On the Boundedness of Globally FF-split varieties

This paper proposes the use of $F$-split and globally $F$-regular conditions in the pursuit of BAB type results in positive characteristic. The main technical work comes in the form of a detailed study of threefold Mori fibre spaces over positive dimensional bases. As a consequence we prove the main theorem, which reduces birational boundedness for a large class of varieties to the study of prime Fano varieties

The Augmented Base Locus in Mixed Characteristic

Let $L$ be a nef and big line bundle on a scheme $X$. It is well known that if $X$ is a projective over a field then the augmented base locus and the exceptional base locus agree. This result is extended to projective schemes over arbitrary excellent Noetherian bases. In particular the result holds in mixed characteristic

Mori Fibrations in Mixed Characteristic

This paper resolves several outstanding questions regarding the Minimal Model Program for klt threefolds in mixed characteristic. Namely termination for pairs which are not pseudo-effective, finiteness of minimal models and the Sarkisov Program.Comment: V2 - Results extended to the case of purely positive characteristic. Some proofs and statements clarifie

On the threefold minimal model program in positive and mixed characteristic

This dissertation explores the Minimal Model Program (MMP) in positive and mixed characteristic in dimension three with a particular focus on outputs of the program. In purely positive characteristic we combine the program with a detailed study of conic bundles to prove a birational boundedness result. We show that given a suitable set of log Calabi-Yau varieties, we can construct a bounded family containing bres birational to any member of the chosen set. For threefolds over a base of dimension at least one, we resolve the Abundance Conjecture for klt pairs in joint work with F. Bernasconi and I. Brivio. Showing in particular that every klt minimal model in mixed characteristic admits an Iitaka Fibration. This is then applied to prove an Invariance of Plurigenera result for suitable families of surfaces. Finally we consider outstanding questions around Mori brations in mixed characteristic. We show that every klt threefold MMP terminates and that any two Mori bre space outputs of an MMP from the same starting pair are connected by a series of Sarkisov links. As part of this we prove a mixed characteristic Finiteness of Minimal Models result. While the proof is focused in dimension three, the arguments work in any generality given that the requisite MMP results are known.Open Acces

Non-optimality of the Greedy Algorithm for subspace orderings in the method of alternating projections

The method of alternating projections involves projecting an element of a Hilbert space cyclically onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm and that one can obtain estimates for the rate of convergence in terms of quantities describing the geometric relationship between the subspaces in question, namely their pairwise Friedrichs numbers. We consider the question of how best to order a given collection of subspaces so as to obtain the best estimate on the rate of convergence. We prove, by relating the ordering problem to a variant of the famous Travelling Salesman Problem, that correctness of a natural form of the Greedy Algorithm would imply that $\mathrm{P}=\mathrm{NP}$, before presenting a simple example which shows that, contrary to a claim made in the influential paper [Kayalar-Weinert, Math. Control Signals Systems, vol. 1(1), 1988], the result of the Greedy Algorithm is not in general optimal. We go on to establish sharp estimates on the degree to which the result of the Greedy Algorithm can differ from the optimal result. Underlying all of these results is a construction which shows that for any matrix whose entries satisfy certain natural assumptions it is possible to construct a Hilbert space and a collection of closed subspaces such that the pairwise Friedrichs numbers between the subspaces are given precisely by the entries of that matrix.Comment: To appear in Results in Mathematic

Mandy Stigant: Trace Show Card

Show card for Mandy Stigant: Trace. Master of Arts Thesis Exhibition. January 23 - February 1, 2008.https://digitalcommons.udallas.edu/ma_07-08/1002/thumbnail.jp

Power transformers winding fault diagnosis by the on-load exciting current extended Park's vector approach

This paper presents the application of the on-load exciting current Extended Park's Vector Approach to diagnose incipient turn-to-turn winding faults in operating power transformers. Experimental and simulation test results demonstrate the effectiveness of the proposed technique, which is based on the spectral analysis of the AC component of the on-load exciting current Park's Vector modulus

Divide

As human beings we have an innate hunger for meaning and, not coincidentally, an interesting ability to assimilate patterns, to recognize working systems. For all our ability to reason and assimilate, however, concrete answers to our questions of meaning and our hunger for understanding are elusive, vague and often lacking. In my work I pursue a two-fold exploration. On the one hand I want to express my fascination with that riddle of the human condition, of our need for meaning and our parallel inability to pinpoint it concretely. On the other hand I am fascinated with the fact that our ability to assimilate and reason is not limited to a weighty existential crisis. We also celebrate that ability when we play: we figure things out for fun, and because we like to. To keep grounded in the spirit of play, I base my forms on the contours of unorthodox jigsaw puzzle pieces. I then incorporate elements of division, scale, topography, surface, arrangement and imagery that highlight the original contour even while they lift it wholly out of its original context. The enigmatic form that results is intended to pose an open-ended question to the viewer concerning the underlying meaning to an implied organization. An immediate formal encounter demonstrates a visual relationship among the parts, a pattern to the surface treatments and an intention with the overall composition. Through that encounter, I want to stimulate in the viewer the desire to seek the source of a visually evident system. By not proffering concrete answers about that source, I intend to encourage the viewer to bring elements from his own experience and perspective, which will play a significant part in any conclusions he may draw. On a broader scale, this work is intended to call to the viewer’s attention the more mysterious aspects of the human experience, aspects in which we can take a measure of joy without necessarily fully understanding the

Jig jog [music] /

B.2016 (Publisher number). Also available online http://nla.gov.au/nla.mus-an8440289; MUS: N, MUS/187