We study powers of prefixes of Sturmian words.

The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is used to obtain estimates for

on the Terman Revision of the Binet Scale involve almost exclusively language ability, rote memory, appropriateness, clearness and adequacy of detail in imagery, power of conceptual thought and reasoning, those peculiarly human qualities of mind which mark off, from the defective or immature, the normal completely developed intelligence. On the other hand experiments on animal learning have sho...

Introduction* It has long been known that every positive rational number can be represented as a finite sum of reciprocals of distinct positive integers (the first proof having been given by Leonardo Pisano [6] in 1202). It is the purpose of this paper to characterize {cf. Theorem 4) those rational numbers which can be written as finite sums of reciprocals of distinct nth. powers of integers, w...

Admixture mapping is the first experimentally practical method for carrying out a whole-genome association scan, and is thus a promising method for detecting risk factors for common disease. The goal of the community should now be to aggressively test whether the method is useful in practice for localizing disease genes, by carrying out at least three high-powered studies. We also propose a str...

Article history: Received 8 July 2015 Received in revised form 26 July 2015 Accepted 29 July 2015 tion to the era of factory-scale analysis. The great acceleration of progress we've seen in other fields is now coming to healthcare. At Google, we have more than 15 years of experience with finding the value in information. We have built tools to organize information and make it accessible and use...

Question 1.2. Suppose g(k) is the least number of powers to make Theorem 1.1 hold. How big is g(k)? To provide some intuition, take n = 2−1. In its decomposition any ai can’t be greater than 1, since 2 k > 2 − 1. Therefore, ai = 1 for all i and g(k) ≥ s = 2 − 1. The real value of g(k) is only a little worse than that. Thus, the number g(k) grows at least exponentially with respect to k. However...

People often neglect opportunity costs: They do not fully take into account forgone alternatives outside of a particular choice set. Several scholars have suggested that poor people should be more likely to spontaneously consider opportunity costs, because budget constraints should lead to an increased focus on trade-offs. We did not find support for this hypothesis in five high-powered experim...

Firstly, we will show the following extension of the results on powers of p-hyponormal and log-hyponormal operators: let n andm be positive integers, if T is p-hyponormal for p ∈ (0,2], then: (i) in case m ≥ p, (Tn+mTn+m)(n+p)/(n+m) ≥ (TnTn)(n+p)/n and (TnTn ∗ )(n+p)/n ≥ (Tn+mTn+m)(n+p)/(n+m) hold, (ii) in case m < p, Tn+mTn+m ≥ (Tn ∗ Tn)(n+m)/n and (TnTn ∗ )(n+m)/n ≥ Tn+mTn+m hold. Secondly, w...