We study Einstein manifolds admitting a transitive solvable Lie group of isometries (solvmanifolds). It is conjectured that these exhaust the class of noncompact homogeneous Einstein manifolds. J. Heber [H] has showed that under certain simple algebraic condition (such a solvmanifold is called standard), Einstein solvmanifolds have many remarkable structural and uniqueness properties. In this p...

The Trichotomy Principle says that a pair of sets A and B either admits a bijection or else precisely one of these sets injects into the other. Hartogs established logical equivalence between the Trichotomy Principle and the Well-Ordering Principle. As ZF suffices to prove the Schröder-Bernstein theorem, the heart of Trichotomy lies in the existence of some injection connecting A and B (in eith...

In mid-1995, a government effort to reduce the supply of methamphetamine precursors successfully disrupted the methamphetamine market and interrupted a trajectory of increasing usage. The price of methamphetamine tripled and purity declined from 90 percent to 20 percent. Simultaneously, amphetaminerelated hospital and treatment admissions dropped 50 percent and 35 percent, respectively. Methamp...

This paper presents mechanisms implementing the core correspondence of many-toone matching markets, such as college admissions problems, where the students have preferences over the other students who would attend the same college. With an unrestricted domain of preferences the non-emptiness of the core is not guaranteed. We present a sequential mechanism implementing the core without any restr...

We show that the nonlinear equation that describes nonparaxial Kerr propagation, together with the already reported bright-soliton solutions, admits of (1 + 1)D dark-soliton solutions. Unlike their paraxial counterparts, dark solitons can be excited only if their asymptotic normalized intensity u2infinity is below 3/7; their width becomes constant when u2infinity approaches this value.

Dr. Hehir appears to be of opinion that a drop of blood on a glass slide, if sealed up with vaseline or paraffin, undergoes no spontaneous changes in the Indian climate. I expect that if he makes a preparation of normal blood, and examines it with as much faith and imagination as he appears to have devoted to his observations of the blood of cholera patients, he will again meet with his monstro...

The aim of intermediate care, according to the National Service Framework for Older People, is to provide integrated services to promote faster recovery from illness, prevent unnecessary acute hospital admissions, support timely discharge, and maximise independent living. In Hackney, east London, this has resulted in two innovative approaches to meeting the NSF target. Homerton University Hospi...