458 citations
- Williams (United States)US124 papers
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4 papers · 1 filter
A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem
Nicholas A. Loehr, Bruce E. Sagan, Gregory S. Warrington
Consider lattice paths in Z^2 taking unit steps north (N) and east (E). Fix positive integers r,s and put an equivalence relation on points of Z^2 by letting v,w be equivalent if v…
First principles studies of the Born effective charges and electronic dielectric tensors for the relaxor PMN (PbMg1/3Nb2/3O3)
Narayani Choudhury, R. E. Cohen, Eric J. Walter
We report first principles density functional calculations of the Born effective charges and electronic dielectric tensors for the relaxor PMN (PbMg1/3Nb2/3O3). Visualization of th…
Correlation effects in the ground state of trapped atomic Bose gases
Wirawan Purwanto, Shiwei Zhang
We study the effects of many-body correlations in trapped ultracold atomic Bose gases. We calculate the ground state of the gas using a ground-state auxiliary-field quantum Monte C…
Positive eigenvalues and two-letter generalized words
Christopher Hillar, Charles R. Johnson, Ilya M. Spitkovsky
A generalized word in two letters and is an expression of the form in which the exponents , are nonzero real n…