5 research outputs found

    Dieudonné-type theorems for lattice group-valued kk-triangular set functions

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    summary:Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for kk-triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems

    American pure and applied mathematics, 1940-1975

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    Thesis (Ph. D. in History, Anthropology, and Science, Technology and Society (HASTS))--Massachusetts Institute of Technology, Program in Science, Technology and Society, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (pages 317-336).This study investigates the status of mathematical knowledge in mid-century America. It is motivated by questions such as: when did mathematical theories become applicable to a wide range of fields from medicine to the social science? How did this change occur? I ask after the implications of this transformation for the development of mathematics as an academic discipline and how it affected what it meant to be a mathematician. How did mathematicians understand the relation between abstractions and generalizations on the one hand and their manifestation in concrete problems on the other? Mathematics in Cold War America was caught between the sciences and the humanities. This dissertation tracks the ways this tension between the two shaped the development of professional identities, pedagogical regimes, and the epistemological commitments of the American mathematical community in the postwar period. Focusing on the constructed division between pure and applied mathematics, it therefore investigates the relationship of scientific ideas to academic and governmental institutions, showing how the two are mutually inclusive. Examining the disciplinary formation of postwar mathematics, I show how ideas about what mathematics is and what it should be crystallized in institutional contexts, and how in turn these institutions reshaped those ideas. Tuning in to the ways different groups of mathematicians strove to make sense of the transformations in their fields and the way they struggled to implement their ideological convictions into specific research agendas and training programs sheds light on the co-construction of mathematics, the discipline, and mathematics as a body of knowledge. The relation between pure and applied mathematics and between mathematics and the rest of the sciences were disciplinary concerns as much as they were philosophical musings. As the reconfiguration of the mathematical field during the second half of the twentieth century shows, the dynamic relation between the natural and the human sciences reveals as much about institutions, practices, and nations as it does about epistemological commitments.by Alma Steingart.Ph.D.in History, Anthropology, and Science, Technology and Society (HAST

    Inductive Pattern Formation

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    With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete spacetime model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat

    Annual register. 1919-20

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    Imprint varies in volumes preceding 1893/94

    Spacelab Science Results Study

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    Beginning with OSTA-1 in November 1981 and ending with Neurolab in March 1998, a total of 36 Shuttle missions carried various Spacelab components such as the Spacelab module, pallet, instrument pointing system, or mission peculiar experiment support structure. The experiments carried out during these flights included astrophysics, solar physics, plasma physics, atmospheric science, Earth observations, and a wide range of microgravity experiments in life sciences, biotechnology, materials science, and fluid physics which includes combustion and critical point phenomena. In all, some 764 experiments were conducted by investigators from the U.S., Europe, and Japan. The purpose of this Spacelab Science Results Study is to document the contributions made in each of the major research areas by giving a brief synopsis of the more significant experiments and an extensive list of the publications that were produced. We have also endeavored to show how these results impacted the existing body of knowledge, where they have spawned new fields, and if appropriate, where the knowledge they produced has been applied
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