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The action of power ultrasound in controlling the supersaturation, nucleation and crystal growth during the acid-base reaction crystallization of 7-amino-3-desacetoxy cephalosporanic acid (7-ACDA) has been investigated. The experimental results show that ultrasound can mix the reaction more efficiently and uniformly than conventional agitation methods. Insonation leads to the reduction of both the induction period and metastable zone width of the crystallization, so that the process of crystallization can be more efficiently controlled than without insonation. Agglomeration is also greatly reduced. Adjusting the ultrasonic parameters can modulate the crystal size and size distribution. The mechanism of the sonoprocess has been analyzed and comments are made on the potential applicability of sonication in large-scale crystallization practice.

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An allowable generalized quantum gate (introduced by Long, Liu and Wang) has the form of 1 0 d k k k U cU − = = , ∑ where U k 's are unitary operators on a Hilbert space H and 1 0 1 d k k c − = | | ≤ ∑ and 1 k c | |≤ (0≤k≤d−1). In this work we consider a kind of AGQGs, called restricted allowable generalized quantum gates (RAGQGs), satisfying 1 0 0 1 d k k c − = < | |≤ . ∑ Some properties of the set RAGQG(H) of all RAGQGs on H are established. Especially, we prove that the extreme points of RAGQG(H) are exactly unitary operators on H and that B(H)=R + RAGQG(H). duality computer, Hilbert space, unitary, quantum gate, restricted allowable generalized quantum gate Citation: Cao H X, Li L, Chen Z L, et al. Restricted allowable generalized quantum gates.

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