Spaces of Maps into Classifying Spaces for Equivariant Crossed Complexes, II: The General Topological Group Case

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for crossed complexes, using detailed results on the appropriate Eilenberg–Zilber theory, and of its relation to simplicial homotopy coherence. Again, our results give information not just on the homotopy classification of certain equivariant maps, but also on the weak equivariant homotopy type of the corresponding equivariant function spaces.     

Tunneling between double wells of atom in crossed electromagnetic fields

The tunneling between double wells of atom in crossed electromagnetic fields is investigated by a one-dimensional Hamiltonian model. The crossed fields induced outer well is apart from the nuclear origin and it is very difficult to access by means of spectroscopy but it will be possible if there exists the tunneling of the electron between the outer well and the Coulomb potential predominated well at the nuclear origin. A one-dimensional quantum calculation with B-spline basis has been performed for hydrogen atom in crossed fields accessible in our laboratory, at B=0.8~T and F=-220~V.cm^-1. The calculation shows that the wavefunctions of some excited states close to the Stark saddle point in the outer well extend over to the Coulomb potential well, making it possible to penetrate the quantum information of the outer well. However, the tunneling rate is very small and the spectral measurement of the transitions from the ground state should be of a high resolution and high sensitivity.     

Hereditary crossed products

We characterize when a crossed product order over a maximal order in a central simple algebra by a finite group is hereditary. We need only concentrate on the cases when the group acts as inner automorphisms and when the group acts as outer automorphisms. When the group acts as inner automorphisms, the classical group algebra result holds for crossed products as well; that is, the crossed product is hereditary if and only if the order of the group is a unit in the ring. When the group is acting as outer automorphisms, every crossed product order is hereditary, regardless of whether the order of the group is a unit in the ring.

     

散斑照相孔径优化的研究

本文提出了三种新的散斑照相孔径方法:一维调频孔径法,交叉孔径法和旋转孔径法。给出了理论分析和实验证明。这些方法简单实用,能有效地改变衍射晕的能量分布。适当选择孔径的参数,实验者能相当任意地控制散斑图的空间频率成份。新方法兼顾了突出某一频率成份、灵敏度连续可调、获得多个方向散斑场运动信息等各方面的特性。     

Existence of traveling wave solutions for influenza model with treatment

To investigate the spreading speed of influenza and the influence of treatment on the spreading speed, a reaction–diffusion influenza model with treatment is established. The existence of traveling wave solutions is shown by introducing an auxiliary system and applying the Schauder fixed point theorem. The non-existence of traveling wave solutions is proved by a two-sided Laplace transform, which needs a new approach for the prior estimate of exponential decay of traveling wave solutions.     

NH4H2PO4/SiO2: a recyclable,efficient heterogeneous catalyst for crossed aldol condensation reaction

Abstract

Crossed aldol condensation of aromatic aldehydes with cyclic ketones in the presence of catalytic amount of NH₄H₂PO₄/SiO₂ (as a safe, green, and cheap heterogeneous catalyst) under solvent-free condition afforded α,?-bis(substituted-benzylidene) cycloalkanones in high yields. This method is general with respect to all types of aromatic aldehydes and is an eco-friendly procedure. And the catalyst is easily prepared, stable, reusable, and efficient under the reaction conditions.     

A note on p-supersolvable groups

The notion of Hankel operators associated with analytic crossed products were introduced and researched in [2]. In this paper, we study the adjoint of Hankel operators and give necessary and sufficient condition that the adjoint of a Hankel operator is again a Hankel operator. This work was supported in part by a Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science.     

优化的合班问题

首次提出了我国高校排课中的合班工作对于排课的影响问题,建立了优化合班问题的数学模型,它是一个非线性的整数规划问题.集中讨论二维合班问题.文章中给出了两个适用于合班模型的其它例子,在此基础上归纳出适用于合班模型的一般数学模式,称之为交叉分类问题.     

AF-embeddability of crossed products of Cuntz algebras

We investigate crossed products of Cuntz algebras by quasi-free actions of abelian groups. We prove that our algebras are AF-embeddable when actions satisfy a certain condition. We also give a necessary and sufficient condition that our algebras become simple and purely infinite, and consequently our algebras are either purely infinite or AF-embeddable when they are simple.