We study the question of whether for each n there is an m �= n with λ(m) = λ(n), where λ is Carmichael’s function. We give a “near” proof of the fact that this is the case unconditionally, and a complete conditional proof under the Extended Riemann Hypothesis. –To Professor Carl Pomerance on his 65th birthday

Working papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded offi cial Federal Reserve Bank of Cleveland publications. The views stated herein are those of the authors and are not necessarily those of the Federal Reserve Ban...

S (in alphabetic order by speaker surname) 1. Speaker: Albert Atserias (UPC) Title: Sherali-Adams Relaxations and Indistinguishability in Counting Logics Abstract: Two graphs with adjacency matrices A and B are isomorphic if there exists a permutation matrix P for which the identity PTAP = B holds. Multiplying through by P and relaxing the permutation matrix to a doubly stochastic matrix leads ...

skin and hair, and is synthesized in melanosomes transferred from melanocytes. Although melanin plays an important protective role against UV light, over production and accumulation of melanin pigment it could create serious skin problems such as freckles, age spots, and melasma. Thus, the inhibition of melanogenesis has been the focus of medicinal and cosmetic treatments for skin depigmenting ...

Working papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded offi cial Federal Reserve Bank of Cleveland publications. The views stated herein are those of the authors and are not necessarily those of the Federal Reserve Ban...