Realizing enveloping algebras via moduli stacks

Let $\mathop{\rm CF}\nolimits(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$

Effects of corrective feedback on EFL speaking task complexity in China’s university classroom

Corrective feedback (CF) and task complexity are two important pedagogical topics in second language acquisition research in recent years, but there is few research investigating effects of CF on speaking task complexity in China’s university classroom settings. This research, through conducting different versions of speaking task experiments among 24 university students in China, explores the effect of teachers’ CF on English as a Foreign Language (EFL) speaking task complexity. According to the analysis of first-hand data, this research finds CF has different effects on EFL oral production with different task complexity. In simple speaking task, the effects of five kinds of CF (from largest to smallest) are listed as follows: clarification quest, metalinguistic feedback, recast, repetition and confirmation check. Regarding complex speaking task, the effects of five categorized CF are ranked from largest to smallest as follows: metalinguistic feedback, confirmation check, recast, clarification request and repetition. Improving to provide CF in pedagogical practice is an important contribution to promote EFL speaking task, so, on the basis of above research results, appropriate ways and forms of providing CF are expected to promote efficiency of CF in EFL classroom under the context of Chinese university classroom

Multiplicative Lidskii's inequalities and optimal perturbations of frames

In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame \cF for \hil\cong\C^d we compute those dual frames \cG of \cF that are optimal perturbations of the canonical dual frame for \cF under certain restrictions on the norms of the elements of \cG. On the other hand, for a fixed finite frame \cF=\{f_j\}_{j\in\In} for \hil we compute those invertible operators $V$ such that $V^*V$ is a perturbation of the identity and such that the frame V\cdot \cF=\{V\,f_j\}_{j\in\In} - which is equivalent to \cF - is optimal among such perturbations of \cF. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.Comment: 22 page

Experimental investigation of the low molecular weight fluoropolymer for the ultracold neutrons storage

The experimental setup for examining the low-molecular-weight fluoropolymer CF$_{3}$(CF$_{2})_{3}$-O-CF$_{2}$-O-(CF$_{2})_{3}$CF$_{3}$, which is a promising coating material for the walls of storage chambers for ultracold neutrons, is described. The results are detailed. The measurement data are interpreted in the model of a multilayer complex quantum-mechanical potential of the chamber walls.Comment: Corrected version of the paper published in Phys. of Part. and Nucl Lett., 15 (No.5) (2018) 54

Genes Encoding Recognition of the Cladosporium fulvum Effector Protein Ecp5 Are Encoded at Several Loci in the Tomato Genome

The molecular interactions between tomato and Cladosporium fulvum have been an important model for molecular plant pathology. Complex genetic loci on tomato chromosomes 1 and 6 harbor genes for resistance to Cladosporium fulvum, encoding receptor like-proteins that perceive distinct Cladosporium fulvum effectors and trigger plant defenses. Here, we report classical mapping strategies for loci in tomato accessions that respond to Cladosporium fulvum effector Ecp5, which is very sequence-monomorphic. We screened 139 wild tomato accessions for an Ecp5-induced hypersensitive response, and in five accessions, the Ecp5-induced hypersensitive response segregated as a monogenic trait, mapping to distinct loci in the tomato genome. We identified at least three loci on chromosomes 1, 7 and 12 that harbor distinct Cf-Ecp5 genes in four different accessions. Our mapping showed that the Cf-Ecp5 in Solanum pimpinellifolium G1.1161 is located at the Milky Way locus. The Cf-Ecp5 in Solanum pimpinellifolium LA0722 was mapped to the bottom arm of chromosome 7, while the Cf-Ecp5 genes in Solanum lycopersicum Ontario 7522 and Solanum pimpinellifolium LA2852 were mapped to the same locus on the top arm of chromosome 12. Bi-parental crosses between accessions carrying distinct Cf-Ecp5 genes revealed putative genetically unlinked suppressors of the Ecp5-induced hypersensitive response. Our mapping also showed that Cf-11 is located on chromosome 11, close to the Cf-3 locus. The Ecp5-induced hypersensitive response is widely distributed within tomato species and is variable in strength. This novel example of convergent evolution could be used for choosing different functional Cf-Ecp5 genes according to individual plant breeding needs