Let A be a set of n > n0(ε) positive real numbers, all at least 1 apart. We show that, if δa,b and δ� a,b are arbitrary real numbers satisfying |δa,b| < n 1−ε a , and |δ � a,b| < n1−ε b , we have |{(a + δa,b)(b + δ� a,b) : a, b ∈ A}| + |A + A| � n1+ε/9 log n . – Dedicated to Mel Nathanson and Carl Pomerance on the occasion of their 65th birthdays

This book is a treat. A psychologist (Hurlburt) and a philosopher (Schwitzgebel) join forces to interview a young college graduate (Melanie). They ask Melanie what she experiences at randomly selected times. They debate what Melanie reports and what can be learned from it. They often disagree -but in a candid, humble, and open-minded way. Their imaginative and insightful dialogue, lightly edite...

This paper presents the lubrication characteristics between a bush and a blade of a swing compressor that was developed for a new type of compressor for an air conditioner using alternative refrigerants. The mixed lubrication analysis that simultaneously solved the motion equations of the bush and the blade, the lubrication equation and the rough surface contact equation was performed. Moreover...

Use of herbal remedies from medicinal plants (bush medicines) was studied in 622 people with diabetes mellitus attending 17 government health centers on the island of Trinidad, Trinidad and Tobago. Bush medicines were used by 42% of patients surveyed and were used for diabetes by 24%. Bush medicine use was more frequent in Afro-Trinidadians and in those of mixed ethnicity than in Indo-Trinidadi...

Increasing Australian bush-fire frequencies over the last decade has indicated a major climatic change in coming future. Understanding such climatic change for Australian bush-fire is limited and there is an urgent need of scientific research, which is capable enough to contribute to Australian society. Frequency of bush-fire carries information on spatial, temporal and climatic aspects of bush...

For the area of the United States the Shuttle Radar Topography Mission (SRTM) height models are available with 1 arcsec spacing instead of the 3 arcsec spacing outside the country. Only special users are getting the 1 arcsec height information outside the USA. 1 arcsec and also 3 arcsec SRTM height models have been investigated in a mountainous area, covered nearly completely by forest, in an u...

Abstract Wemake explicit the geometric content of Mel’nikov’s method for detecting heteroclinic points between transversally hyperbolic periodic orbits. After developing the general theory of intersections for pairs of family of Lagrangian submanifolds N ε , with N + 0 = N − 0 constrained to live in an auxiliary family of submanifolds, we explain how the heteroclinic orbits are detected by the ...

In this paper we study an example-machine Bush(S, T ) where S and T are disjoint dense subsets of R. We find some topological properties that Bush(S, T ) always has, others that it never has, and still others that Bush(S, T ) might or might not have, depending upon the choice of the disjoint dense sets S and T . For example, we show that every Bush(S, T ) has a point-countable base, is heredita...