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RELATION BETWEEN DEMYANOV DIFFERENCE ANDMINKOWSKI DIFFERENCE OF CONVEX COMPACTSUBSETS IN R2
CHUN-LING SONG,ZUN-QUAN XIA,LI-WEI ZHANG,SHU-YANG LI 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
A necessary and sufficient condition for Demyanov difference and Minkowski difference of compact convex subsets in R2 being equal is given in this paper. Several examples are computed by Matlab to test our result. The necessary and sufficient condition makes us to compute Clarke subdifferential by quasidifferential for a special of Lipschitz functions.
RELATION BETWEEN DEMYANOV DIFFERENCE AND MINKOWSKI DIFFERENCE OF CONVEX COMPACT SUBSETS IN $R^2$
Song, Chun-Ling,Xia, Zun-Quan,Zhang, Li-Wei,Li, Shu-Yang 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
A necessary and sufficient condition for Demyanov difference and Minkowski difference of compact convex subsets in $R^2$ being equal is given in this paper. Several examples are computed by Matlab to test our result. The necessary and sufficient condition makes us to compute Clarke subdifferential by quasidifferential for a special of Lipschitz functions.
Shou-Sen Shi,Shu-hong Shao,Bang-ping Yuan,Fang Pan,Zun-Ling Li 연세대학교의과대학 2010 Yonsei medical journal Vol.51 No.5
Purpose: The purpose of this study is to explore the dynamic change of brainderived neurotrophic factor (BDNF) mRNA, protein, and tyrosine kinase-coupled receptor (TrkB) mRNA of the rat hippocampus under different stress conditions and to explore the influence of senescence on the productions expression. Materials and Methods: By using forced-swimming in 4°C cold ice water and 25°C warm water, young and aged male rats were randomly divided into acute stress (AS) and chronic mild repeated stress (CMRS) subgroups, respectively. BDNF productions and TrkB mRNA in the hippocampus were detected by using Western-blotting and reverse transcription-polymerase chain reaction (RT-PCR),separately, at 15, 30, 60, 180, and 720 min after the last stress session. Results: The short AS induced a significant increase in BDNF mRNA and protein in both age groups, but the changes in the young group were substantially greater than those of the aged group (p < 0.005). The CMRS resulted in a decrease in BDNF mRNA and protein, but a significant increase in TrkB mRNA in both young and age groups. The expression of BDNF mRNA and protein in the AS groups were higher than in the CMRS groups at 15, 30, and 60 min after stress. Conclusion: The results indicated that the up/down-regulation of BDNF and TrkB were affected by aging and the stimulus paradigm, which might reflect important mechanisms by which the hippocampus copes with stressful stimuli.