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)
It is known that Escherichia coli methionine mutants can grow on both enantiomers of methionine sulfoxide (met(o)), i.e., met-R-(o) or met-S-(o), indicating the presence of enzymes in E. coli that can reduce each of these enantiomers to methionine (met). Previous studies have identified two members of the methionine sulfoxide reductase (Msr) family of(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)
It is known that reactive oxygen species can oxidize methionine residues in proteins in a non-stereospecific manner, and cells have mechanisms to reverse this damage. MsrA and MsrB are members of the methionine sulfoxide family of enzymes that specifically reduce the S and R forms, respectively, of methionine sulfoxide in proteins. However, in Escherichia(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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