A characterization of generalized derivations of JSL algebras

Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.     

An Extragradient-Based Alternating Direction Method for Convex Minimization

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings. However, many problems arising from statistics, image processing and other fields have the structure that while one of the two functions has an easy proximal mapping, the other function is smoothly convex but does not have an easy proximal mapping. Therefore, the classical alternating direction methods cannot be applied. To deal with the difficulty, we propose in this paper an alternating direction method based on extragradients. Under the assumption that the smooth function has a Lipschitz continuous gradient, we prove that the proposed method returns an \(\epsilon \)-optimal solution within \(O(1/\epsilon )\) iterations. We apply the proposed method to solve a new statistical model called fused logistic regression. Our numerical experiments show that the proposed method performs very well when solving the test problems. We also test the performance of the proposed method through solving the lasso problem arising from statistics and compare the result with several existing efficient solvers for this problem; the results are very encouraging.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

自旋为1/2的XY模型亚铁磁棱型链的物性和有序-无序竞争

利用不变本征算符法, 计算低温下自旋为1/2的XY模型一维亚铁磁棱型链系统的元激发谱, 讨论在此系统中不同的特殊情形下的元激发能量, 从而给出体系的三个临界磁场强度的解析解H_C1, H_C2, H_peak. 分析不同外磁场下 体系的磁化强度随温度的变化规律, 发现三个临界磁场强度的解析解H_C1, H_C2, H_peak是正确的, 并从三个元激发对磁化强度的贡献进行了说明. 低温下磁化强度随外磁场的变化呈现1/3磁化平台. 体系的磁化率随温度或者外磁场的变化都出现了双峰现象. 这说明双峰源于二聚体分子内电子自旋平行排列的铁磁交换作 用能和二聚体与单基体分子间电子自旋反平行排列的反铁磁交换作用能, 热无序能, 外磁场强度相关的自旋磁矩势能之间的竞争.     

有机发光二极管的光致磁电导效应

制备了结构为ITO/CuPc/NPB/Alq₃/LiF/Al的常规有机发光二极管, 之后对器件采用波长为442 nm和325 nm的激光线进行照射产生激子, 并在小偏压下(保证器件没有开启)对激子的演化过程进行控制, 同时测量器件的光致磁电导(photo-induced magneto-conductance, PIMC). 实验发现, 不同于电注入产生激子的磁电导效应, PIMC在正、反小偏压下表现出明显不同的磁响应结果. 当给器件加上正向小偏压时, 器件的PIMC在0-40 mT范围内迅速上升; 随着磁场的进一步增大, 该PIMC增加缓慢, 并逐渐趋于饱和. 反向小偏压时, 器件的PIMC随着磁场也是先迅速增大(0-40 mT), 但达到最大值后却又逐渐减小. 通过分析外加磁场对器件光生载流子微观过程的影响, 采用'电子-空穴对'模型和超精细相互作用理论对正向偏压下的PIMC进行了解释; 反向偏压下因各有机层的能级关系, 为激子与电荷相互作用提供了必要条件, 运用三重态激子与电荷的反应机制可以解释PIMC出现高场下降的实验现象.     

Insulator, semiclassical oscillations and quantum Hall liquids at low magnetic fields

Magneto-transport measurements are performed on two-dimensional GaAs electron systems to probe the quantum Hall (QH) effect at low magnetic fields. Oscillations following the Shubnikov-de Haas (SdH) formula are observed in the transition from the insulator to QH liquid when the observed almost temperature-independent Hall slope indicates insignificant interaction correction. Our study shows that the existence of SdH oscillations in such a transition can be understood based on the non-interacting model.     

The effect of interfacial energy anisotropy on planar interface instability in a succinonitrile alloy under a small temperature gradient

The morphological stability of a planar interface with different crystallographic orientations is studied under a small positive temperature gradient using a transparent model alloy of succinonitrile.Novel experimental apparatus is constructed to provide a temperature gradient of about 0.37 K/mm.Under this small temperature gradient,the planar interface instability depends largely on the crystallographic orientation.It is shown experimentally that the effect of interfacial energy anisotropy on planar interface stability cannot be neglected even in a small temperature gradient system.Higher interfacial energy anisotropy leads the planar interface to become more unstable,which is different from the stabilizing effect of the interfacial energy on the planar interface.The experimental results are in agreement with previous theoretical calculations and phase field simulations.     

Application of high-precision temperature-controlled FBG filter and light source self-calibration technique in the BOTDR sensor system

A high-precision temperature-controlled narrow band-stop fiber Bragg grating(FBG) filter and light source self-calibration technique are proposed for application in the Brillouin optical time domain reflectometer (BOTDR) sensor system.With the proposed application,the BOTDR sensor system maintains good long-term stability and temperature precision through the reduction of the center wavelength drift in the FBG filters and corresponding decrease in the changes in light intensity.The experiment result shows that temperature precision of 1℃and temperature stability of 0.7℃can be achieved in a temperature sensor over a range of 8 km.     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.     

Rigidity Theorems for Complete Sasakian Manifolds with Constant Pseudo-Hermitian Scalar Curvature

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor of Sasakian manifolds with constant pseudo-Hermitian scalar curvature and the Chern–Moser tensor of the Sasakian pseudo-Einstein manifolds, respectively. By means of either subelliptic estimates or maximum principle, some rigidity theorems are established to characterize Sasakian pseudo-Einstein manifolds among Sasakian manifolds with constant pseudo-Hermitian scalar curvature and Sasakian space forms among Sasakian pseudo-Einstein manifolds, respectively.