The antipode of a quasitriangular quasi-Turaev group coalgebra is bijective

In order to construct a class of new Turaev-braided group category with nontrivial associativity, the concept of a quasitriangular quasi-Turaev group coalgebras was recently introduced. Inside the definition, the conditions of invertibility of the R-matrix R and bijectivity of the antipode S are required. In this article, we prove that the antipode of a quasitriangular quasi-Turaev group coalgebra without the assumptions about invertibility of the antipode and R-matrix is inner, and a fortiori, bijective. As an application, we prove that for a quasitriangular quasi-Turaev group coalgebra, two conditions mentioned above are unnecessary.     

基于持续同调的边坡土颗粒应力链失稳分析

采用颗粒离散元方法和持续同调理论,研究了内排土场堆叠至不同高度时的边坡稳定性。为便于研究,现采用一水平金属板向下施加压力,代替不同厚度土层的重力荷载,对边坡在竖向荷载作用下的失稳破坏过程进行了颗粒离散元模拟。研究了二维边坡土颗粒速度总矢量、边坡失稳破坏时滑移开裂面的角度以及边坡坡顶y方向的平均速度等宏观响应过程,并构建了自然堆积下边坡堆积体颗粒的法向力链无向网络模型。最后,用持续同调方法对边坡坡顶颗粒接触力链网络的拓扑特征进行分析,获得条码图,建立了岩体结构持续同调特征与失稳演化的关系。本文为研究边坡失稳拓扑识别提供了一种新方法,从而可以有效预测边坡的失稳破坏。     

On the structure of the automorphism group of certain automorphic loop

Automorphic loops, or A-loops, are loops in which all inner mappings are automorphisms. We investigated A-loops arising from a Lie algebra and describe their automorphism group. Also, we identify and describe their inner mapping group.     

Applications of two-sided α-generalized derivations to 3-prime near rings

Let N be a zero symmetric 3-prime right near ring and α:N→N be an endomorphism. In this paper, the notions of two-sided α-(generalized) derivations on N are studied. Some results characterize commutativity of 3-prime near rings are obtained. Examples proving the necessity of the 3-primeness hypothesis are given. When α = id_N, one can easily obtain the main results of [5 Bell, H. E., Boua, A., Oukhtite, L. (2015). Semigroup ideals and commutativity in 3-prime near rings. Commun. Algebra 43:1757–1770.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]].     

Synchronization of complex networks with time‐varying inner coupling and outer coupling matrices

Synchronization of complex networks with time‐varying coupling matrices is studied in this paper. Two kinds of time‐varying coupling are taken into account. One is the time‐varying inner coupling in the node state space and the other is the time‐varying outer coupling in the network topology space. By respectively setting linear controllers and adaptive controllers, time‐varying complex networks can be synchronized to a desired state. Meanwhile, different influences of the control parameters of linear controllers and adaptive controllers on the synchronization have also been investigated. Based on the Lyapunov function theory, we construct appropriate positive‐definite functions, and several sufficient synchronization criteria are obtained. Numerical simulations further illustrate the effectiveness of conclusions. Copyright © 2017 John Wiley & Sons, Ltd.     

A Buzano type inequality for two Hermitian forms and applications

A Buzano type inequality for two nonnegative Hermitian forms is obtained. Applications to inequalities for norm and numerical radius of bounded linear operators in complex Hilbert spaces are given.     

经典N=2李共形超代数的导子和第二上同调群

研究了经典N=2李共形超代数的导子和第二上同调群的结构,并应用第二上同调群的结果确定了该李共形超代数的泛中心扩张.     

How deeply are core electrons perturbed when valence electrons are spin polarized? The case study of transition metal compounds

The ferromagnetic and antiferromagnetic wave functions of the KMnF₃ perovskite have been evaluated quantum-mechanically by using an all electron approach and, for comparison, pseudopotentials on the transition metal and the fluorine ions. It is shown that the different number of α and β electrons in the d shell of Mn perturbs the inner shells, with shifts between the α and β eigenvalues that can be as large as 6 eV for the 3s level, and is far from negligible also for the 2s and 2p states. The valence electrons of F are polarized by the majority spin electrons of Mn, and in turn, spin polarize their 1s electrons. When a pseudopotential is used, such a spin polarization of the core functions of Mn and F can obviously not take place. The importance of such a spin polarization can be appreciated by comparing (i) the spin density at the Mn and F nuclear position, and then the Fermi contact constant, a crucial quantity for the hyperfine coupling, and (ii) the ferromagnetic–antiferromagnetic energy difference, when obtained with an all electron or a pseudopotential scheme, and exploring how the latter varies with pressure. This difference is as large as 50% of the all electron datum, and is mainly due to the rigid treatment of the F ion core. The effect of five different functionals on the core spin polarization is documented.