Thesis--M. Phil., University of Hong Kong, 1978.

Following Hopkins and Singer, we give a definition for the differential equivariant K-theory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant K-theory is developed explicitly. We also construct a pushforward map which parallels the topological pushforward in equivariant K-theory. An analytic formula for the pushforward to the differential equivariant K-theory of a point is conjectured, and proved in the boundary case and for ordinary differential K-theory in general. The latter proof is due to K. Klonoff. / text

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

This thesis consists of three topics. The first one is on quadratic Waring-Goldbach problems. The second topic is about some additive problems involving fourth powers. The last topic is to consider an average result for the divisor problem in arithmetic progressions. Chapter 1 is an introduction. In Chapter 2 the Lagrange equation with almost prime variables is studied, based on a method of Heath-Brown and Tolev. The techniques involve the circle method and the sieve method in analytic number theory. It is established that every sufficiently large integer, congruent to 4 modulo 24, can be represented as the sum of four squares of integers, each of which has at most four prime factors. In order to derive the desired result, it is important to study the asymptotic formula for a smooth counting function involving the sum of one square of a prime number and three squares of integers in arithmetic progressions. For this purpose, the square sieve of Heath-Brown and the Kloosterman refinement are employed. This is the main task of Chapter 3. Chapter 4 is devoted to the investigation on the sum of four squares of primes and K powers of two. Inspired by the work of Wooley, this problem is dealt with by applying the linear sieve instead of the four dimensional vector sieve. The theme of Chapter 5 is the three squares theorem with almost prime variables, firstly investigated by Blomer and Br?udern. A sharper result is obtained, in this chapter, by developing the three dimensional weighted sieve. In Chapter 6, the main concern is the exceptional set for the sum of fourth powers. By developing Vaughan's p-adic iteration method, some new estimations are established. The new estimations improve upon the earlier result obtained by Kawada and Wooley. As a consequence of the new estimates, it is established that every sufficiently large integer under a natural congruence condition can be expressed as a sum of six fourth powers of primes and six fourth powers of integers. Moreover, a pair of diagonal quartic forms is considered. In Chapter 7, it is shown that a pair of diagonal quartic equations with 23 variables has nonzero integral solutions under certain reasonable conditions. The purpose of Chapter 8 is to consider a Waring-Goldbach type problem involving twelve fourth powers of primes and one fourth power of a positive integer. The idea of proof is to combine Chen's switching principle and Iwaniec's linear sieve. A new result is obtained, which refines that of Ren and Tsang on this topic. In the last chapter, a distribution problem for the divisor function on arithmetic progressions is investigated. Denote by ?q,b(X) the error term in the divisor problem in the arithmetic progression b(mod q). New asymptotic formulae for the variance A(q, X) =?qb=1|?q,b(x)|2 for X1=4+E ?· q?·X1=2-E and X1=2+E ? q ·?X1-E are derived. The distinct behaviors of A(q, X) in these two ranges are unveiled. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

My dissertation studies the application of economic theory in various settings. Each chapter begins with a basic intuition or question, and then develops the most appropriate methods to investigate. The questions addressed and results generated are interesting both from a theoretical and practical standpoint. The first chapter provides a general model for analyzing affiliate marketing contracts in online advertising, and presents a novel explanation for the diversity of contracts which exist in the industry. Affiliate marketing is an online, pay-per-performance advertising industry, where advertisers must specify the user action (impression of the ad, user click, final sale, etc.) on which to remunerate publishers "affiliates" who advertise on their behalf. In practice, many different actions are utilized. The main result here is that if users are heterogenous, and publishers know more about their users than advertisers, then the specified action serves as a selection mechanism that incentivizes the publisher to advertise only to a desirable set of users. Also, choosing the appropriate action minimizes expenses to the advertiser. When there are many different user types, each with varying worth to both the advertiser and publisher, achieving both of these goals requires a rich set of contractible actions. More generally, the approach used here can be implemented in other environments where asymmetric information and adverse selection play a role. The second chapter studies the rebound effect, or the increased use of energy services following an increase in the efficiency of that service. This effect is widely studied in the literature, but it usually only considered in a single-service environment. Such a framework ignores the potentially significant indirect rebound effects which occur through increased purchasing power for other services, and does not allow for joint efficiency improvements across many services, what we call ``efficiency correlation.'' We develop a household production model with two energy services and distinct but simultaneous efficiency changes to test the implications of efficiency correlation on net energy elasticities and the rebound effect. Positively correlated efficiency choices across end-uses increase technically feasible energy reductions but also drive additional rebound responses that erode these savings. Moreover, we find that negative correlation can significantly reverse any energy savings (e.g. a household installs energy-saving window panes but then trades in their sedan for a SUV), but that current Federal efficiency standards make this scenario unlikely. This paper offers new insight into a host of additional behavioral responses to efficiency improvements, particularly the incidence of efficiency correlation across different energy services, and highlights its implication for realized energy savings. The third chapter studies the effect of negative equity and landlock on household mobility and employment. This paper incorporates a novel friction -- that households which are both underwater and insolvent cannot sell their home -- into a search model where agents face a restriction of job opportunities based on their net asset positions. Ultimately, agents in deep-enough negative equity and insolvency quit searching altogether, reducing labor supply and mobility. Data from the Survey of Consumer Finances present empirical evidence which is consistent with this result. The welfare gains from removing this friction suggest that a median income earner is willing to pay about 2% of her income, or between 3-4 percentage points in additional interest on her debt to remove this constraint. This suggests that the landlock effect represents an incomplete lending market. If feasible, homeowners would be willing to compensate lenders to swap-out mortgage debt with other loans which do not constrain mobility. Removing the landlock restriction also results in higher search effort and lower durations, as households are better off being able to search and obtain better employment opportunities when they are underwater, rather than receiving interest reductions typical of current mortgage-finance policy. / text

Not available / text

Not available / text

Not available / text

<p> This dissertation studies the applications of reputation games in social media and finance as well as decision games in political economy. Chapter 1 develops a reputation game in which a biased but informed expert makes a statement to attract audiences. The biased expert has an ideological incentive to distort his information as well as having a reputation concern. The expert knows that his expertise may vary in different topics, while the audiences cannot identify such differences. The biased expert is more likely to announce his favorite message when he knows less about it. Moreover, the biased expert is less willing to lie when the audiences have better outside options, and such improvements in outside options may benefit both the expert and the audiences. </p><p> Chapter 2 studies a credit rating game with a credit rating agency(CRA), an issuer and an investor. The privately informed and biased CRA provides a rating on the issuer's project, and the investor decides to purchase the project or not according to the report. As long as the CRA obtains a contract, he will inflate the rating. When the default risk is high, the CRA tells the truth. Moreover, he is more likely to tell the truth when the issuer's private benefit is larger. When the default risk is low, the CRA sends a good rating. He is more likely to inflate the rating if the issuer has a higher private benefit. </p><p> Chapter 3 presents a model in secessions and nationalism, with a special emphasis on the role of civil war. In our model, a disagreement on secession between the central government and the minority group leads to disastrous military conflicts. As a result, the tremendous potential cost of the war distorts the political choice of the minority group, and helps the central government to exploit them both economically and politically. Several key ingredients, such as population, per capita income and perceived winning chance of the civil war, play an essential role in the decision making process of the minority group. I also conduct an empirical test of this model, which supports the major findings stated above.</p>

No description available.