On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Non-cellulosic cell wall polysaccharides are subject to genotype × environment effects in sorghum (Sorghum bicolor) grain

Sorghum is a staple food for half a billion people and, through growth on marginal land with minimal inputs, is an important source of feed, forage and increasingly, biofuel feedstock. Here we present information about non-cellulosic cell wall polysaccharides in a diverse set of cultivated and wild Sorghum bicolor grains. Sorghum grain contains predominantly starch (64–76) but is relatively deficient in other polysaccharides present in wheat, oats and barley. Despite overall low quantities, sorghum germplasm exhibited a remarkable range in polysaccharide amount and structure. Total (1,3;1,4)-β-glucan ranged from 0.06 to 0.43 (w/w) whilst internal cellotriose:cellotetraose ratios ranged from 1.8 to 2.9:1. Arabinoxylan amounts fell between 1.5 and 3.6 (w/w) and the arabinose:xylose ratio, denoting arabinoxylan structure, ranged from 0.95 to 1.35. The distribution of these and other cell wall polysaccharides varied across grain tissues as assessed by electron microscopy. When ten genotypes were tested across five environmental sites, genotype (G) was the dominant source of variation for both (1,3;1,4)-β-glucan and arabinoxylan content (69–74), with environment (E) responsible for 5–14. There was a small G × E effect for both polysaccharides. This study defines the amount and spatial distribution of polysaccharides and reveals a significant genetic influence on cell wall composition in sorghum grain.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Non-linear bending of beams of variable cross-section

For the non-linear bending of cantilever beams of variable cross-section, the effect of large deformations, but with linear elasticity, is considered. The governing integral equation is solved by a numerical iterative procedure. Results for some typical cases are obtained and compared with some of those available in the literature.

Experimental investigation of catalytic and non-catalytic surface reactions on SiO2 thin films with shock heated oxygen gas

The present study is to investigate the interaction of strong shock heated oxygen on the surface of SiO2 thin film. The thermally excited oxygen undergoes a three-body recombination reaction on the surface of silicon dioxide film. The different oxidation states of silicon species on the surface of the shock-exposed SiO2 film are discussed based on X-ray Photoelectron Spectroscopy (XPS) results. The surface morphology of the shock wave induced damage at the cross section of SiO2 film and structure modification of these materials are analyzed using scanning electron microscopy and ion microscopy. Whether the surface reaction of oxygen on SiO2 film is catalytic or non-catalytic is discussed in this paper.

Democratic Party invitation (form letter)

Form political letter. Printed on Executive Committee stationery with handwritten salutation in blue ink. Invitation to be a Vice President to ratify nominations of Greely and Brown, Democratic party.