Galois G-covering of quotients of linear categories

In this paper, we introduce the notion of G-liftable ideals, which extends the liftable ideas defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the Galois G-coverings of quotients of categories associated to the G-liftable ideals. In particular, we study the behavior of G-liftable admissible ideals under Galois G-coverings. Furthermore, we show that the ideals generated by finite dimensional projective modules over a locally bounded linear categories are admissible G-liftable ideals. As an application, we provide a reduction technique for dealing with the existence of Serre functors in the stable categories of Gorenstein projective objects.     

Interactions of DNA with graphene and sensing applications of graphene field-effect transistor devices: A review

Graphene field-effect transistors (GFET) have emerged as powerful detection platforms enabled by the advent of chemical vapor deposition (CVD) production of the unique atomically thin 2D material on a large scale. DNA aptamers, short target-specific oligonucleotides, are excellent sensor moieties for GFETs due to their strong affinity to graphene, relatively short chain-length, selectivity, and a high degree of analyte variability. However, the interaction between DNA and graphene is not fully understood, leading to questions about the structure of surface-bound DNA, including the morphology of DNA nanostructures and the nature of the electronic response seen from analyte binding. This review critically evaluates recent insights into the nature of the DNA graphene interaction and its affect on sensor viability for DNA, small molecules, and proteins with respect to previously established sensing methods. We first discuss the sorption of DNA to graphene to introduce the interactions and forces acting in DNA based GFET devices and how these forces can potentially affect the performance of increasingly popular DNA aptamers and even future DNA nanostructures as sensor substrates. Next, we discuss the novel use of GFETs to detect DNA and the underlying electronic phenomena that are typically used as benchmarks for characterizing the analyte response of these devices. Finally, we address the use of DNA aptamers to increase the selectivity of GFET sensors for small molecules and proteins and compare them with other, state of the art, detection methods.     

Polymeric materials for lithium‐ion cells

Lithium‐ion (Li‐ion) cells have gained considerable attention in recent years as a power source for various applications owing to their high voltage, high energy density, low self‐discharge, and excellent cycle life. Polymeric materials play a pivotal role in the processing, performance, and safety of Li‐ion cells. The polymeric materials used in Li‐ion cells include: binder for electrode processing, separator, electrolyte, and electrode active material. Active research is being pursued in all of these areas to improve the energy density, power density, cycle life, and safety of Li‐ion cells. This review article gives an overview of the various polymeric materials used in Li‐ion cells and the recent advances in these materials. Copyright © 2017 John Wiley & Sons, Ltd.     

代数$\Omega$-范畴的等价范畴

本文基于$\Omega$-范畴研究了(连续) $\mathcal{I}$-余万备$\Omega$-范畴的一些性质. 我们给出了双完备$\Omega$-范畴和逼近双模的概念并讨论了它们的性质, 证明了任何$\mathcal{I}$-余万备$\Omega$-范畴都是双完备$\Omega$-范畴. 得到了代数$\Omega$-范畴范畴等价于双完备$\Omega$-范畴.     

On categories associated to a Quasi-Hopf algebra

A quasi-Hopf algebra H can be seen as a commutative algebra A in the center 𝒵(H-Mod) of H-Mod. We show that the category of A-modules in 𝒵(H-Mod) is equivalent (as a monoidal category) to H-Mod. This can be regarded as a generalization of the structure theorem of Hopf bimodules of a Hopf algebra to the quasi-Hopf setting.     

Positions of characters in finite groups and the Taketa inequality

We define the position of an irreducible complex character of a finite group as an alternative to the degree. We then use this to define three classes of groups: position reducible (PR)-groups, inductively position reducible (IPR)-groups and weak IPR-groups. We show that IPR-groups and weak IPR-groups are solvable and satisfy the Taketa inequality (ie, that the derived length of the group is at most the number of degrees of irreducible complex characters of the group), and we show that any M-group is a weak IPR-group. We also show that even though PR-groups need not be solvable, they cannot be perfect.     

Bounded complexes of cotorsion sheaves

We provide a necessary and su?cient condition which ensure that every flat quasi-coherent sheaf has finite cotorsion dimension. Also, we will show that every locally noetherian scheme with a dualizing complex has this requirement.     

香港大屿山残坡积土的残余强度试验研究

粘性土的残余强度是边坡稳定性评价、桩基与土的相互作用机理研究及填土边坡设计中的重要参数。本文在综述大量文献的基础上，结合香港大屿山火山岩风化残坡积土的残余强度试验研究，分析了残余强度的测试方法和影响残余强度的因素。研究结果表明，残余强度与有效法向应力间具有明显的非线性关系；与单剪测试结果相比，多级剪测试结果明显偏高。     

L-fuzzy Q-convergence structures

In this paper, we construct a topological category of pretopological L-fuzzy Q-convergence spaces, which contains the category of topological L-fuzzy Q-convergence spaces as a bireflective full subcategory. Considering the connections with L-fuzzy topology, it is proved that the category of topological L-fuzzy Q-convergence spaces is isomorphic to the category of topological L-fuzzy quasi-coincident neighborhood spaces, and the latter is isomorphic to the category of L-fuzzy topological spaces. Moreover, we find that our pretopological L-fuzzy Q-convergence spaces can be characterized as a kind of L-fuzzy quasi-coincident neighborhood spaces, which is called strong L-fuzzy quasi-coincident neighborhood space.     

模范畴Recollement的Koenig定理

Koenig定理描述了环的导出范畴允许recollement的一个充分必要条件.本文给出环的模范畴版本的Koenig定理及其应用.应用一是可以导出Morita等价定理,应用二是可以描述三角矩阵环与模范畴的recollement之间的密切联系.