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The purpose of this paper is to present a discussion on the basic fundamentals of the theory of sets. Primarily, the discussion will be confined to the study of cardinal and ordinal numbers. The concepts of sets, classes of sets, and families of sets will be undefined quantities, and the concept of the class of all sets will be avoided.

The purpose of this composition is to develop a rigorous, axiomatic proof of the comparability of the cardinals of infinite sets.

Thesis (Ph. D.)--University of Chicago, Dept. of Philosophy, March, 2001. / Includes bibliographical references. Also available on the Internet.

This thesis is on ordered pairs of cardinal numbers.

No / Precortical color vision is mediated by three independent opponent or cardinal mechanisms that linearly combine receptoral outputs to form L/M, S/(L+M), and L+M channels. However, data from a variety of psychophysical and physiological experiments indicate that chromatic processing undergoes a reorganization away from the basic opponent model. Frequently, this post-opponent reorganization is viewed in terms of the generation of multiple ¿higher order¿ chromatic mechanisms, tuned to a wide variety of axes in color space. Moreover, adaptation experiments have revealed that the synthesis of these mechanisms occurs at a level in the cortex following the binocular integration of the inputs from each eye. Here we report results from an experiment in which the influence of chromatic adaptation on the perceived visual location of a test stimulus was explored using a Vernier alignment task. The results indicate that not only is positional information processed independently within the L/M, S/(L+M), and L+M channels, but that when adapting and test stimuli are extended to non-cardinal axes, the existence of multiple chromatically tuned mechanisms is revealed. Most importantly, the effects of chromatic adaptation on this task exhibit little interocular transfer and have rapid decay rates, consistent with chromatic as opposed to contrast adaptation. These findings suggest that the reorganization of chromatic processing may take place earlier in the visual pathway than previously thought.

Thesis (M.A.)--The University of North Carolina at Greensboro, 2010. / Directed by Jerry Vaughan; submitted to the Dept. of Mathematics and Statistics. Title from PDF t.p. (viewed Jul. 14, 2010). Non-Latin script record Includes bibliographical references (p. 30).

Thesis advisor: James Keenan / This dissertation argues that humility is a cardinal virtue that governs our ecological relationality. I define humility as the virtue of knowing and valuing the truth of our place in the world as interdependent beings. Humility is acquired via the practice of other-centeredness and other-acceptance and enabled by the “graces" of self-doubt and self-affirmation. A global survey of recent Christian scholarship on environmental issues and magisterial Roman Catholic teaching supports three conclusions: 1) interconnectedness characterizes human relationships with creation; 2) current ecological crises indicate the presence of sin and 3) we need to understand our place within creation and appreciate other-centered ways of knowing. Utilizing these three themes, I expand upon James Keenan's framework of rethinking cardinal virtues in terms of human relationality in order to account for an underdeveloped aspect of human relationality, that is, ecological relationality. I propose a more robust account of humility as a mean between two equally problematic extremes: pride and self-deprecation. Furthermore, humility helps us better identify sin both by recognizing how pride and self-deprecation can lead to indifference, understood as a failure to bother to love, that stems from our strength, and by rejecting the isolation that enables the sin of indifference so understood. The final chapter addresses how humility can be understood and cultivated in the United States today. In particular, I argue that the adoption of a plant-based diet generally fosters humility in individuals living in wealthy nations with high rates of meat consumption. In conclusion, I suggest that Catholics reinvigorate the Lenten penitential practice of Friday abstinence from meat by seeing it also as an opportunity to foster the virtue of humility. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Theology.

This project explores the design of a rail-trail in the Midwest utilizing visual preference methods with ArcGIS and 3D visualization technologies. It has been found that visually preferred environments are more enjoyable, more frequently used places that positively influence overall health of individuals and communities. Aesthetic attributes of environments, in particular, are directly related to overall physical, social, and mental health. Research conducted on environment, behavior, and human preference suggests that environmental settings can influence perceptions of quality of life, sense of place, and mental states, which affect stress levels, which are physically manifested in the body (Kaplan 1982, 1987, 1995, 1998; Lusk 2002; RWJF 2006; Shafer 2000).One way of providing healthier environments is by improving aesthetics according to the visual characteristics that promote understanding and exploration of the environment, specifically perceptual values of smoothness, density, and landcover type (Kaplan and Kaplan 1998; Brown 1994). This technique allows social issues such as public opinion and health benefits to be integrated with environmental and cultural issues to thoroughly address design and management solutions, especially in recreation areas. Spatial Analyst and 3D Analyst extensions facilitated the analysis by adapting the United States Forest Service visual analysis framework to the visual preference research to assess the use of GIS and 3D technology in a design oriented application. This included the addition of a 3D element to allow the designer to experience how a scene changes through space and time. Use of 2D, 3D, and animation capabilities of ArcGIS assisted in the visualization of landscape preference from the trail-user's point of view to assess the perceptual qualities of the landscape along the Cardinal Greenway.The project findings outline the capabilities of ArcGIS 3D Analyst and Spatial Analyst for mapping and measuring these perceptual and physical landscape qualities. The resulting design concepts reflect the findings of this study. It is anticipated that the process followed could be adapted and applied to recreation areas in similar geographic regions, and thereby advance daily recreation and lifestyle change for healthier individuals and communities. / Department of Landscape Architecture

This is a study of educational aims discourses (aims-talk) in the Journal of Negro Education between 1932 and 1953. In this era of segregation, economic depression, and war, educators and other champions of education for African Americans struggled to define and then develop objectives, goals, and curricula for African American students in secondary schools and colleges. This study considers the different aims discourses, how they evolved, and how they were affected by economic depression and war. Using literary analysis, this historical analysis considers the influence of philanthropy, The Cardinal Principles, segregation, the American social order, democracy, and the “peculiar” needs of African Americans as themes within the disparate discourse. This study uses the taxonomy of critical race theory to inform the discourse and supplement the theory of whiteness as property with the related theory that education is also property. The study’s analysis is informed by Nel Noddings’ theoretical position that aims can be used as a critique of society. Finally, this study adds empirical evidence to support Eddie S. Glaude, Jr.’s theory of nation language. The conditions of segregation significantly influenced the discourse of the 100 authors and the 137 articles considered by the study. The conditions of segregation did not change during the period of this study but the economy improved and war provided more job opportunities for African Americans. While there was a heightened call for the elimination of segregation and resetting of the social order during World War II in the Journal of Negro Education, the educational condition of the African American as reported by these researchers did not significantly evolve over the same period. However, a new discourse developed in which both philanthropists and African-American educators recognized the need for some combination of industrial and academic education for their students. The period examined in this study begins with the publication of the first issue of the Journal of Negro Education in 1932 and ends on the eve of the Brown vs. Board of Education decision in 1953. / text