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1. F. P. Ramsey (1) proved the following theorem. Let 7~ be a positive integer, and let A be an arbitrary distribution of all sets of n positive integers into a Jinite number of classes. Then there exists an in.nite set M of positive integers which has the property that all sets of n numbers of M belong to the Same class of A. Apart from its intrinsic… (More)

- F. P. Ramseyt, Richard Rado
- 1951

Given any positive integers k, n, ANT, there is a positive integer M which has the following property. If S = {1, 2, . . ., A1}, and A is any distribution of Q,(S) into k classes, there is always an element S' of OAS) such that the (--,a,') elements of belong to the same class of A . We denote by R(k., n, N) the least number _J1 possessing this property,… (More)

Such relations were introduced in [3] and [1] . They are called I-relations, Ii-relations and III-relations respectively, and they will be defined in 3 . 1, 3 . 2 and 3 . 3 . In sections 18 and 19 we shall introduce certain generalizations of these relations . Our whole theory can be considered as having arisen out of the classical theorem of RAMSEY [18] .… (More)

1. Introduction. Dedekind's pigeonhole principle, also known as the box argument or the chest of drawers argument (Schubfach-prinzip) can be described, rather vaguely, as follows. If sufficiently many objects are distributed over not too many classes, then at least one class contains many of these objects. In 1930 F. P. Ramsey [12] discovered a remarkable… (More)

- Dina Lipkind, Fernando Nottebohm, Richard Rado, Anna Barnea
- Behavioural brain research
- 2002

Many new neurons are added to the adult avian brain. Most of them die 3-5 weeks after they are born (Nature (Lond.) 335 (1988) 353; J. Comp. Neurol 411 (1999) 487). Those that survive replace, numerically, older ones that have died (Neuron 25 (2000) 481). It has been suggested that the new neurons enhance the brain's ability to acquire new long-term… (More)

- Gilles Bronchti, Richard Rado, Joseph Terkel, Zvi Wollberg
- Brain research. Developmental brain research
- 1991

The mole rat Spalax ehrenbergi is a fossorial rodent. Although its peripheral visual system--eye and optic nerve--is highly degenerated, it shows some sensitivity to light. However, in the usual sense, it is essentially blind. An auditory take-over of the visual lateral geniculate nucleus and at least part of the visual cortices was recently demonstrated.… (More)

- Richard Rado
- 2006

where the a^, 6M are complex numbers. Let A be a set of numbers, for instance all numbers of a number field, all complex numbers different from zero, etc. We call (1) regular in A if the following condition holds: however we split A into a finite number of subsets Av A2, ..., Ak, always at least one of these subsets AK contains a solution of (1). Roughly… (More)

- Richard Rado
- 1969

In this paper we present the complete solution of the problem which was considered in [1], with the exception of the case in which both the given cardinal numbers are finite. The results of [1] will not be assumed. We begin by introducing some definitions, f A system Li = (Bv: veiV) of sets Bv, where v ranges over the index set N, is said to contain the… (More)

- Richard Rado, Mordechai Z. Himelfarb, Baruch Arensburg, Joseph Terkel, Zvi Wollberg
- Hearing research
- 1989

The anatomy of the middle ear of the blind mole rat, a subterranean rodent that uses seismic signals for long distance communication, is described qualitatively and quantitatively. The ossicular chain is of the parallel type with a lever arms ratio of 0.55 and an effective areal ratio of stapedial footplate to eardrum of 0.09. Assuming an ideal mechanical… (More)

- P. ERDiiS, Richard Rado, E. C. Milner
- 2001

1. 1ntrodocti0n. Since 1958 we have published a number of joint papers on set theory [l] . . . [K?] and some triple papers with R. Rado, E. C. Milner, J. Czipszer, G. FGdor 1131. I . [17]. During this period we collected a fair amount of problems we could not solve. Some of them are stated in the papers we have published, some are connected with unpublished… (More)