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We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists 0 < c ≤ 1 such that for every r > 0, there is R > 0 for which, if ν is a positive locally finite Borel measure on X, H is a separable infinite(More)
We give some necessary and su‰cient conditions of when the product of two Hankel operators is a compact perturbation of a Hankel operator on the Hardy space. r For f in L y , the Hankel operator with symbol f is the operator H f on the Hardy space H 2 of the unit circle, defined by H f h ¼ PðUf hÞ, for h in H 2. Here P is the orthogonal projection from L 2(More)
Impaired sleep patterns are common symptoms of Alzheimer’s disease (AD). Cellular mechanisms underlying sleep disturbance in AD remain largely unknown. Here, using a Drosophila Aβ42 AD model, we show that Aβ42 markedly decreases sleep in a large population, which is accompanied with postdevelopmental axonal arborization of wake-promoting pigment-dispersing(More)
OBJECTIVE To detect maternal serum fetal DNA for prenatal diagnosis of fetal sex. METHODS Five to ten ml maternal serum was obtained from 24 pregnant women with 16 male fetuses and 8 female fetuses (including 4 carriers with X-linked diseases). The fetal sex was detected by analyzing the karyotype from amniotic fluid and villus. Serum DNA was extracted,(More)
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