Quasi-range-preserving Operator

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“Hopf Algebra”(E.Abe)中若干基本结论的修正或改进

本文对专著“Hopf Algebra”（E．Abe）中若干基本结论或其证明的不妥或错误之进行了修正和改进。     

Ideals and the binary discriminator in universal algebra

We introduce the binary discriminator and the dual binary discriminator and the corresponding universal algebras with 0. The latter are related to permutability and distributivity at 0. For A finite the dual binary discriminator is in the intersection of all maximal subclones of the clone of all f satisfying f (0,...,0) = 0 (except certain maximal subclones if A is of prime power cardinality). An algebra with a special binary term function and a special unary term function is a dual binary discriminator algebra if and only if it is ideal-free. Finally we characterize binary and dual binary discriminator varieties. Received April 3, 1997; accepted in final form July 28, 1998.     

地震作用下结构的基于阻尼柔性连接MTMD控制

研究了基于阻尼柔性连接多重高谐质量阻尼器(MTMD)在减小结构地震反应方面的动力特性。利用导出的设置MTMD结构的传递函数，建立了设置MTMD结构的动力放大系数(DMF)设计公式，于是MTMD的优化准则可定义为结构最大动力放大系数的最小值的最小化(Min．Min．Max．DMF)。根据优化准则，得不同刚度比MTMD的最优参数和相应的Min.Min.Max．DMF值。为比较，同时给出了基于阻尼刚性连接(R＝0)MTMD的结果，广泛的数值分析表明，传统的阻尼刚性连接MTMD的性能可以扩展至一定刚度比范围的阻尼柔性连接MTMD。     

结构主动开闭环多重调谐质量阻尼器（AMTMD）新控制策略

提出了一种新控制策略——主动开闭环多重调谐质量阻尼器(AMTMD)。AMTMD控制系统频率呈线性分布。AMTMD中的MTMD保持相同的刚度和阻尼系数但质量变化。基于TMD的工作原理定义了AMTMD的主动控制力构成即保持相同的位移和速度反馈增益系数但变化结构和地震加速度反馈增益系数。基于结构的广义振型模型，导出了设置AMTMD时结构的动力放大系数(DMF)，于是优化准则可定义为：Min．Min．Max．DMF．通过最优搜寻，研究了反映AMTMD有效性和鲁棒性的参数。这些参数包括：频率间隔、平均阻尼比、调谐频率比、总数、质量比和标准化加速度反馈增益系数。为了比较，多重调谐质量阻尼器(MTMD)和主动开闭环调谐质量阻尼器(ATMD)也被考虑。     

Poisson deleting derivations algorithm and Poisson spectrum

Cauchon [5 Cauchon, G. (2003). Effacement des dérivations et spectres premiers des algèbres quantiques. J. Algebra 260(2):476–518.[Crossref], [Web of Science ®] , [Google Scholar]] introduced the so-called deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and then to show that torus-invariant primes in these algebras are generated by quantum minors. Since then this algorithm has been used in various contexts. In particular, the matrix version makes a bridge between torus-invariant primes in generic quantum matrices, torus orbits of symplectic leaves in matrix Poisson varieties and totally non-negative cells in totally non-negative matrix varieties [12 Goodearl, K. R., Launois, S., Lenagan, T. (2011). Torus invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves. Math. Z. 269(1):29–45.[Crossref], [Web of Science ®] , [Google Scholar]]. This led to recent progress in the study of totally non-negative matrices such as new recognition tests [18 Launois, S., Lenagan, T. (2014). E?cient recognition of totally non-negative matrix cells. Found. Comput. Math. 14:371–387.[Crossref], [Web of Science ®] , [Google Scholar]]. The aim of this article is to develop a Poisson version of the deleting derivations algorithm to study the Poisson spectra of the members of a class 𝒫 of polynomial Poisson algebras. It has recently been shown that the Poisson Dixmier–Moeglin equivalence does not hold for all polynomial Poisson algebras [2 Bell, J., Launois, S., Sanchez, O. L., Moosa, R. Poisson algebras via model theory and differential-algebraic geometry. J. Eur. Math. Soc. (to appear). [Google Scholar]]. Our algorithm allows us to prove this equivalence for a significant class of Poisson algebras, when the base field is of characteristic zero. Finally, using our deleting derivations algorithm, we compare topologically spectra of quantum matrices with Poisson spectra of matrix Poisson varieties.     

On the negative cyclic homology of <Emphasis Type="Italic">shc</Emphasis>-algebras

Let be a field of characteristic and S ¹ the unit circle. We prove that the shc-structure on a cochain algebra (A,d _A ) induces an associative product on the negative cyclic homology HC _*⁻ A. When the cochain algebra (A,d _A ) is the algebra of normalized cochains of the simply connected topological space X with coefficients in , then HC _*⁻ A is isomorphic as a graded algebra to the S ¹-equivariant cohomology algebra of LX, the free loop space of X. We use the notion of shc-formality introduced in Topology 41, 85–106 (2002) to compute the S ¹-equivariant cohomology algebras of the free loop space of the complex projective space when n + 1 = 0 [p] and of the even spheres S ²ⁿ when p = 2.      

L-模糊伪理想及其性质

给出了L-模糊伪理想的概念,借助L-模糊集的几种截集给出了它的刻画,研究了它的运算性质。     

EI代数

为了更好地解决模糊概念的表示问题,文[1]引入了AFS代数和AFS结构,为了讨论AFS代的拓扑性质,本文在[1]的基础上,进一步了讨论了EI代数的性质与结构,并对其子代数EM－{φ}的性质和结构进行了讨论。