We present a new approach to deal with Fraenkel’s conjecture, which describes how the integers can be partitioned into sets of rational Beatty sequences, in the case where the numerators of the moduli are equal. We use this approach to give a new proof of the known n = 4 case when the numerators are equal.

inspected n = 213 Full text articles retrieved n = 17 Full text articles inspected n = 17 Articles for appraisal and data extraction n = 17 Excluded n = 196 Not primary research = 91 Not imatinib = 10 Not chronic phase CML = 20 Biological/preclinical/genetic studies = 46 Not first-line treatment of CML = 16 Animal studies = 2 Other = 11 (complications 9, outcome measures 2) Excluded n = 16 Biol...

Interleukin-17 is a proinflammatory cytokine. Recent animal studies have shown that IL-17 plays a role in the initiation and progression of arthritis. However, whether IL-17 has a prominent role in human rheumatoid arthritis (RA) or not remains unclear. Here we investigated the role of IL-17 in patients with RA. cDNA was prepared from knee joint synovial tissues of RA (n = 11) and osteoarthriti...