The sum of square roots of integers problem is to find the minimum nonzero difference between two sums of square roots of integers. Let r(n,k) denote the minimum nonzero positive value: |∑i=1 √ ai −∑i=1 √ bi|, where ai and bi are positive integers not larger than integer n. We prove by an explicit construction that r(n,k) = O(n−2k+ 3 2 ) for fixed k and any n. Our result implies that in order t...

CONTEXT A decade of increasing antidepressant medication treatment for adolescents and corresponding declines in suicide rates raise the possibility that antidepressants have helped prevent youth suicide. OBJECTIVE To evaluate the relationship between regional changes in antidepressant medication treatment and suicide in adolescents from 1990 to 2000. DESIGN Analysis of prescription data fr...

Understanding the extent and limits of non-conscious processing is an important step on the road to a thorough understanding of the cognitive and cerebral correlates of conscious perception. In this article, we present a critical review of research on subliminal perception during masking and other related experimental conditions. Although initially controversial, the possibility that a broad va...

In this paper we construct a cover {as(mod ns)}s=1 of Z with odd moduli such that there are distinct primes p1, . . . , pk dividing 2 n1 − 1, . . . , 2k − 1 respectively. Using this cover we show that for any positive integer m divisible by none of 3, 5, 7, 11, 13 there exists an infinite arithmetic progression of positive odd integers the mth powers of whose terms are never of the form 2 ± p w...

Tests evaluating the attentional-executive system are widely used in clinical practice. However, proximity of an objective cognitive test with real-world situations (ecological validity) is not frequently investigated. The present study evaluate the association between measures of the Five Digit Test (FDT) and the Oral Trails Test (OTT) with self-reported cognitive failures in everyday life as ...

We prove that the ratio of the Newman sum over numbers multiple of a fixed integer which is not multiple of 3 and the Newman sum over numbers multiple of a fixed integer divisible by 3 is o(1) when the upper limit of summing tends to infinity. We also discuss a connection of our results with a digit conjecture on primes.

Tetrapods have two pairs of limbs, each typically with five digits, each of which has a defined number of phalanges derived from an archetypal formula. Much progress has been made in understanding vertebrate limb initiation and the patterning processes that determine digit number in developing limb buds, but little is known about how phalange number is controlled. We and others previously showe...

OBJECTIVE To gather data on cats living in US households, document their neuter status, and identify demographic characteristics associated with neuter status. DESIGN Cross-sectional, random-digit-dial telephone survey. SAMPLE POPULATION 1,205 adults in the continental United States contacted between April 24, 2007, and May 14, 2007. PROCEDURES Information was gathered by means of compute...

Fink et al. (2006) have reported that men with higher grip strength (GS) have lower digit ratios (2D:4D), interpreting this as evidence for organizational effects of prenatal androgens on strength. In this study, I attempted to replicate their finding with 99 women. I found no evidence that digit ratios were associated with GS, suggesting that 2D:4D is not associated with GS in women. The null ...

Consider the sequence (3k)k≥0 written in base two representation and reduce the sum of digits s2(3k) mod 2. A well-known result of Newman [10] says that the resulting sequence shows an overplus of 0’s with respect to 1’s. It is also known [3] that, asymptotically speaking, s2(7k)k≥0 is more often 0 than 1 or 2. We investigate similar phenomena for the sequence (7k + i)k≥0 with 0 < i ≤ 6 as well...