• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권3호
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• pp.233-251
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• 2011

The Gauge-Uzawa method [GUM] in [9] which is a projection type algorithm to solve evolution Navier-Stokes equations has many advantages and superior performance. But this method has been studied for backward Euler time discrete scheme which is the first order technique, because the classical second order GUM requests rather strong stability condition. Recently, the second order time discrete GUM was modified to be unconditionally stable and estimated errors in [12]. In this paper, we contemplate several GUMs which can be derived by the same manner within [12], and we dig out properties of them for both stability and accuracy. In addition, we evaluate an stability condition for the classical GUM to construct an adaptive GUM for time to make free from strong stability condition of the classical GUM.

• Kyungpook Mathematical Journal
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• 제51권4호
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• pp.435-456
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• 2011

The Chebyshev collocation method in [21] to solve stiff initial-value problems is generalized by using arbitrary degrees of interpolation polynomials and arbitrary collocation points. The convergence of this generalized Chebyshev collocation method is shown to be independent of the chosen collocation points. It is observed how the stability region does depend on collocation points. In particular, A-stability is shown by taking the mid points of nodes as collocation points.

• Clinical and Experimental Reproductive Medicine
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• 제44권1호
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• pp.8-14
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• 2017

Objective: The aim of this study was to analyze the effect of supplementing vitrification and warming solutions with two types of antifreeze proteins (AFPs) and the combination thereof on the follicular integrity of vitrified-warmed mouse ovaries. Methods: Ovaries (n=154) were obtained from 5-week-old BDF1 female mice (n=77) and vitrified using ethylene glycol and dimethyl sulfoxide with the supplementation of 10 mg/mL of Flavobacterium frigoris ice-binding protein (FfIBP), 10 mg/mL of type III AFP, or the combination thereof. Ovarian sections were examined by light microscopy after hematoxylin and eosin staining, and follicular intactness was assessed as a whole and according to the type of follicle. Apoptosis within the follicles as a whole was detected by a terminal deoxynucleotidyl transferase deoxyuridine triphosphate nick-end labeling assay. Results: The proportion of overall intact follicles was significantly higher in the type III AFP-supplemented group (60.5%) and the combination group (62.9%) than in the non-supplemented controls (43.8%, p<0.05 for each). The proportion of intact primordial follicles was significantly higher in the FfIBP-supplemented (90.0%), type III AFP-supplemented (92.3%), and combination (89.7%) groups than in the non-supplemented control group (46.2%, p<0.05 for each). The proportions of non-apoptotic follicles were similar across the four groups. Conclusion: Supplementation of the vitrification and warming solutions with FfIBP, type III AFP, or the combination thereof was equally beneficial for the preservation of primordial follicles in vitrified mouse ovaries.