Probe‐assisted spin manipulation in one‐dimensional quantum dots

We study a spin structure that arises in a one‐dimensional quantum dot with zero total spin under the action of a charged tip of a scanning probe microscope in the presence of a weak magnetic field. The evolution of spin structure with changing the probe position is traced to show that the movable probe can be an effective tool to manipulate the spin. The spin structures are formed when the probe is located in certain regions along the dot due to Coulomb interaction of electrons as they are redistributed between the two sections in which the quantum dot is divided by the potential barrier created by the probe. There are two main states: spin‐polarized and non‐polarized ones. The transition between them is accompanied by a spin precession governed by the Rashba spin–orbit interaction induced by the electric field of the probe. In the transition region the spin density changes strongly while charge distribution remains nearly unchanged. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

An improved strongly sub-feasible SSLE method for optimization problems and numerical experiments

In this paper, the super-linearly and quadratically convergent strong sub-feasible method [J.L. Li, J.B. Jian, A superlinearly and quadratically convergent strongly subfeasible method for nonlinear inequality constrained optimization, OR Transactions, 7 (2) (2003) 21-34] for nonlinear inequality constrained optimization is improved, such that the iterative points can get into the feasible region after a finite number of iterations. As a result, a strict restricted condition can be overcome. Another two contributions of this paper are that a new bidirectional Armijo line search is presented and a lot of numerical comparison results are reported.     

Stable rigged configurations for quantum affine algebras of nonexceptional types

For an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the Dynkin diagram to the rest, and the fermionic formula of not type A can be expressed as a sum of that of type A with Littlewood–Richardson coefficients. Combining this result with Kirillov et al. (2002) [13] and Lecouvey et al. (2011) [18] we settle the X=M conjecture under the large rank hypothesis.     

基于次梯度选取的非光滑优化强次可行方向法

本文结合次梯度选取技术及割平面法和强次可行方向法的思想,提出了一个求解目标函数非光滑约束优化问题的强次可行方向算法.通过设计一个新的寻找搜索方向子问题和构造新型线搜索,算法不仅能接受不可行的初始点,而且能保持迭代点的强次可行性,同时避免在可行域外目标函数值的不适度增加.算法具备全局收敛性,且初步的数值试验表明算法是稳定有效的.     

Group extensions and free actions by finite groups on solvmanifolds

The purpose of this paper is to generalize Yalçin's result [Trans. Amer. Math. Soc. 352 , 2689–2700 (2000)] from tori to solvmanifolds. As a result, we prove that if (?_p)^r acts freely on a solvmanifold M of dimension n, then r ≤ n (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Density Functional Theory Calculations of Structural,Electronic, and Magnetic Properties of the 3d Metal Trifluorides MF3 (M = Ti-Ni) in the Solid State

We employ density functional theory with Hubbard U correction or hybrid functionals to study the series of magnetic 3d metal trifluorides MF₃ (M = Ti-Ni). Experimental lattice parameters are reproduced with an error margin of 0.5%–4.3%. Cooperative Jahn–Teller distortions are reproduced for MnF₃, but also found in TiF₃ and CoF₃ at smaller levels compared to MnF₃. Trends in electronic structure with respect to positions of the d bands are linked to the magnetic properties where M = Ti-Cr are weak magnetic Mott–Hubbard insulators, M = Fe-Ni are strong magnetic charge-transfer insulators and MnF₃ falls in between. Our work contributes to the characterization of the relatively unknown NiF₃, since FeF₃ and CoF₃ have similar electronic and magnetic properties. However, NiF₃ does not show a Jahn–Teller distortion as present in CoF₃. © 2019 Wiley Periodicals, Inc.     

Modified Roper-Suffridge operator for some holomorphic mappings

In this paper, we will study the operator given by

弦图子类的全控制函数

本文首先证明了k-全控制问题和符号全控制问题在双弦图上均为NP-完全的.其次,在强消去序已给定的强弦图上,给出了求解符号全控制、负全控制、k-全控制和k-全控制问题的统一的O(m+n)时间算法.     

Weighted estimates for strongly singular integral operators with rough kernels

The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.     

Propagation of optical vortex solitons due to the Gouy phase in strongly nonlocal nonlinear media

In this paper,we present a study on the propagation of the symmetrical optical vortices formed by two collinear Laguerre-Gauss solitons in strongly nonlocal nonlinear media.The optical vortices,which move along the beam axis as the light propagates,result in a rotation of the beam’s transverse profile.This physical reason of the rotation is the Gouy phase acquired by the component beams.