J{\o}rgensen Number and Arithmeticity

A J{\o}rgensen group is a non-elementary Kleinian group that can be generated by two elements for which equality holds in J{\o}rgensen's Inequality. This paper shows that the only torsion-free J{\o}rgensen group is the figure-eight knot group, identifies all non-cocompact arithmetic J{\o}rgensen groups, and establishes a characterization of cocompact arithmetic J{\o}rgensen groups. The paper also defines and computes the J{\o}rgensen number of several non-cocompact Kleinian groups including some two-bridge knot and link groups.Comment: 27 pages, 2 figure

The arithmetic and geometry of two-generator Kleinian groups

textThis thesis investigates the structure and properties of hyperbolic 3-manifold groups (particularly knot and link groups) and arithmetic Kleinian groups. In Chapter 2, we establish a stronger version of a conjecture of A. Reid and others in the arithmetic case: if two elements of equal trace (e.g., conjugate elements) generate an arithmetic two-bridge knot or link group, then the elements are parabolic (and hence peripheral). In Chapter 3, we identify all Kleinian groups that can be generated by two elements for which equality holds in Jørgensen’s Inequality in two cases: torsion-free Kleinian groups and non-cocompact arithmetic Kleinian groups.Mathematic

Aesthetics in a Mathematics for Liberal Arts Project

We present and assess a project and its rubric developed and assigned in Mathematics for Liberal Arts, a general education course for non-science and non-business majors, to incorporate different skills including aesthetic design, written and oral communication, and mathematical analysis to tackle a common optimization problem with an aesthetic slant: construct a beverage can (i.e., right circular cylinder) of a given volume while taking into account the cost of materials (i.e., surface area) and aesthetic qualities (e.g., the golden ratio)

Motivation for Change in Heroin and Opiate Users

Opioid and heroin abuse is a continuing problem in the United States that has been increasing dramatically since 2000. Common treatment programs tend to use methadone and behavioral therapies that do not focus on motivational factors despite the research suggesting it is an important element to treatment retention and sustained abstinence. Motivation for the purposes of this study is defined as an individual’s inner reasons for change. The current study focused on differences in motivation for change among different substance abusers. We found that opiate and heroin abusers had higher motivational scores in comparison to other substance abusers. These results imply that treatment programs should focus on increasing motivation and explore the circumstances and factors that may hinder it

Why do People Blog: A Q Analysis of Perceptions for Blogging

The purpose of this article is to understand user perceptions of new media formats, in this case blogging. While much of the blog research identifies blogging in terms of blog types, this research identifies user perceptions of why they like to blog. By applying Q-methodology to the blogging process, this research asked bloggers to rank subjective statements of blogging. Factor analyses were then applied to the rankings, which provided three main user factors (perspectives) of blogging motivations: Memorians, Bonders, and Soap Boxers. These perspectives provide an alternative to traditional views of social media use and categories of subjective media experience

Employment Benefits from California Climate Investments and Co-investments

From the launch of California Climate Investments in 2013 through 2016, the state appropriated about $2.2 billion to 29 programs aimed at reducing GHGs. Of these, 13 were transportation programs that received nearly$1.8 billion in California Climate Investments, including the High-Speed Rail Project, the Affordable Housing and Sustainable Communities Program, the Transit and Intercity Rail Capital Program, the Clean Vehicle Rebate Project, and otherLow CarbonTransportation investments.How do these programs translate into jobs? Researchers at the UCLA Luskin Center for Innovation conducted the state’s largest study of the employment impacts of CCI transportation investments

Initial Trade Study for In-line Silver Sensor for Spacecraft Potable Water Systems

Ionic silver is currently baselined as the biocide for microbial control in potable water systems for future space exploration missions. In-line monitoring of silver ion concentration is desired for system feedback control to introduce and maintain sufficient and safe levels of biocide in the water. To date, NASA testing of silver biocide system prototypes has made use of an Ion-Selective Electrode (ISE) for in-line silver concentration measurements. However, known issues with ISE technology have continued to motivate a search for alternate sensor systems. Although devices capable of detecting silver are available for terrestrial applications, these systems are generally not well-suited for the unique demands of spaceflight. Desired attributes include: low weight, volume, and power consumption; stable, autonomous, and in-line measurement capability; long calibration lifetime; and limited maintenance requirements. This paper provides the results from a preliminary trade study conducted on three candidate silver sensor technologies: ISEs, Anodic Stripping Voltammetry (ASV), and Fiber Optic Chemical Sensors (FOCS). The review of these technologies includes the rationale for their selection, an overview of the principles of their operation, and a detailed assessment of their strengths and weaknesses relative to the anticipated requirements of future spacecraft applications. The study concluded that none of the currently-available versions of these technologies is suitable for immediate application to spacecraft systems; further technology development should be considered. To that end, recommendations for forward development work have been proposed and provided herein

Examining the Relationship between Parental Educational Expectations and a Community-Based Children’s Savings Account Program

Children’s Savings Account (CSA) program and parents’ educational expectations for their children. We examine survey data collected as part of the rollout and implementation of The Promise Indiana CSA program. Although results differ by parental income and education, results using the full sample suggest that parents are more likely to expect their elementary school-age children to attend college if they have a 529 account or were exposed to the additional aspects of the Promise Indiana program (i.e., the marketing campaign, college and career classroom activities, information about engaging champions, trip to a University, and the opportunity to enroll into The Promise). Parents who were both exposed to the additional aspects of the Promise Indiana program and have a 529 account are over three times more likely to expect their child to attend college than others, increasing to 13 times more likely among parents with no college education. Overall, results suggest a community-based CSA program – Promise Indiana – is associated with nontrivial benefits for families