Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Rhode Island, 2006. / Includes bibliographical references (leaves 175-178).

University, Diss., 2002--Kiel.

The Lie algebra Vec(ℝ) of polynomial vector fields on the line acts naturally on ℂ[]. This action has a one-parameter family of deformations called the tensor density modules F_λ. The bounded indecomposable modules of Vec(ℝ) of length 2 composed of tensor density modules have been classified by Feigin and Fuchs. We present progress towards describing the annihilators of the unique indecomposable extension of F_λ by F_(λ+2) in the non-resonant case λ ≠ -½. We give the intersection of the annihilator and the subalgebra of lowest weight vectors of the universal enveloping algebra (Vec(ℝ)) of Vec(ℝ). This result is found by applying structural descriptions of the lowest weight vectors of (Vec(ℝ)).

This dissertation consists of three research papers on cheap talk game and satisficing behaviour. The first chapter examines the potential for communication via cheap talk between an expert and a decision maker whose type (preferences) is uncertain. The expert privately observes states for each type of the decision maker and wants to persuade the decision maker to choose an action in his favour by informing her of the states. The decision maker privately observes her type and chooses an action. An optimal action for the decision maker depends upon both her type and type-specific states. In equilibrium the expert can always inform the decision maker in the form of comparative statements and the decision maker also can partially reveal her type to the expert or public. The second and third chapters build a dynamic model of satisficing behaviour in which an agent’s “expected” payoff is explicitly introduced, where this expectation is adaptively formed. If the agent receives a payoff above her satisficing level she continues with the current action, updating her valuation of the action. If she receives a payoff below her satisficing level and her valuation falls below her satisficing level she updates both her action and satisficing level. In the second chapter, we find that in the long run, all players satisfice. In individual decision problems, satisficing behaviour results in cautious, maximin choice and in normal form games like the Prisoner’s Dilemma and Stag Hunt, they in the long run play either cooperative or defective outcomes conditional on past plays. In coordination games like the Battle of the Sexes, Choosing Sides and Common Interest, they in the long run coordinate on Pareto optimal outcomes. In the third chapter, we find that satisficing players in the long run play subgame dominant paths, which is a refinement of subgame perfection, and identify conditions with which they ‘always cooperate’ or ‘fairly coordinate’ in repeated Prisoner’s Dilemma and Battle of the Sexes games, respectively, and truthfully communicate in sender-receiver games. Proofs and simulations are provided in appendices.

Superhydrophobic surfaces are able to entrap gas pockets in-between surface roughness elements when submerged in water. These entrapped gas pockets give these surfaces the potential to reduce drag due to the overlying flow being able to locally slip over the gas pockets, resulting in a mean slip at the surface. This thesis investigates the different effects that slip and the texturing of the surface have on turbulence over superhydrophobic surfaces. It is shown that, after filtering out the texture-induced flow, the background, overlying turbulence experiences the surface as a homogeneous slip boundary condition. For texture sizes, expressed in wall units, up to $L^+ \lesssim 20$ the only effect of the surface texture on the overlying flow is through this surface slip. The direct effect of slip does not modify the dynamics of the overlying turbulence, which remains canonical and smooth-wall-like. In these cases the flow is governed by the difference between two virtual origins, the virtual origin of the mean flow and the virtual origin experienced by the overlying turbulence. Streamwise slip deepens the virtual origin of the mean flow, while spanwise slip acts to deepen the virtual origin perceived by the overlying turbulence. The drag reduction is then proportional to the difference between the two virtual origins, reminiscent of drag reduction using riblets. The validity of slip-length models to represent textured superhydrophobic surfaces can resultantly be extended up to $L^+ \lesssim 20$. However, for $L^+ \gtrsim 25$ a non-linear interaction with the texture-coherent flow alters the dynamics of the background turbulence, with a reduction in coherence of large streamwise lengthscales. This non-linear interaction causes an increase in Reynolds stress up to $y^+ \lesssim 25$, and decreases the obtained drag reduction compared to that predicted from homogeneous slip-length models.

<p>The paper begins with a short survey of monotone functions. The functions of bounded variation are introduced and some basic properties of these functions are given. Finally the jump function of a function of bounded variation is defined.</p>

The paper begins with a short survey of monotone functions. The functions of bounded variation are introduced and some basic properties of these functions are given. Finally the jump function of a function of bounded variation is defined.

We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths that have explicit guarantees on when they will return a feasible path. We phrase our guarantees and run time analysis in terms of the complexity of the desired solution (see k and λ below). In a sense, our algorithms are output sensitive, which is particularly desirable because there are no known bounds on the solution complexity amid arbitrary polygonal environments. Our first major result is an algorithm that given Ε, αs, αt, and a positive integer k either (i) verifies that every feasible path has a descriptive complexity greater than k or (ii) outputs a feasible path. The run time of this algorithm is bounded by a polynomial in n (the total number of obstacle vertices in Ε), m (the bit precision of the input), and k. This result complements earlier work by Fortune and Wilfong: their algorithm considers paths of arbitrary descriptive complexity (it has no dependence on k), but it never outputs a path, just whether or not a feasible path exists. Our second major result is an algorithm that given E, αs, αt, a length λ, and an approximation factor Ε, either (i) verifies that every feasible path has length greater than λ or (ii) constructs a feasible path that is at most (1+ Ε) times longer than the shortest feasible path. The run time of this algorithm is bounded by a polynomial in n, m, Ε-1, and λ. This algorithm is the result of applying the techniques developed earlier in our thesis to the previous approximation approaches. A shortcoming of these prior approximation algorithms is that they only search a special class of feasible paths. This restriction implies that the path that they return may be arbitrarily longer than the shortest path. Our algorithm returns a true approximation because we search for arbitrary shortest paths.

Since equity premium puzzle had long been a problem, many economists tried to give reasonable interpretations to the puzzle. I focus on the type of theories using bounded rationality as the answer to the problem. I am willing to find out that whether the puzzle still exists in recent decades. If it does exist, are the theories of bounded rationality still able to explain the puzzle? In the beginning, I introduce two theories referring to bounded rationality. Afterwards, I empirically analyze the data of the U.S., Japan and Euro-area by using a simpler model based on rationality. Interestingly, circumstances vary a lot from country to country. One theory may be suitable for one country but not for the others. Even so, the “suitable” theory fails to completely explain the whole tendency of variation during the observed period in the country. In the future, we still need to explore in depth of the puzzle.