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SOLUTIONS OF HIGHER ORDER INHOMOGENEOUS PERIODIC EVOLUTIONARY PROCESS
김도한,Rinko Miyazaki,Toshiki Naito,신종손 대한수학회 2017 대한수학회지 Vol.54 No.6
Let $\{U(t,s)\}_{t\ge s}$ be a periodic evolutionary process with period $\tau>0$ on a Banach space $X$. Also, let $L$ be the generator of the evolution semigroup associated with $\{U(t,s)\}_{t\ge s}$ on the phase space $P_{\tau}(X)$ of all $\tau$-periodic continuous $X$-valued functions. Some kind of variation-of-constants formula for the solution $u$ of the equation $(\alpha I-L)^nu=f$ will be given together with the conditions on $f\in P_{\tau}(X)$ for the existence of coefficients in the formula involving the monodromy operator $U(0,-\tau)$. Also, examples of ODEs and PDEs are presented as its application.
배정훈 ( Jeong Hoon Bae ),김연희 ( Yeun Hee Kim ),박인양 ( In Yang Park ),황성진 ( Seong Jin Hwang ),손정빈 ( Jung Bin Son ),김현경 ( Hyun Kyung Kim ),이동현 ( Dong Hyun Lee ),최은주 ( Eun Ju Choi ),이석우 ( Suk Woo Lee ),신종철 ( 대한산부인과학회 2004 Obstetrics & Gynecology Science Vol.47 No.6
Objective : Threatened abortion, one of the most common problems of pregnancy, develops 15-20% of pregnant women and progresses into the abortion in 20-50%. It is related to many obstetrical sequelae. We analyzed the prevalence of complication, disruption of pregnancy and the effect of recent treatments. In ultrasonographic examination, we divided all cases into two groups according to existence of hematoma. We compared the difference of two groups about the prognosis of pregnancy and maternal serum concentration of FP. Methods : A total 88 cases of threatened abortion and 5741 cases of normal pregnancy were studied from Jan., 1999 through Dec., 2003 at St. Paul Hospital in Seoul, Korea. We analyzed age, gestational age of menstruation and ultrasonogram, parity, results of triple test, existence of hematoma, efficacy of treatment. In all cases, we carrided out ultrasonic examination with LogiQ-400 (General Electronics Medical System, Tokyo, Japan). We checked the concentration of FP from triple test. Results : The mean gestational age at diagnosis was 9.2±3.4 weeks. After threatened abortion, successful cases were 71 and mean gestational age at diagnosis was 9.6±3.6 weeks. In comparison with 17 unsuccessful cases, whose mean gestational age at diagnosis was 6.6±1.8 weeks, it was thought to be significant differences (p=0.001). The success rates of pregnancy prolongation between groups of different treatments modalities are nearly similar. Existence of hematoma seems to have little impact on prognoses of pregnancy outcome and there were no meaningful differences of maternal serum FP concentration. Conclusion : In this study, we could find no difference between the groups those were treated with various methods. We thought that more systematic analysis about the treatment of threatened abortion would be needed. Un the cases that were diagnosed threatened abortion at later gestational age, we could find obvious improvement of the pregnancy outcome. So we conclude that gestational age at the diagnosis is potential parameter of prognosis.