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Whaley’s Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 3 . It is also shown that that every finite modular lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 2 , and every finite distribut...
OBJECTIVES To investigate the relationship between accumulated health-related problems (deficits), which define a frailty index in older adults, and mortality in population-based and clinical/institutional-based samples. DESIGN Cross-sectional and cohort studies. SETTING Seven population-based and four clinical/institutional surveys in four developed countries. PARTICIPANTS Thirty-six tho...
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