The Necessary And Sufficient Condition for Generalized Demixing

Demixing is the problem of identifying multiple structured signals from a superimposed observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. We present a new solution to determine whether or not a specific convex optimization problem built for generalized demixing is successful. This solution will also bring about the possibility to estimate the probability of success by the approximate kinematic formula

Urbanization Process and Land Use Policy

Within a framewaork of New Economic Geography (NEG) model, this paper intends to show that urbanization rate in an isolated region is determined as a synthetic rerult of rational behavior of each socio-economic agent. In particular, a model is constructed with bearing to explain the urbanization process in Chaina in mind such that the role of government in managing land use allocation is explicitly incorporated and its policy effects can be evaluated. Some results of theoretical analysis and numerical simulation analysis are contrasted with the ones in Fujita and Krugman (1995) incorporating land into an NEG model as well.

Three Essays on Financing Corporate Activities

This study answered how firms finance their corporate activities and how accounting and marketing activities impinge on these financing activities. The findings pointed out some relatively new financing sources other than traditional equity and debt

Synthesis of heterocycles: Versatile aryne annulations via Michael addition, [3+2] cycloaddition, and palladium catalysis

Arynes are one of the most interesting species in organic synthesis because of their remarkably high reactivity. Although the structures of arynes were confirmed more than sixty years ago, the study of aryne chemistry was largely hindered by the harsh conditions needed to generate these reactive intermediates. Very recently, the discovery of o-silylaryl triflates, which can generate the corresponding arynes under very mild conditions, opened the way for a more thorough investigation into the remarkable chemistry of arynes. In the past several years in the Larock group, many aspects of the chemistry of arynes have been studied systematically and a variety of useful synthetic methodologies employing arynes have been discovered. The simple arylation of amines, phenols, carboxylic acids, carbamates, and sulfonamides by arynes was investigated first. It has also been discovered that the carbanion generated from nucleophilic attack on an aryne is able to further attack a neighboring electrophile to afford cyclization products. These tandem coupling-cyclization reactions have been employed to prepare various heterocycles exhibiting interesting biological activities. Furthermore, many heterocycles can be easily synthesized by the [3+2] cycloaddition of arynes by 1,3-dipoles. This dissertation reports in Chapters 1 and 2 one new methodology in each of the last two areas. Palladium-catalyzed reactions have found numerous applications in organic synthesis, especially in processes involving C-C bond or C-X bond formation. The Larock research group has developed numerous palladium-mediated annulations, which generally involve multiple bond formation. These methodologies afford efficient and general protocols for the preparation of biologically active heterocycles. In the last several years, the Larock group and other groups have been extending these metal-catalyzed annulation processes to arynes. By taken advantage of both the high reactivity of arynes and the high catalytic activity of palladium, polycyclic aromatic and heteroaromatic hydrocarbons can be synthesized from aryl halides. Chapters 3 and 4 describe two new palladium-catalyzed annulation reactions of arynes with aryl halides, in which C-C and C-N bonds can be formed simultaneously. The methods presented in this dissertation cover different areas of aryne chemistry and certainly underscore the synthetic versatility of arynes