Daniel Spector

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To Pei Chen, whose love and support lift me daily Abstract. In this paper we give simpler proofs of the classical continuity and lower semicontinuity theorems of Reshetnyak. In 1968, Reshetnyak [20] proved two important results concerning the continuity and lower semicontinuity of functionals with respect to weak-star convergence of measures. These theorems(More)
The neurocognitive effects of aluminum (Al) were studied in 35 hemodialysis patients. Higher Al levels were associated with a decline in visual memory. As Al levels increased, patients with lower vocabulary scores (a measure of premorbid intelligence) showed a decline in attention/concentration, frontal lobe functions, and on several neurocognitive(More)
This work presents some new characterizations of Sobolev spaces and the space of functions of Bounded Variation. Additionally it gives new proofs of continuity and lower semicontinuity theorems due to Reshetnyak. In the recent paper [12], Bourgain, Brezis, and Mironescu studied the limiting behavior of the semi-norm |f | W s,p (Ω) := Ω Ω |f (x) − f (y)| p(More)
BACKGROUND Early diagnosis and treatment are associated with an improved prognosis in blastomycosis. The diagnosis of blastomycosis may be missed by cytology, histopathology, culture, or serology. An enzyme immunoassay (EIA) for detection of Blastomyces dermatitidis galactomannan antigen in body fluids has been used for rapid diagnosis of blastomycosis in(More)
In this paper, we study nonlocal gradients and their relationship to classical gradients. As the nonlocality vanishes we demonstrate the convergence of nonlocal gradients to their local analogue for Sobolev and BV functions. As a consequence of these localizations we give new characterizations of the Sobolev and BV spaces that are in the same spirit of(More)
for their help during my stay here at Pittsburgh. Finally, I would like to thank the Department of Mathematical Sciences at Carnegie Mellon University for creating a comfortable environment of study. In particular, I want to thank Professor William J. Hrusa for being such an understanding and generous graduate advisor. Special thanks go to my family for(More)
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