD camera and iodine cell from the two CCDs in conventional PDV. This removes the error sources associated with the misalignment of the two camera images and polarisation effects due to the beam splitters used in conventional PDV. The construction of a single velocity component 2n-PDV system is described and measurements made on the velocity field of a rotating disc and an axisymmetric air jet. The system was then modified to make 3D velocity measurements using coherent imaging fibre bundles to port multiple views to a single detector head. A method of approximately doubling the sensitivity of the technique was demonstrated using the measurements made on the velocity field of the rotating disc and was shown to reduce the error level in the final orthogonal velocity components by ~40 to 50%. Error levels of between 1.5ms-1 and 3.1ms-1 depending upon observation direction are demonstrated for a velocity field of ±34ms-1. The factors that will influence the selection of a viewing configuration when making 3D PDV measurements are then investigated with the aid of a computer model. The influence of the observation direction, the magnitude of the flow velocity, and the transformation to orthogonal velocity components are discussed. A new method using additional data in this transformation is presented and experimental results calculated using four-measured velocity components are compared to those found conventionally, using only three components. The inclusion of additional data is shown to reduce the final error levels by up to 25%.