基于FNP-ADC模型的弹药调度系统保障效能评估

正确评估诸如弹药调度系统此类复杂武器装备的系统效能,可为作战指挥决策提供重要支撑依据,从装备系统结构组成及复杂性出发,合理地表示工作状态及其转移过程,在流水网络计划(flow network planning,FNP)技术框架下应用ADC模型开展效能评估.以FNP时间参数为基础,确定了组成分系统故障一般概率分布下的可用性、可信性和保障能力表示方法,分别表示为影响因素的函数关系,最终建立了FNP-ADC模型.综合进行保障效能评估,可进一步分析因素对效能的影响程度,并给出了案例分析.     

无界形式Hamilton算子的可逆性

利用算子分块方法研究了具有一般定义域的形式Hamilton算子的可逆性和可逆补,还进一步给出了无穷维Hamilton算子的相关结论.     

Linear and nonlinear generalized consensuses of multi-agent systems

Consensus in directed networks of multiple agents, as an important topic, has become an active research subject. Over the past several years, some types of consensus problems have been studied. In this paper, we propose a novel type of consensus, the generalized consensus （GC）, which includes the traditional consensus, the anti-consensus, and the cluster consensus as its special cases. Based on the Lyapunov＇s direct method and the graph theory, a simple control algorithm is designed to achieve the generalized consensus in a network of agents. Numerical simulations of linear and nonlinear GC are used to verify the effectiveness of the theoretical analysis.     

定向集指标非交换鞅的几种收敛性

本文研究了定向集指标非交换鞅的几种收敛性.利用非交换鞅的理论,得到了如下结果:设{xα,Mα}α∈I是一个定向集指标的非交换鞅.则{xα}依L1范数收敛(或弱收敛)的充要条件是{xα}一致可积且满足条件(B):对任意的ε0,存在投影e∈M,使得对任意的y∈M,y≤1及任意的α∈I,有|τ(exαey)|ε.当1p∞时,{xα}依Lp范数收敛(或弱收敛)的充要条件是{xα}在Lp(M)中依Lp范数有界.这也等价于存在一个x∞∈Lp(M),使得xα=Eα(x∞)(α∈I).推广了交换情形中的相应结果.     

二维耦合定向输运模型研究

建立了外部驱动力及噪声作用下的二维耦合定向输运模型, 其中的一个维度上为周期性分段棘齿势, 另一垂直维度上为周期性对称非棘齿势, 外部驱动力及噪声加在周期对称非棘齿势方向上, 而棘齿势方向不加任何驱动, 采用非平衡统计及非线性动力学理论研究了过阻尼情况下耦合系统在两个维度上的输运性质. 结果显示, 棘齿势与非棘齿势方向均可产生定向输运, 其中棘齿势方向的系统平均速度对耦合强度、噪声强度、驱动力强度及粒子数目均有明显的依赖性, 合适的耦合强度、噪声强度、驱动力强度或粒子数目下均可产生最大输运速度. 而非棘齿势方向的系统平均速度受非棘齿势势垒高度影响显著, 但随耦合强度、驱动力强度、驱动力初相位差及粒子数目的变化均出现波动现象, 表现出平均速度对这些参量的依赖性较弱.     

A mean value algorithm for Toeplitz matrix completion

In this paper, we propose a new mean value algorithm for the Toeplitz matrix completion based on the singular value thresholding (SVT) algorithm. The completion matrices generated by the new algorithm keep a feasible Toeplitz structure. Meanwhile, we prove the convergence of the new algorithm under some reasonal conditions. Finally, we show the new algorithm is much more effective than the ALM (augmented Lagrange multiplier) algorithm through numerical experiments and image inpainting.     

PBW deformations of quadratic monomial algebras

A result of Braverman and Gaitsgory from 1996 gives necessary and sufficient conditions for a filtered algebra to be a Poincaré-Birkhoff-Witt (PBW) deformation of a Koszul algebra. The main theorem in this paper establishes conditions equivalent to the Braverman-Gaitsgory Theorem to efficiently determine PBW deformations of quadratic monomial algebras. In particular, a graphical interpretation is presented for this result, and we discuss circumstances under which some of the conditions of this theorem need not be checked. Several examples are also provided. Finally, with these tools, we show that each quadratic monomial algebra admits a nontrivial PBW deformation.     

Stereoselective synthesis of trisubstituted olefins by a directed allylic substitution strategy

New methodology for the stereoselective synthesis of trisubstituted olefins is presented. The use of ortho-diphenylphosphanyl benzoate (o-DPPB) as a directing leaving group for copper-mediated allylic substitution with Grignard reagents allowed for the stereoselective construction of a wide range of E olefins, without the need for an adjacent electron-withdrawing group. Our modular three-step approach toward trisubstituted alkenes commenced with geminal α-methylene aldehydes. Addition of an organometallic reagent and introduction of the o-DPPB group by esterification was followed by the o-DPPB-directed copper-mediated allylic substitution with a Grignard reagent to furnish stereodefined trisubstituted olefins. Additionally, incorporation of a stereocenter from the chiral pool allowed the preparation of an enantiomerically pure olefin that bore three alkyl substituents in high E/Z selectivity.     

A multistate switchable [3]rotacatenane

Rotacatenanes are exotic molecular compounds that can be visualized as a unique combination of a [2]catenane and a [2]rotaxane, thereby combining both the circumrotation of the ring component (rotary motion) and the shuttling of the dumbbell component (translational motion) in one structure. Herein, we describe a strategy for the synthesis of a new switchable [3]rotacatenane and the investigation of its switching properties, which rely on the formation of tetrathiafulvalene (TTF) radical π-dimer interactions-namely, the mixed-valence state (TTF(2) )(+.) and the radical-cation dimer state (TTF(+.) )(2) -under ambient conditions. A template-directed approach, based on donor-acceptor interactions, has been developed, resulting in an improved yield of the key precursor [2]catenane, prior to rotacatenation. The nature of the binding between the [2]catenane and selected π-electron-rich templates has been elucidated by using X-ray crystallography and UV/Vis spectroscopy as well as isothermal titration microcalorimetry. The multistate switching mechanism of the [3]rotacatenane has been demonstrated by cyclic voltammetry and EPR spectroscopy. Most notably, the radical-cation dimer state (TTF(+.) )(2) has been shown to enter into an equilibrium by forming the co-conformation in which the two 1,5-dioxynaphthalene (DNP) units co-occupy the cavity of tetracationic cyclophane, thus enforcing the separation of TTF radical-cation dimer (TTF(+.) )(2) . The population ratio of this equilibrium state was found to be 1:1. We believe that this research demonstrates the power of constructing complex molecular machines using template-directed protocols, enabling us to make the transition from simple molecular switches to their multistate variants for enhancing information storage in molecular electronic devices.