• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.723-735
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• 2006

In [2] it was shown that a 1-generator quasi-cyclic code C of length n = ml of index l over $\mathbb{Z}_4$ is free if C is generated by a polynomial which divides $X^m-1$. In this paper, we prove that a necessary and sufficient condition for a cyclic code over $\mathbb{Z}_pk$ of length m to be free is that it is generated by a polynomial which divides $X^m-1$. We also show that this can be extended to finite local rings with a principal maximal ideal.

• Journal of Chest Surgery
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• v.29 no.1
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• pp.14-23
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• 1996

Circulatory arrest under deep hypothermia is an important auxiliary means for cardiac surgery, especially useful in pediatric patients. However, its clinical safety, particularly with regard to the neurologic outcome after long duration of circulatory arrest, is still not established. This study is a review of the eight years'clinical experience of hypothermic circulatory arrest at the Seoul national University Children's Hospital. During an eight-year period from January 1986 through December 1993, a total of 589 consecutive cardiac operations were done using circulatory arrest under deep hypothermia. Among them, 434 consecutive patients, in whom the duration of arrest was 20 minutes or more, are the subject of this study. The duration of arrest ranged from 20 minutes to 82 minutes (mean = 38.7 minutes) under rectal temperature in the range from 12.5$^{\circ}C$ to 25.8$^{\circ}C$. Early neurologic abnormalities occurred in 47 patients : seizure attacks in 28 patients, motor paralyses with or w thout seizure in 12, blindness in 2, and no recovery of consciousness in 5 patients. The rate of incidence of early neurologic abnormalities was calculated at 15.7%. 25 patients showed late neuropsychologic sequelae, such as motor paralysis (9 patients), recurrent seizures (6), developmental delay (8), and definitely low intelligence (2). The rate of incidence of late neurologic sequelae was 8.5%, By statistical analysis, the following factors were identified as the risk factors for post-arrest neurologic abnormalities ; 1) long duration of circulatory arrest, 2) lower-than-ideal body weight, 3) preexisting neurological abnormalities, 4) associated non-cardiovascular congenital anouialies, and 5) low blood pressure during the early post-arrest period. It is concluded that circulatory arrest under deep hypothermia is a relatively safe means for pediatric cardiac surgery with acceptable risk. However, to warrant maximal safety, it is desirable to limit the duration of arrest to less th n 40 minutes. In addition, it is our contention that the early post-arrest period is a very critical period during which maintenance of adequate perfusion pressure in important for the neurologic outcome.