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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Aequationes mathematicae 42 (1991), S. 37-46 
    ISSN: 1420-8903
    Keywords: 39B50 ; 20N05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary V. D. Belousov (1925–88) made numerous contributions to the study of quasigroups. In particular, his lengthy 1966 paper “Balanced identities in quasigroups” [4] contains what has been described as a “very significant” and “remarkable” theorem [11, pp. 68–69]. Remarkable though it was, this theorem provided only a partial answer to the question as to which balanced equations on quasigroups gave rise to group isotopes. Although not specifically addressed in the paper [12], a characterization of the balanced equations in question may be derived from a generalization of Belousov's Theorem due to E. Falconer. The first author explicitly solved the problem in 1979; however his characterization was of a technical nature and depended on machinery developed over three papers [13]. In 1985 Belousov found a characterization which is not only elegant but also lends itself to a simple proof [5]. The purpose of this paper is to provide sufficient background for the non specialist to understand and enjoy what we too would describe as “a remarkable theorem”.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-2072
    Keywords: Acoustic startle reflex ; Prepulse inhibition ; Visual stimuli ; Sensitization ; Dopamine ; Activity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract The acoustic startle reflex (ASR) is inhibited by startle-irrelevant stimuli that briefly precede reflex elicitation. This effect, prepulse inhibition (PPI), is reduced in strength for animals that have received dopamine agonists, such as apomorphine (APO). Reduction in PPI is most evident for weak masked noise prepulses, thus suggesting that APO disrupts the reception of stimuli to the extent that they present a low signal-to-noise ratio. Here we examine the effect of APO on PPI produced by non-masked visual prepulses. Light flashes were given at two intensities, 40, 70, 110, or 220 ms before ASR elicitation. In phase 1 (5 weeks in duration) half of the animals received one weekly injection of APO (0.5 mg/kg, IP) and one of vehicle (VEH), while the other half received two injections of VEH. Within these groups, half were tested 30 min after the injections, the other half kept test naive (four groups total). In phase 2, following a 4-week rest, all groups were tested after a low dose of APO (0.1 mg/kg) and VEH, 1 week apart. APO eliminated PPI for a dim flash and reduced PPI for a brighter flash to a level normally obtained with the dim flash, while increasing both ASR control values and activity. The bright light was maximally effective at a lead time of 70 ms and APO did not alter this value. Because in general the time of maximal inhibition varies with prepulse intensity for visual stimuli, the finding that the time of the peak remained constant reveals that APO has its effect on inhibition rather than on effective stimulus intensity. In phase 2, APO reduced PPI with no sign of sensitization from past drug exposure. However, APO increased the ASR only in groups previously exposed to APO, indicating behavioral sensitization. The differential effects of repeated exposure on these response measures suggest that neural substrates for the several behavioral effects of APO function at least in part independently.
    Type of Medium: Electronic Resource
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