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Journals and Conferences
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)
The main results of this paper are new characterizations of W (Ω), 1 < p < ∞, and BV (Ω) for Ω ⊂ R an arbitrary open set. Using these results, we answer some open questions of Brezis  and Ponce .
In this paper we give simpler proofs of the classical continuity and lower semicontinuity theorems of Reshetnyak. 1. Main result In 1968, Reshetnyak  proved two important results concerning the continuity and lower semicontinuity of functionals with respect to weak-star convergence of measures. These theorems are used in a variety of areas in the… (More)
In this paper, we prove L estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are VMO. In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.
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)
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)