Limiting operations for sequences of quantum random variables and a convergence theorem for quantum martingales

We study quantum random variables and generalize several classical limit results to the quantum setting. We prove a quantum analogue of Lebesgue's dominated convergence theorem and use it to prove a quantum martingale convergence theorem. This quantum martingale convergence theorem is of particular interest since it exhibits non-classical behaviour; even though the limit of the martingale exists and is unique, it is not explicitly identifiable. However, we provide a partial classification of the limit through a study of the space of all quantum random variables having quantum expectation zero.Comment: 11 pages, 0 figure

“Who Runs the World? Girls!” A Case Study on the Role that Stacey Abrams Has Played in Changing the African American Political Voice and American Political Realm as a Whole

Stacey Abrams is one of the most prominent up-and-coming politicians in America. From her controversial gubernatorial race in 2018 to her post-election voting rights efforts, she is consistently at the forefront of many political discussions and debates. Nonetheless, with all this notoriety, there has not been much research on her life and impact relative to her peers or predecessors. What makes Stacey Abrams as popular and accepted as she is to the public? How is she the same as other American politicians, both male, and female? Who is Stacey Abrams? This study focuses on answering these questions through a case study built on numerous sources and articles. The goal was to build means of comparison with Abrams at the center. Through this study, I was able to dissect the life of Ms. Abrams on many points that would allow for both the study to be done and for readers to learn about her origins. In the end, my main hope is that readers will be able to learn, understand, and appreciate how amazing Stacey Abrams is and take heed to the many efforts she is taking to make America a better place

Using GIS as a Tool for Mitigating Geologic Hazards and Managing Natural Disasters

GIS is a versatile tool that has widespread application before, during, and after catastrophic geologic events. This research project analyzes results from three recently published case studies each corresponding to a point along the crisis response timeline. Planning for various geologic crises is critical, as demonstrated by Tran and others (2009), who utilized GIS to analyze risk factors and map flood hazards in Vietnam. GIS is also an invaluable tool for search and research activities during a natural disaster. These situations require quick response to ensure fast resolution, and GIS can be rapidly deployed through a four step progression in a search and rescue operation (Pfau and Blanford, 2018). In the aftermath of geologic crises, GIS can be deployed to help distribute and coordinate disaster relief efforts. Using Leon County, Florida as a study area, Horner and Downs (2010) used GIS to create a distribution network for relief efforts in the event of a hurricane. While GIS is best known for its widespread use in disaster management planning, it is also an important tool for rapidly responding to emergencies and for organizing post-disaster relief efforts. These studies demonstrate that GIS technologies are highly versatile before, during, and after geologic crisis events. As such, GIS should be viewed as an important strategy in geologic crisis hazard management

Lifting-Line Predictions for Life and Twist Distributions to Minimize Induced Drag in Ground Effect

The elliptic lift distribution produces the minimum induced drag for a given wingspan and desired lift outside of ground effect. This distribution can be generated on any wing by using geometric and/or aerodynamic twist. However, in ground effect, the elliptic lift distribution is not necessarily that which minimizes induced drag. The present work uses a modern numerical lifting-line algorithm to evaluate how the optimum lift distribution varies as a function of height above ground. The algorithm is also used to obtain the twist distributions that should be applied to wings of varying aspect ratios and taper ratios to produce the optimum lift distribution in ground effect. The results of this work can be used to reduce takeoff distances on morphing wings, or wings that can actively change twist or camber during flight

Dimerization of Neural Cadherin in the Presence of Low Calcium

Cell-cell linkage is a necessity for proper tissue function and stability in many biological systems. One moiety that allows for the proper linking of cells to one another is a family of molecules known as cadherins. This family of proteins can be found within the membrane of many different types of cells and the extracellular portions of the cadherin proteins interact with those of other cells to link adjacent cells together via the formation of a dimer complex. The presence of calcium (Ca2+) is of crucial importance for the formation of this cadherin dimer. In this study, we focused on the dimerization of neural (N-) cadherin proteins in the presence of low calcium concentrations. Consideration of low calcium concentration is of particular importance due to the existence of N-cadherins at neurological synapses. N-cadherin is the marker for long term potentiation within synapses, an environment with exceptionally low Ca2+ concentration compared to that of normal extracellular space (40µm vs 1mM). We hypothesized that this low calcium content would decrease the fraction of cadherins that existed in the dimer conformation. In order to test this theory, we determined the equilibrium constants of N-cadherin at decreasing Ca2+ concentrations (1000µM, 100µM, and 40µM) at physiological pH. This experiment required using a chelator (EDTA) to trap the dimer for all three Ca2+ concentrations. Then, using size exclusion chromatography (SEC), the concentration of N-cadherin in the dimeric state was determined, from which the equilibrium constants were calculated. Circular Dichroism (CD) spectroscopy was also used to monitor the secondary structural changes of the N-cadherin protein at each Ca2+concentration. Results from this experiment are consistent with a change in the equilibrium to favor the monomeric state of N-cadherin at the lower Ca2+ concentrations found in neurological synapses. This observation implies that excitatory synapses have plasticity due to the weak dimerization affinity in the prevailing calcium concentration