Thesis (Ph. D.)--University of Chicago, 1917. / "Private edition, distributed by the University of Chicago Libraries, Chicago, Illinois, 1920." "Reprinted from Transactions of the American mathematical society, Vol. 21, No. 4, October, 1920." Includes bibliographical references. Also available on the Internet.

No description available.

Inaug.-Diss.--Uppsala. / Errata slip inserted. Extra t.p., with thesis statement, inserted. Includes bibliographical references (p. [55]).

Inaug.-Diss.--Uppsala. / Errata slip inserted. Extra t.p., with thesis statement, inserted. Bibliography: p. [55]

Thesis (Ph. D.)--University of Chicago, 1917. / Vita. "Private edition, distributed by the University of Chicago Libraries, Chicago, Illinois, 1920." "Reprinted from American journal of mathematics, vol. XLII, no. 4, Oct., 1920." Includes bibliographical references. Also available on the Internet.

No description available.

The subject of this thesis is the fractional order Sobolev space, H[superscript]r[subscript]p, as considered by Nikol'skii; the goal is to demonstrate an imbedding theorem for H[superscript]r[subscript]p analogous to the classical imbedding theorem for W[superscript]m[subscript]p which was first shown by Sobolev. The properties established here for spaces H[superscript]r[subscript]p defined over all of Rn, including completeness and imbedding theorems, are demonstrated by a technique involving the approximation of functions in those spaces by entire functions of the exponential type. Properties of such entire functions, which are of interest in theire own right, are developed in a separate chapter. An extension theorem for differentiable developed in a separate chapter. An extension theorem for differentiable functions defined over an open subset of Rn is also proved. / Science, Faculty of / Mathematics, Department of / Graduate

In this thesis we are concerned with obtaining an integral representation of a class of nonlinear additive and biadditive functionals on function spaces of measurable functions and on L[superscript] p-spaces, p > 0 . The associated measure space is essentially atom-free finite and o-finite. Also we are concerned to the extend the presence of atoms in a measure space complicates the representation theory for functionals of the type under consideration here. A class of nonlinear transformations on L[superscript] p-spaces, 1 ≤ p ≤ ∞, called Urysohn operators. [11] taking measurable functions to measurable functions is studied and we describe an integral representation for this class when the associated measure space is an arbitrary 0-finite measure space and this characterization extends our previous results where the measure space considered was atom-free. / Science, Faculty of / Mathematics, Department of / Graduate

Students commonly engage in problem behaviors, yet teachers report handling difficult behavior as their biggest challenge. Some research over the last few decades has used functional analyses (FAs) to determine the function of student’s problem behavior and then developed functional-based interventions based on the FA findings. Despite the success of the studies, research has indicated traditional FA methodologies are not always feasible for teachers and/or schools. Therefore, a need still exists to develop better and more efficient ways to train teachers how to conduct FAs in the classroom. Thus, the purpose of the current study was to evaluate the effectiveness of using virtual video models to train future teachers how to conduct trial based functional analyses (TBFAs). Additionally, the current study sought to assess if the participants could generalize their skills learned virtually to an in person setting. Three future teachers enrolled in education courses at a southeastern university participated in the study and watched video models of each of the TBFA conditions (attention, demand, tangible, and ignore). After watching the videos, participants were then asked to conduct each trial virtually, and then complete each trial the following day in person. A multiple baseline design across participants was used, and results indicated the videos were effective at teaching the participants to conduct a TBFA. Specifically, all three future teachers successfully conducted every trial of a TBFA with high procedural integrity virtually. The virtual training then generalized well into an in person setting, with only one participant needing additional feedback. Additionally, results indicate the virtual intervention was socially valid for all participants. Limitations and directions for future research are also discussed.

The trial-based functional analysis (TBFA) has recently emerged for practitioners as a method to determine the function(s) of challenging behavior in natural contexts such as the classroom or residential settings. Comparisons between TBFA and other functional analyses (FA) results have shown high correspondence when identifying the function(s) of challenging behavior. Currently, the TBFA has mainly been conducted in classroom settings with teachers or paraprofessionals. Although important in educational contexts, it is unknown if the TBFA would identify the same function(s) of challenging behavior across different settings, thus possibly limiting its utility. The purpose of the current study was to compare the results of a parent-conducted TBFA in the child’s home and at a university-based autism clinic. TBFA results found minimal differences regardless of the setting, suggesting that the TBFA procedures can be conducted in clinics or at home while producing similar findings. Social validity results for two of the three families were identical across settings, suggesting they had no preference for where to conduct the TBFA or any of the conditions. However, one caregiver preferred the escape and tangible conditions over the attention condition. The same caregiver also preferred the home TBFA over the clinic TBFA. High procedural integrity was reported on the author’s ability to facilitate the TBFA procedures with the families. Taken together, these data will help to guide and inform future treatment recommendations for families.