A note on the CC-numerical radius and the λ\lambda-Aluthge transform in finite factors

We prove that for any two elements $A$, $B$ in a factor $M$, if $B$ commutes with all the unitary conjugates of $A$, then either $A$ or $B$ is in $\mathbb{C}I$. Then we obtain an equivalent condition for the situation that the $C$-numerical radius $\omega_{C}(\cdot)$ is a weakly unitarily invariant norm on finite factors and we also prove some inequalities on the $C$-numerical radius on finite factors. As an application, we show that for an invertible operator $T$ in a finite factor $M$, $f(\bigtriangleup_{\lambda}(T))$ is in the weak operator closure of the set $\{\sum_{i=1}^{n}z_{i}U_{i}f(T)U_{i}^{*}|n\in\mathbb{N},(U_{i})_{1\leq i\leq n}\in \mathscr{U}(M),\sum_{i=1}^{n}|z_{i}|\leq 1\}$, where $f$ is a polynomial, $\bigtriangleup_{\lambda}(T)$ is the $\lambda$-Aluthge transform of $T$ and $0\leq\lambda \leq 1$.Comment: 11pages. arXiv admin note: text overlap with arXiv:math/0512197 by other author

Potential of ABA Antagonists in Promoting Germination of Canola, Chickpea and Soybean Seeds under Low Temperature

Canola (Brassica napus L.), soybean (Glycine max (L.) Merr.) and chickpea (Cicer arietinum L.) are important crops in Canada for their contributions to both the national economy and international markets. However, seed germination of these crops is sensitive to ambient temperature. Cold temperatures in the early spring severely inhibit seed germination, potentially preventing the plant from completing its life cycle within the growing season. One major factor that causes the delay in seed germination is the increased ABA level, which is triggered by cold stress. ABA antagonists, a class of synthetic chemicals, could counteract the effects of ABA and, hence, promote seed germination under low temperature (LT). The main objective of this study was to identify effective ABA antagonists in promoting germination under LT. ABA 1009 was selected for its significant promoting effect on canola seed germination. ABA 1009 was found to be effective across different canola cultivars and it was able to promote radicle growth. The application of ABA 1009 on canola and soybean seeds during germination counteracted the effects of exogenous ABA application. Hormone analysis was done on canola seeds treated with ABA 1009. The increased amount of ABA metabolites in the seeds indicated up-regulation of ABA catabolism caused by the application of ABA 1009. The increased levels of ABA and ABA 1009 concentrations within the seeds over time indicated that overdosage of ABA 1009 caused an increase in ABA biosynthesis. Hormone analysis of similar experiments in soybean and chickpea seeds suggested that the delay in germination was related to the high ABA levels within the seeds. Gene expression analysis on canola seeds treated with ABA 1009 showed that AAO3, AAO4, NCED5, NCED6, and NCED9 genes were involved in ABA biosynthesis, while CYP707A4 was involved in ABA degradation

Class-level Multiple Distributions Representation are Necessary for Semantic Segmentation

Existing approaches focus on using class-level features to improve semantic segmentation performance. How to characterize the relationships of intra-class pixels and inter-class pixels is the key to extract the discriminative representative class-level features. In this paper, we introduce for the first time to describe intra-class variations by multiple distributions. Then, multiple distributions representation learning(\textbf{MDRL}) is proposed to augment the pixel representations for semantic segmentation. Meanwhile, we design a class multiple distributions consistency strategy to construct discriminative multiple distribution representations of embedded pixels. Moreover, we put forward a multiple distribution semantic aggregation module to aggregate multiple distributions of the corresponding class to enhance pixel semantic information. Our approach can be seamlessly integrated into popular segmentation frameworks FCN/PSPNet/CCNet and achieve 5.61\%/1.75\%/0.75\% mIoU improvements on ADE20K. Extensive experiments on the Cityscapes, ADE20K datasets have proved that our method can bring significant performance improvement

Stability Analysis and Reinforcement of the Existing Karst Cave Passing through Yujingshan Tunnel

High-speed Railway tunneling in karst terrain presents a huge challenge to the engineer including the identification, stability analysis and reinforcement of the karst cavities. The Cheng-Gui high-speed railway tunnel had to pass through the largest karst cave discovered in tunnel construction. To guaranteeing the tunnel construction safety, a series of corresponding prevention and control measures are put forward. To begin with, geological drilling, electromagnetic method and surface electrical resistivity tomography are adopted to detect and delineate the underground karst zone. Based on the detection results, this paper has put forward strategies to make the pre-support of karst cave and the main technical of those strategies include: the side-walls or in the crown was applied with shotcret (C40 steel fiber concrete); use expanding-shell pre-stressed hollow anchor rod and pre-stressed cable reinforcement; fix steel-mesh-bolting; the shotcrete sealing was applied. Moreover, if instabilities would develop in the side-walls, it should be sufficient to stabilize the cavities, to do dental cleaning of the broken rocks, and fill the voids with shotcrete or pumped lean concrete. At last, systematic grouting treatment around the excavated section, and was excavated with the layer-step method. The solutions presented here may provide guidance for the design and construction of high-speed railway tunnels to be implemented affected by karst processes. The technical validation of the proposed solutions was demonstrated by the successful completion of the Yujingshan tunnel. Please click Additional Files below to see the full abstract

Moderating effect of classroom sociable norm on the relations between unsociability and internalizing problems in Chinese adolescents

ObjectivesThe goal of the present study was to examine the moderating effect of classroom sociable norm on the relations between unsociability and internalizing problems (the indicators included depression, loneliness and self-esteem) in Chinese adolescents.MethodsParticipants were N = 1,160 adolescents in Grade 4–8 from Shanghai, People’s Republic of China. They completed questionnaires about unsociability, sociability, and social preference via peer nominations, while depression, loneliness, and self-esteem were collected via self-report.ResultsIt was found that unsociability was positively associated with depression and loneliness, and negatively associated with self-esteem. Moreover, the relations between unsociability and indicators of internalizing problems were moderated by classroom sociable norm. More specifically, the significant positive associations between unsociability and depression and loneliness were stronger in classrooms with high sociable norm, and the negative association between unsociability and self-esteem was only significant in such classrooms.ConclusionThe findings suggest that classroom sociable norm plays an important role in unsociable adolescents’ psychological adjustment in China. Researchers should focus more on the influence of classroom environment on adolescents’ development in future