1. When the few individuals still alive in a dissolved culture of Bacillus coli are transplanted on slanted agar, a culture results which possesses new characteristics. First observed by Bordet and Ciuca, this culture received the temporary name of modified coli. In the study described above, we found that this modified coli is very heterogeneous and that its three principal characteristics, re...

Answering a problem posed by Keisler and Leth, we prove a theorem in nonstandard analysis to reveal a phenomenon about sumsets, which says that if two sets A and B are large in terms of \measure", then the sum A+B is not small in terms of \order{topology". The theorem has several corollaries about sumset phenomenon in the standard world; these are described in sections 2{4. One of these is a ne...

Transient ischaemic attacks often have very similar, sometimes identical, characteristics. This implies that the same area of the brain is rendered ischaemic at each attack. The cause is usually an atherothrombo-embolism. To produce stereotypical episodes of ischaemia, such emboli must lodge in the same small artery each time. As the embolus starts from a point far from its eventual destination...

Raynaud's phenomenon is an episodic vasospasm of the peripheral arteries, causing pallor followed by cyanosis and redness with pain and sometimes paraesthesia, and, rarely, ulceration of the fingers and toes. Primary or idiopathic Raynaud's phenomenon (Raynaud's disease) occurs without an underlying disease. Secondary Raynaud's phenomenon (Raynaud's syndrome) occurs in association with an under...

1 The child as scientist The goal of this paper is to clarify an important thesis related to human intellectual development. The thesis is stated in its most persuasive form in a recent bookby Allison Gopnik and Andrew Meltzoo Gopnik and Meltzoo, 1996. They say: We want to argue that the cognitive processes that underlie science are similar to, or indeed even identical with, the cognitive proce...

Frank Benford introduced the significant-digit logarithmic law which stresses that certain digits in numbers collected randomly can occur often more than other numbers. Such logarithmic phenomenon has been recognized and accepted by many mathematicians. Such logarithmic law can be applied in detecting accounting fraud or fabrication of data in financial documents, predicting stock indices and i...

To the Editor: In reviewing no-reflow, Rezkalla and Kloner1 indicted injuryinduced microvascular changes, but did not mention spasm of resistance vessels, which might be the basic mechanism of no-reflow. I proposed in 1971 that no-reflow (“stasis”) is due to ischemic injury-induced spasm, and the evidence seemed convincing.2 Short coronary occlusions reversed no-reflow, and this was interpreted...

We generalize Fomin and Zelevinsky’s cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.

In this paper, we undertake a systematic study of recurrences xm+nxm = P (xm+1, . . . , xm+n−1) which exhibit the Laurent phenomenon. Some of the most famous among these sequences come from the Somos and the Gale-Robinson recurrences. Our approach is based on finding period 1 seeds of Laurent phenomenon algebras of Lam-Pylyavskyy. We completely classify polynomials P that generate period 1 seed...