摘要:

A pair design is an ordering of all pairs in {1, 2,…,n} such that pairs that share an element have at least [(n − 3)/2] pairs separating them. Such designs can be constructed for alln. We present a shorter proof of a result of Simmons and Davis, that pair designs for oddnare unique up to permuting the numbers or reversing the order of the pa

ISSN:0022-2526    

DOI:10.1002/sapm19785811

年代:1978

数据来源: WILEY

摘要:

A van der Pol relaxation oscillator that is subjected to external sinusoidal forcing can exhibit stable and unstable periodic and almost periodic responses. For some forcing amplitudes it even happens that two stable subharmonics having different periods may coexist. We investigate here the stable responses of such forced oscillators. By numerically computing the rotation number of stable oscillations for various values of the forcing amplitude and oscillator tuning, we obtain descriptions of regions of phase locking, successive bifurcation of stable subharmonic and almost periodic oscillations, and overlap regions where two distinct stable oscillations can coexist.

ISSN:0022-2526    

DOI:10.1002/sapm19785815

年代:1978

数据来源: WILEY

摘要:

In 1967 a new method of mathematical physics was discovered by Gardner, Greene, Kruskal, and Miura. Their significant results have received much attention, and numerous developments have occurred within the decade. In this paper a survey of some of these developments is made. By and large the emphasis is on relating the key ideas via typical examples.

ISSN:0022-2526    

DOI:10.1002/sapm197858117

年代:1978

数据来源: WILEY