Riemann-Roch for Toric Rank Functions

In this thesis we study toric rank functions for chip firing games and prove special cases of a conjectural Riemann-Roch. The original motivation for an investigation into this area of study came for the adaptation (due to Matt Baker) of Riemann-Roch into a graph theoretic analogue through the use of chip-firing games. Here, we collect known results and present new observations that indicate Riemann--Roch holds for trees and polygons. We also prove an asymptotic case of Riemann--Roch (i.e.~Riemann--Roch for divisors of large degree). Finally, we also provide magma code and computational evidence that Riemann--Roch holds for the toric rank function.Comment: Submitted for the requirements of Masters of Science in Mathematic

Intersection Structures on Secants of Grassmannians

Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to k-planes with the restriction that their intersection has a prescribed dimension. This thesis calculates dimensions of restricted, cyclic, and path geometric secants of Grassmannians and relate them to the analogous question for secants of Grassmannians via an incidence variety construction. Next, it defines a notion of expected dimension and gives a formula, which holds if the BDdG conjecture on non-defectivity of Grassmannians is true, for the dimension of all restricted secant varieties of Grassmannians. It also demonstrates example calculations in Macaulay 2 and points out ways to make these calculations more efficient. The thesis also shows a potential application to coding theory

Restricted Secant Varieties of Grassmannians

Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to $k$-planes with the restriction that their intersection has a prescribed dimension. We study dimensions of restricted secant of Grassmannians and relate them to the analogous question for secants of Grassmannians via an incidence variety construction. We define a notion of expected dimension and give a formula for the dimension of all restricted secant varieties of Grassmannians that holds if the Baur-Draisma-deGraaf Conjecture on non-defectivity of Grassmannians is true. We also demonstrate example calculations in Macaulay2, and point out ways to make these calculations more efficient. We also show a potential application to coding theory.Comment: 19 page

Atmospheric transport of organochlorines in the North Atlantic gyre

Chlorinated pesticides and polychlorinated biphenyls (PCB) circulating over the North Atlantic were measured during 1977-78 at Barbados and during the 1977 summer at the southern tip of Newfoundland. Total organochlorines were collected using a glass fiber filter backed up by a polyurethane foam trap, and were analyzed by electron capture gas chromatography on packed and glass capillary columns...

Status, sources and contamination levels of organochlorine pesticide residues in urban and agricultural areas: a preliminary review in central–southern Italian soils

Organochlorine pesticides (OCPs) are synthetic chemicals commonly used in agricultural activities to kill pests and are persistent organic pollutants (POPs). They can be detected in different environmental media, but soil is considered an important reservoir due to its retention capacity. Many different types of OCPs exist, which can have different origins and pathways in the environment. It is therefore important to study their distribution and behaviour in the environment, starting to build a picture of the potential human health risk in different contexts. This study aimed at investigating the regional distribution, possible sources and contamination levels of 24 OCP compounds in urban and rural soils from central and southern Italy. One hundred and forty-eight topsoil samples (0–20 cm top layer) from 78 urban and 70 rural areas in 11 administrative regions were collected and analysed by gas chromatography–electron capture detector (GC–ECD). Total OCP residues in soils ranged from nd (no detected) to 1043 ng/g with a mean of 29.91 ng/g and from nd to 1914 ng/g with a mean of 60.16 ng/g in urban and rural area, respectively. Endosulfan was the prevailing OCP in urban areas, followed by DDTs, Drins, Methoxychlor, HCHs, Chlordane-related compounds and HCB. In rural areas, the order of concentrations was Drins > DDTs > Methoxychlor > Endosulfans > HCHs > Chlordanes > HCB. Diagnostic ratios and robust multivariate analyses revealed that DDT in soils could be related to historical application, whilst (illegal) use of technical DDT or dicofol may still occur in some urban areas. HCH residues could be related to both historical use and recent application, whilst there was evidence that modest (yet significant) application of commercial technical HCH may still be happening in urban areas. Drins and Chlordane compounds appeared to be mostly related to historical application, whilst Endosulfan presented a complex mix of results, indicating mainly historical origin in rural areas as well as potential recent applications on urban areas. Contamination levels were quantified by Soil Quality Index (SoQI), identifying high levels in rural areas of Campania and Apulia, possibly due to the intensive nature of some agricultural practices in those regions (e.g., vineyards and olive plantations). The results from this study (which is in progress in the remaining regions of Italy) will provide an invaluable baseline for OCP distribution in Italy and a powerful argument for follow-up studies in contaminated areas. It is also hoped that similar studies will eventually constitute enough evidence to push towards an institutional response for more adequate regulation as well as a full ratification of the Stockholm Convention

Toxaphene and Other Organochlorines in Arctic Ocean Fauna: Evidence for Atmospheric Delivery

Residues of the insecticide toxaphene (polychlorinated camphenes, PCCs) and other organochlorines (OCs) were determined in air, snow, seawater, zooplankton, and benthic amphipods collected from an ice island in the Canadian Arctic. The simultaneous determination of OCs in the atmospheric, hydrologic, and biologic compartments provided evidence of an atmospheric link to polar food chains. PCCs were identified and quantified using capillary gas chromatography - negative ion mass spectrometry. The order of OCs abundance in arctic air was: hexachlorocyclohexanes (HCHs) > hexachlorobenzene > PCCs > polychlorinated biphenyls (PCBs) > chlordanes > DDTs. In seawater, PCCs were exceeded only by the HCHs. Concentrations of PCBs and PCCs in two samples of benthic amphipods were the highest of the OCs detected.Key words: Arctic, Canada, pollution, organochlorines, air, water, biotaMots clés: Arctique, Canada, pollution, organochlorés, air, eau, biot