Doctor of Philosophy

dissertationIn this dissertation, we take a cohomological approach to study positive properties of higher codimensional subvarieties. First, we prove generalizations of Fujita vanishing theorems for $q$-ample divisors. We then apply them to study positivity of subvarieties with nef normal bundle in the sense of intersection theory. We also study the positivity of the cycle class of an ample curve or a curve with ample normal bundle. After Ottem's work on ample subschemes, we introduce the notion of a nef subscheme (resp. locally ample subscheme), which generalizes the notion of a subvariety with nef normal bundle (resp. ample normal bundle). We show that restriction of a pseudoeffective (resp. big) divisor to a nef subvariety is pseudoeffective (resp. big). We also show that ampleness, nefness and locally ampleness are transitive properties. We define the weakly movable cone as the cone generated by the pushforward of cycle classes of nef subvarieties via proper surjective maps. This cone contains the movable cone and shares similar intersection-theoretic properties with it, thanks to the aforementioned properties of nef subvarieties. On the other hand, we prove that if $Y\subset X$ is an ample subscheme of codimension $r$ and $D|_Y$ is $q$-ample, then $D$ is $(q+r)$-ample. This is analogous to a result proved by Demailly-Peternell-Schneider. We also show that the cycle class of an ample curve (resp. locally ample curve) lies in the interior of the movable cone of curves (cone of curves)

Characterization and Quantification of Monomers, Oligomers, and By-Products from Xylan During Biomass Pretreatment

Biomass pretreatment generates inhibitory products, which reduce the overall yield of xylose for ethanol production. Understanding of hemicellulose depolymerization into xylose is essential to identify the pretreatment conditions that maximize xylose formation, but minimize the generation of these inhibitory products, such as formic acid and furfural. Thus, the goal of this project is to understand how dilute acid pretreatment parameters affect hemicellulose depolymerization, maximize xylose concentrations, and minimize by-products formation. To progress towards this goal, rates and mechanisms of hemicellulose release must be determined. Birchwood xylan was used as the starting material to produce xylose oligomers. The hydrolyzed birchwood xylan was then fractionated using centrifugal partition chromatography (CPC) with the solvent system composed of butanol: methanol: water at a 5:1:4 volumetric ratio. The oligomers in the fractionated CPC were identified and quantified using high performance liquid chromatography (HPLC) and high performance anion exchange chromatography with pulsed amperometric detection (HPAEC-PAD), with the calibration curves setup based on the analysis of the commercial grade xylose oligomers reference standards. The identity of fractionated xylose oligomers was also confirmed using mass spectrometry (MS) analysis. The fractionated xylose oligomers were subsequently used in the kinetic study. The developed kinetic model demonstrated that the formation or degradation of the compounds could be predicted using first order kinetics. At all hydrolysis conditions, DP 1 degraded mostly into formic acid, rather than into furfural. The degradation rates of DP 1 and formic acid were determined to be most influenced by temperature and pH, as reflected by the Arrhenius Equation parameters calculated for the respective compounds. Pretreatment condition was more favorable for maximizing the yield of xylose monomer at the temperatures between 120 and 160 deg C, at a pH between 0.43 and 7, because of lower degradation rate of DP 1, and higher degradation rates of xylose oligomers, resulting in a net accumulation of DP 1

Stellar rotation formalisms of γ Doradus stars from gravity-mode period spacings

The oscillation frequencies of stars are used to constrain our theoretical models, from which we can derive stellar internal properties including rotation rates. The g-mode pulsations of γ Doradus stars are highly sensitive to the near-core regions. Two of the most common rotation formalisms, the second-order Perturbative Approach and the Traditional Approximation of Rotation, are compared to investigate their validity domains. We compute grids of 1-D γ Doradus models for (1,0) modes with the two rotation descriptions, using benchmark models instead of real stars to be the targets. Results show that the grids are generally capable of reproducing the benchmark to within observational uncertainties. However, the two formalisms disagree with each other at rotation rates beyond Omega/Omega_k=0.04. A method of distinguishing the formalisms without presupposing the stars’ rotation rates is successfully found: Their models diverge at periods longer than 2.5 days, given that the gradient of the period spacing is greater than -0.0122. The comparison results also reveal that our method of fitting period spacing series is not sufficient for taking rotational mixing effects fully into account. These findings offer potential for refining our current rotation theories with observational data, and contribute to the development of new techniques for improving modelling accuracies

Sir John Jordan and the Afffairs of China, 1906-1916, With Special Reference to the 1911 Revolution and Yuan Shih-k'ai.

Apart from several journalistic articles there is no major work on Sir John Jordan who was the British minister to Peking from 1906 to 1920. This can probably be explained by the fifty years' rule which had until recently prevented the opening to the public of Foreign Office materials pertaining to the later years of Jordan's service. This thesis is a study of his work as British minister in Peking between 1906 and 1916. However, as the title indicates, not every aspect of Jordan's ministry nor every major event in China in these ten years is dealt with in the thesis. The emphasis is on those which have a direct bearing on his role in the 1911 revolution and his relationship with Yiian Shih-k'ai. This also accounts for choosing 1916, when Ytlan died, as the closing year of the study. Jordan's ministry between 1906 and 1916 is worthy of study in that it throws light on a vital period of Chinese internal history which was crammed with dramatic changes. Institutionally, China changed from being a dynasty to a republic and then almost to a dynasty again; militarily, she suffered from three civil wars; and politically, she was to reap from these ten years decades of internal chaos and strife which was only brought to a temporary end with the institution of the communist regime in the middle of the century. Jordan, as the British representative, as a senior diplomat with great knowledge of China and as a friend of Yiian Shih-k'ai, played an important part in these events. The primary purpose of the thesis is to identify and assess his role. It is also hoped that the thesis will throw light on British policy towards China and, to a lesser extent, Japan during these years. In this respect, it is important to bear in mind that it was during this period that Britain's predominance in China, and the Far East, was for the first time being seriously challenged. Finally, Jordan himself is an interesting person to study. His activities during these ten years serve as a case study of the place of personal influence in policy-making in the peculiar political and international setting of the time

Motivic integration on Berkovich spaces over trivially valued fields

We define a motivic measure on the Berkovich analytification of an algebraic variety defined over a trivially valued field, and introduce motivic integration in this setting. The construction is geometric with a similar spirit as Kontsevich's original definition, and leads to the formulation of a functorial theory which mirrors, in this aspect, the approach of Cluckers and Loeser via constructibe motivic functions.Comment: 36 page