Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.     

On the Indecomposable Modules of Uq（sl（2）） Constructed via Ore-extension

Let A be a subalgebra of Uq (sl(2)) generated by K, K-1 and F and Aδ be a subalgebra of Uq (sl(2)) generated by K, K-1 (and also Fd if q is a primitive d-th root of unity with d an odd number). Given an Aδ -module M, a Uq (sl(2))-module AAδ M is constructed via the iterated Ore extension of Uq (sl(2)) in a unified framework for any q. Then all the submodules of AAδ M are determined for a fixed finite-dimensional indecomposable Aδ -module M . It turns out that for some indecomposable Aδ -module M , the Uq (sl(2))-module AAδ M is indecomposable, which is not in the BGG-categories Oq associated with quantum groups in general.     

Cartan Invariants in the Category of Restricted Representation for gl(m|n)

Let k be an algebraically closed field of characteristic p 2, and gl(m|n) be the general linear Lie superalgebra over k. The Cartan invariants for the restricted supermodule category for gl(m|n) are presented.     

Corrigendum to: on the inheritance of the strongly π-extending property

In this corrigendum, we provide correct versions of Theorem 2.8 and Corollary 3.2, retract two consequences of the previous form of the Theorem 2.8. To this end, the main results of the article remain after the aforementioned changes.     

Gorenstein平坦模与Frobenius扩张

设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的.     

完备化Witt代数中自然出现的一些非有限阶化李代数的表示

讨论了完备化Witt代数的三类非有限阶化子代数的不可约非权模的实现,并利用它们的表示得到一些有趣的组合恒等式.     

Polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal

In this paper, we give a polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal in terms of Minkowski sums of extremal Mirkovi?–Vilonen polytopes. As an immediate consequence of this result, we provide a necessary (but not sufficient) polytopal condition for a Mirkovi?–Vilonen polytope to lie in a Demazure crystal.     

基于单片机和光电开关的通用计数器设计

At presrent, the photoelectric switch is more and more widely used in the industrial automation equipment.It can be finished counting industrial products by using the characteristic of the photoelectric switch which can detect the objects without touching them. This design uses the modular design method,including power-supply module, The photoelectric conversion module, optocoupler isolation circuit module, power off protection module, matrix keyboard module, counting module and The display module. It mainly uses 51 single-chip microcomputer to control the system,uses the keilC51 software to design program,uses the Proteus software to complete the simulation. Through the experiment, it proves the design is feasible.     

钙钛矿太阳能电池的商业化进展与挑战

钙钛矿太阳电池是一项颠覆性的光伏技术,具有能量转化效率高、生产成本低、制备工艺简单等优势。当前,钙钛矿太阳能电池的认证效率已达25.7%,但其面临着严重的商业化瓶颈,如稳定性差、模组效率相对低、铅毒性等,且这些问题相互关联。本文简述了钙钛矿太阳能电池的工作原理和器件结构,并归纳总结了在解决钙钛矿太阳能电池稳定性、封装和模组化等商业化瓶颈问题方面的主要研究进展。最后,本文提出了钙钛矿光伏商业化进程中值得关注的解决措施。