This project centers around finding specific examples of quintic polynomials that were and were not solvable. This helped to devise a method for finding examples of solvable and unsolvable quintics.

We study the Cohen-Macaulay property of Rees algebras of modules of Kähler differentials. When the module of differentials has projective dimension one, it is known that condition $F_1$ is sufficient for the Rees algebra to be Cohen-Macaulay. The converse was proved if the module of differentials is already $F_0$. We weaken the condition $F_0$ globally by assuming some homogeneity condition.<br> <br> We are also interested in the defining ideal of the Rees algebra of a Jacobian module. If the Jacobian module is an ideal, we prove a formula for computing the defining ideal. Using the formula, we give an explicit description of the defining ideal in the monomial case. From there, we characterize the Cohen-Macaulay property of the Rees algebra.<br> <br> In the last chapter, we study Gorenstein linkage mostly in the graded case. In particular, we give an explicit example of a class of monomial ideals that are in the homogeneous Gorenstein linkage class of a complete intersection. To do so, we prove a Gorenstein double linkage construction that is analogous to Gorenstein biliaison.

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Let S ⊆ V be an arbitrary subset of vertices of a graph G = (V,E). The differential ∂(S) equals the difference between the cardinality of the set of vertices not in S but adjacent to vertices in S, and the cardinality of the set S. The differential of a graph G equals the maximum differential of any subset S of V . A set S is called a zero set if ∂(S) = 0. In this thesis we introduce the study of zero sets in graphs. We give proofs of the existence of zero sets in various kinds of graphs such as even order graphs, bipartite graphs, and graphs of maximum degree 3. We also give proofs regarding the existence of graphs which contain no zero sets and the construction of zero-free graphs from graphs which contain zero sets.

This dissertation includes three chapters. The first and second chapters are related to economics of immigration, and the last one is about environmental economics. The first chapter studies people who work and live in the US on work visas such as H-1B, and compares them to natives. In this chapter I examine whether or not there exists any wage premium for or against college graduate immigrants who are on work visa compared to college graduate natives. I also check for any change of such a premium from 2003 to 2010. On the contrary to the common belief that foreign workers are cheap labor force, my results show that skilled immigrants holding temporary work visas on average have a significant wage premium over natives, and this premium has even increased significantly from 2003 to 2010 (from 14% to 22%). My results show that such a wage premium is different for men, women, and countries of origin, but I found no evidence supporting different premiums across different fields of study. The second chapter of this dissertation studies the dynamics of the earnings gap between those immigrants and US-born individuals with bachelor's degrees or higher in science and engineering fields. The research question is that in case a gap exists for or against immigrants, how is it changing with the amount of time immigrants reside in the United States? I employ cross-sectional and longitudinal approaches to answer this question, and study the earnings gap between three groups of immigrants (based on the current residency status) and natives at entry and over time. I also compare natives with immigrants who migrated to the United States on different types of visas (permanent residence visa, work visa, study visa, and dependent visa). Results show that, upon arrival, immigrants on average have a considerable premium over the US-born, and this gap, surprisingly, even gets bigger with an approximate rate of 0.25% for the first 5-10 years of immigrants' residence in the US. This phenomenon could be due to the higher level of abilities and motivation among immigrants compared to natives. Another reason can be the selectivity among immigrants, meaning that more successful stays and others return. Unfortunately, due to the lack of information in data regarding these issues, they could not be controlled for in my models. The last chapter is about environmental economics. This chapter exploits a daily time series data on pollen count and PM2:5 level from 2009 to 2015 to study the separate impacts of PM2:5 and pollen on the number of total, in-patient, and out-patient respiratory hospital admissions within different age groups in the Reno/Sparks metropolitan area in Northern Nevada. The results show that although PM2:5 has a positive impact on the number of out- patient admissions in most of the age groups, there is no evidence that shows any relationship between the pollen count and the number of in-patient or out-patient respiratory admissions. / Ph. D.

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Chow Shing Yuk. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 64-66). / Abstracts in English and Chinese. / Chapter Chapter 1: --- Introduction --- p.1 / Chapter Chapter 2: --- Literature Review --- p.4 / Chapter 2.1 --- First-Generation Studies --- p.4 / Chapter 2.2 --- Second-Generation Studies --- p.5 / Chapter 2.3 --- Third-Generation Studies --- p.7 / Chapter Chapter 3: --- Empirical Methodology --- p.13 / Chapter 3.1 --- Fixed Effect Estimation --- p.13 / Chapter 3.2 --- Within-twin Differencing --- p.14 / Chapter 3.3 --- Adjustment for Measurement Errors --- p.15 / Chapter 3.4 --- Value of Within-twin Differencing --- p.16 / Chapter Chapter 4: --- Data Descriptions --- p.29 / Chapter 4.1 --- Twins Data --- p.29 / Chapter 4.2 --- Non-twins Data --- p.32 / Chapter Chapter 5: --- Empirical Results --- p.35 / Chapter 5.1 --- Cross Sectional Results: Twins Sample --- p.35 / Chapter 5.2 --- Within-twin Differencing --- p.42 / Chapter 5.3 --- Cross Sectional Results: Non-twins Sample --- p.45 / Chapter 5.4 --- Female Results --- p.48 / Chapter Chapter 6: --- Conclusion --- p.50 / Tables --- p.52 / Appendix l: Some Other Thoughts on Marriage Premium --- p.60 / References --- p.64

This master’s thesis deals with the design of equipment for testing differentials. The aim of the thesis is therefore the design of a special device that will be able to measure the steady and transient characteristics of differentials. Master’s thesis is divided into four chapters. The first chapter points out the disadvantages of fully open and closed differentials, the second deals with a basic overview of the structures and design of self-locking differentials. The third chapter deals with research of existing devices that test and measure the characteristics of differentials. The fourth chapter then discusses the possible drives of the tested unit. The fifth chapter focuses on the actual construction design of the test equipment. The subsequent sixth chapter then solves the strength calculations of the chosen structural elements of this device.

Master of Science / Department of Agricultural Economics / Glynn T. Tonsor / The purpose of this analysis is to examine two aspects of price analysis in the stocker industry in order to better assist producers making purchasing decisions. One analysis looks at forecasting value of gain, while the second looks at drivers of price differentials between calves and yearlings. When analyzing forecasts on value of gain, weekly data was collected to compare a naïve approach and futures market implied basis-adjusted approaches that include one to five years of historical average basis. This allowed for the assessment of five different models for nine scenarios. The conclusions from this were inconsistent with what was hypothesized and the naïve approach was either worse or no better when compared to using the futures market implied basis-adjusted approaches to forecast value of gain. The drawback to this analysis was that it was solely influenced by error on forecasting the selling price and in future work a forecasting horizon will be incorporated on the buying price. In order to analyze the price premiums and discounts between calves and yearlings, a confirmation, update and expansion were completed following monthly models by Marsh (1985). Three elements are considered when predicting price premiums and discounts between two weight classes; cost of gain (proxied by corn price), slaughter price, and seasonality. Estimated models in the confirmation for years 1972 to 1982 and the update for years 1973 to 2013, show that premiums and discounts are influenced by expected changes in corn price and/or slaughter price, but not highly affected by seasonality. However, in the expansion for years 1993 to 2013, corn price, slaughter price, and seasonality were all significant to the models and in higher magnitude when compared to those results in the confirmation and update. Understanding the relationships between all variables in these models allows producers in the cattle-feeding industry to make management decisions based on current marketing conditions and trends.

The thesis aims at identifying the reasons behind the heterogeneous inflation performance of countries across Central and Eastern Europe. The impact of a large number of variables is being assessed in a dynamic panel data model covering 20 countries over the period 2003-2013. The empirical results suggest that cross-country differences in inflation are attributed to the structure of the economy, to the capital deepening effects and openness. Along with the structural factors, cyclical positions also prove to be of particular importance in explaining inflation across the region, since during the last decade most of the Central and Eastern European countries have experienced fast GDP growth, a credit boom and increased domestic demand that in turn fueled inflation.