Pointed Hopf Algebras and Quasi-isomorphisms

We show that a large class of finite-dimensional pointed Hopf algebras is quasi-isomorphic to their associated graded version coming from the coradical filtration, i.e. they are 2-cocycle deformations of the latter. This supports a slightly specialized form of a conjecture of Masuoka. Presented by A. Verschoren Mathematics Subject Classification (2000) 17B56. Daniel Didt: This work will be part of the author's PhD thesis written under the supervision of Professor H.-J. Schneider. The author is a member of the Graduiertenkolleg ‘Mathematik im Bereich ihrer Wechselwirkung mit der Physik’ at Munich University.     

The behavior on fundamental group of a free pro-homotopy equivalence

We study the question: given a morphism $\text{?{(X}{}_{\mathrm{n}}\text{, x}{}_{\mathrm{n}}\text{)}→{(Y}{}_{\mathrm{n}}\text{, y}{}_{\mathrm{<mtext>n</mtext>}}\text{)}}$ in the category pro-(Poi nted. Homotopy) where the domain and range are inverse sequences of well-pointed CW complexes, and given that ? induces an isomorphism {X_n}→{Y_n} in pro-(Homotopy), what additional hypotheses force ? to be an isomorphism in pro-(Pointed Homotopy)? Conjecture. If the dimensions of the Y_n's are bounded, then ? is an isomorphism in pro-(Pointed Homotopy). We first prove the special case of this conjecture in which dim Y_n?d<∞ for all n, and $\text{lim}\text{{H}{}_{\mathrm{d}}\text{Y}{}_{\mathrm{n}}\text{}≠0}$, Y_n being the universal cover of Y_n. Then we deal with the general case: we show that there are certain elements of each π₁Y_n with the properties: (i) these elements commute if and only if ? is an isomorphism in pro-(Pointed Homotopy); (ii) if dim Y_n?d<∞ for all n, then powers of these elements commute. While (i) and (ii) are not incompatible, this result puts severe restrictions on the nature of any possible counter-example to the conjecture.Our method also gives pro-homotopy analogues of the well-known fact that if a K(π, 1) is N-dimensional, then π is torsion-free and contains no abelian subgroup of rank>N. The latter theorems apply to inverse sequences {Y_n} of CW complexes where dim Y_n is finite but not necessarily bounded, hence in particular to infinite-dimensional shape-aspherical compacta.     

密勒补偿技术在电子线路中的作用

提出一种如不采用相位补偿技术,则施加反馈,组成实际应用电路时往往会引起放大器自激。因此,应用电路中,采用密勒补偿技术,具有一定的应用价值。     

A study of the pointed observation methods and sensitivity of HXMT

The Hard X-ray Modulation Telescope （HXMT） is an X-ray astronomy satellite consisting of three slat-collimated instruments, the High Energy X-ray Instrument （HE）, the Medium Energy X-ray Instrument （ME）, and the Low Energy X-ray Instrument （LE）. HXMT will carry out an all sky survey and make pointed observations in the 1-250 keV energy band. In order to get the source and background fluxes simultaneously in the pointed observations, two methods, i.e., the combined field of view （FOV） method and the off-axis pointing method are proposed in this paper. Comprehensive analyses of the sensitivities of the three instruments by using these two methods are presented, respectively. It is found that the off-axis pointing method has a higher sensitivity for HE and ME but a lower sensitivity for LE. Since the axes of the three instruments are aligned along the same direction, the off-axis pointing method is recommended as the main method in the pointed observation for HXMT; the combined FOV method can be used when LE is the most relevant instrument in order to satisfy the scientific objective of the observation.     

Adjunctions and Locally Transferable Factorization Systems

We present an approach to construct factorization systems in abstract categories. It gives new factorization systems from some given ones, when we have a relevant family of adjunctions between slice categories. The approach is based on the notion of a local factorization system, which is introduced in this paper. Relations between local factorization systems and full replete reflective subcategories of corresponding slice categories are investigated. Several applications of this approach are given.     

The Conley Index Over the Circle

We study the Conley index over a base in the case when the base is the circle. Such an index arises in a natural way when the considered flow admits a Poincaré section. In that case the fiberwise pointed spaces over the circle generated by index pairs are semibundles, i.e., admit a special structure similar to locally trivial bundles. We define a homotopy invariant of semibundles, the monodromy class. We use the monodromy class to prove that the Conley index of the Poincaré map may be expressed in terms of the Conley index over the circle.     

Hopf代数的Kaplansky十大猜想的一些新进展

本文介绍了Hopf代数中众所周知的Kaplansky十大猜想及其进展.     

锥伪单调和锥严格拟凸映射向量平衡问题

研究在锥伪单调、锥拟凸、锥严格拟凸和次连续条件下几类二元向量平衡问题解的关系，利用KyFan不动点定理证明了解的存在性。     

一类积分微分包含的周期解

研究了一类积分微分包含的周期解,利用Kakutani不动点定理和Tichonoff不动点定理给出了凸和非凸两种情形下周期解存在的充分条件.