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We study the maximum size of Sidon sets in unions of integer intervals. If A ⊂ N is the union of two intervals and if | A | = n (where | A | denotes the cardinality of A ), we prove that A contains a Sidon set of size at least 0 , 876 n . On the other hand, by using the small differences technique, we establish a bound of the maximum size of Sidon sets in the union of k intervals. [ABSTRACT FROM AUTHOR]

We have further investigated the phenomenon of spontaneous anti-(Coombs) antiidiotypic antibodies in the FI hybrids of New Zealand black (NZB) and CBA mice. These mice show an age-related increase in incidence of such antiidiotype during the first year of life. There is no difference between males and females in the occurrence of antiidiotype. Reciprocal hybrids are both affected, so that maternal influence from the NZB strain is not critical. The antiidiotype also occurs in spite of the .xid gene. We have so far detected such spontaneous antiidiotype only in (CBA × NZB)F1 hybrids, and not in hybrids of NZB with two other strains or in a variety of recombinant inbred strains between NZB and C58. Our results to data suggest extensive shared idiotypy among NZB mice and a limited number of total idiotypes. [ABSTRACT FROM AUTHOR]