Orlicz模空间中复端点的刻画

复空间几何性质在鞅论、算子理论、调和分析、Banach代数、微分方程、流体力学及量子力学等理论和学科中有着广泛的应用,复端点的刻画对于空间几何性质的研究具有重要作用.我们首先在Orlicz模空间中引入复端点的概念,利用单位球这一具体的空间几何结构,进一步分别给出了Orlicz模函数空间和Orlicz模序列空间单位球中复端点判据的充分必要条件.

赋p-Amemiya范数的Musielak-Orlicz函数空间的复凸性

主要研究了赋p-Amemiya范数的Musielak-Orlicz函数空间,当1≤p<∞且p是奇数时,给出了该空间中单位球的复端点和复强端点的充要条件,进而可得出该空间是复严格凸和复中点局部一致凸的判别准则.

Early mortality and safety after transcatheter aortic valve replacement using the SAPIEN 3 in nonagenarians

Background Transcatheter aortic valve replacement （TAVR） has been performed for many elderly patients with severe aortic stenosis （AS）. The SAPIEN 3 is one of the latest balloon-expandable prosthesis. This study aimed to investigate the early clinical outcomes after TAVR using the SAPIEN 3 in nonagenarians. Methods A total of 97 consecutive patients underwent TAVR for severe AS between De- cember 2015 and December 2016. Of these, 85 consecutive patients who underwent TAVR using the SAPIEN 3 were included. According to the age, patients were classified into age 〉 90 years group （17 patients） or age 〈 90 years group （68 patients）. The clinical outcomes in- cluding all-cause mortality and composite endpoint of early safety at 30 days were evaluated. Results The Society of Thoracic Surgeons score in age 〉 90 years group was higher than age 〈 90 years group （12.3 ±6.1% vs. 8.5 ± 5.1%, P 〈 0.01）. There was no significant difference in 30-day mortality between the two groups. However, the life-threatening bleeding and major vascular complications in age 〉 90 years group were greater than age 〈 90 years group （11.8% vs. 1.5%, P = 0.04 and 11.8% vs. 1.5%, P = 0.04, respectively）. The composite endpoint of early safety at 30 days was similar between the two groups. Multivariate logistic regression analysis showed that prior myocardial infarction was an independent predictor of the composite endpoint of early safety （odds ratio： 4.76, 95% confidence interval： 1.02-22.21, P = 0.047）. Conclusions The early mortality and safety after TAVR using the SAPIEN 3 in nonagenarians were similar and acceptable despite of higher operative risk.

赋p-Amemiya范数的Musielak-Orlicz序列空间的复凸性

讨论了赋p-Amemiya范数的Musielak-Orlicz序列空间的复凸性问题.当1≤p<∞时,得到该空间中单位球的复端点和复强端点是等价的,并给出了它们的充要判据,进一步得到该空间是复严格凸和复中点局部一致凸的判别准则.

Which Endpoints Can Be Reliably Assessed in Semi-field Pollinator Species Testing without Estimating False Positive or False Negative？ MDD’s and Replicates Issue

Statistical power, number of replicates and experiment complexity of semi-field and field studies on Apis and non-Apis bee species has become a major issue after publication of the draft European Food Safety Authority （EFSA） Guidance on risk assessment of plant protection products （PPP） on bees （Apis mellifera, Bombus spp. and solitary bees）. According to this guidance document, field studies have to be designed to be able to detect significance differences as low as 7% for certain endpoints such as reduction in colony size. This will require an immense number of replicates which is obviously not feasible. In the present study, key endpoints such as mortality, termination rate and number of brood cells in honeybee studies, cocoon production and flight activity in solitary bee studies and number of gynes in bumble bee studies （just to mention some of the endpoints considered） in semi-field studies were analyzed, with Apis mellifera, Bombus terrestris and Osmia bicornis during the past five years （2013-2017）. The results indicate huge differences in the percentage minimal detectable differences （%MDDs） （MDD expressed as median of control value of the endpoint in percent） depending on endpoint and species tested. For honeybee semi-field studies, the lowest %MDDs recorded were between 10% and 15% for the endpoints foraging, number of brood cells and colony strength. The highest %MDDs were observed for the endpoint termination rate, with a %MDD of almost 50%. For the endpoints in bumble bee semi-field studies the %MDDs varied between 17% for bumble bee colony weight and 53% for average mortality during the exposure period in the tunnel. The %MDD for the number of gynes （young queens） was slightly below 25%. For the semi-field solitary bee test system, the %MDDs for the measured endpoints seem to be lower than those for the other two species tested. The %MDDs for the endpoints hatching of offspring, nest occupation and number of cocoons were 8%, 13% and 14%, respectively. Most of the %MDDs were between 10% and 30% indicating clearly that the currently performed experimental design for the semi-field pollinator studies allowed to determine relatively small effects on key study endpoints. The analysis indicated that for all the three bee species tested, the semi-field test design detected low %MDDs for most of the endpoints. It was also observed that detectable differences between the control and PPP treatments were much lower in semi-field test designs than in field studies with these bee species. The “perfect sample size” really does not exist but test design and statistical analysis can be adapted to lower the %MDDs. Measured and simulated （according to Student’s t-test-distribution） data and results showed that statistical evaluations parameter selection （e.g., alpha value）, data transformation （log10） and the number of replicates had a direct effect on the ability of the test design to detect lower or higher %MDD values. It could show that a change of alpha value from 0.05 to 0.1, increases the ability of the studies to detect lower %MDDs. For most of the measured endpoints, increasing the number of replicates e.g., from four to eight, improved the power of the test design by decreasing the %MDD. The reduction magnitude of the %MDD is dependent on the endpoint and selection of statistical parameters such as the alpha value. Parameters that display effects at a biologically relevant scale will be a better indicator for effects than parameters that are able to detect minor differences that are not biologically relevant.

Extreme points, support points and the Loewner variation in several complex variables

In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class So（Bn） of biholomorphic mappings on Bn which have parametric representation, i.e., they are the initial elements f（-, O） of a Loewner chain f（x,t） = etz ＋ ... such that {e-tf（.,t）}t≥o is a normal family on Bn. We show that if f（.,O） is an extreme point （respectively a support point） of So（Bn）, then e-t f（., t） is an extreme point of So（Bn） for t≥0 （respectively a support point of So（Bn） for t C [O, t0] and some to〉 0）. This is a generalization to the n-dimensional case of work due to Pell. Also, we prove analogous results for mappings which belong to So（Bn） and which are bounded in the norm by a fixed constant. We relate the study of this class to reachable sets in control theory generalizing work of Roth. Finally we consider extreme points and support points for biholomorphic mappings of Bn generated by using extension operators that preserve Loewner chains.