给定度序列图的覆盖成本和反向覆盖成本的研究

具有n个顶点且度序列为(m,2,…,2,1,…,1)(1的重数为m)的连通图不止一个(这些图均为树),而每个树对应唯一一个段序列(l₁,l₂,…,l_m).通过对任意一树移动最长段的悬挂点到最短段悬挂点的方式得到另一树,比较前后两树的覆盖成本和反向覆盖成本,给出了具有最小覆盖成本和反向覆盖成本的极树,并且进一步给出了取得最小覆盖成本和反向覆盖成本的顶点.     

汽配件颜色喷涂顺序问题的TSP转化与建模

汽配件颜色喷涂顺序问题通常以生产线上相邻汽配件颜色切换次数少为最优目标,以进一步降低生产成本.该类问题具有所有汽配件都必须喷涂一次且只喷涂一次的特点,为此提出了TSP转化与建模的方法.将待喷涂汽配件定义为TSP顶点,任意两个待喷涂汽配件的颜色切换定义为顶点的距离,仿照TSP问题构建0-1规划模型;类似于顶点距离,将某些汽配件的颜色或类别不相邻要求定义为0-1矩阵,巧妙地构造了喷涂生产的约束条件.该建模方法简单快速,通用性高,适用于具有类似特点的各类生产实践问题.     

通过超宽139La固体核磁共振波谱研究层状La(OH)2NO3

层状稀土氢氧化物是一类新型的稀土功能材料，本文采用固体核磁共振（SSNMR）方法研究了同时具备离子交换能力和非线性光学特性的层状La（OH）₂NO₃化合物，探讨了通过四极核CPMG（QCPMG）脉冲序列和变频谱图采集获取超宽¹³⁹La SSNMR谱图的方法，并描述了适用于此类实验的滤波方程和谱图重建方法.重建谱图同时包含四极核中心跃迁和卫星跃迁信息，本文使用QUEST软件对超宽¹³⁹La NMR谱图进行了模拟，获取的四极耦合常数C_Q和非对称因子η_Q均与CASTEP密度泛函理论计算值高度吻合.SSNMR实验结果证实层状La（OH）₂NO₃化合物属于非中心对称结构（P2₁），解决了对其结构长期以来存在的争论.     

Rapid and Scalable Access to Sequence-Controlled DHDM Multiblock Copolymers by FLP Polymerization

An immortal N-(diphenylphosphanyl)-1,3-diisopropyl-4,5-dimethyl-1,3-dihydro-2H-imidazol-2-imine/diisobutyl (2,6-di-tert-butyl-4-methylphenoxy) aluminum (P(NIⁱPr)Ph₂/(BHT)AlⁱBu₂)-based frustrated Lewis pair (FLP) polymerization strategy is presented for rapid and scalable synthesis of the sequence-controlled multiblock copolymers at room temperature. Without addition of extra initiator or catalyst and complex synthetic procedure, this method enabled a tripentacontablock copolymer (n=53, k=4, dp_n=50) to be achieved with the highest reported block number (n=53) and molecular weight (M_n=310 kg mol⁻¹) within 30 min. More importantly, this FLP polymerization strategy provided access to the multiblock copolymers with tailored properties by precisely adjusting the monomer sequence and block numbers.     

Optical diffusers based on uniform nano-sized polymer balls/nematic liquid crystals composite films

ABSTRACT

Optical diffusers are promising diffusing materials in the optical devices such as monitors, projectors, fibre optics, light-emitting diode (LED) systems and liquid crystal displays (LCDs). We report optical diffusers comprising uniformly distributed nano-sized polymer balls/nematic liquid crystals (LCs) by ultraviolet (UV) click reaction of ene monomer and thiol monomer. By optimising the mass ratio 1:1 of ene and thiol, of which the average diameter of the corresponding nano-sized polymer balls is about 900 nm, relatively high optical transmission and haze with 88.99% and 94.49% are yielded, respectively. Furthermore, by controlling the curing time, the average diameter of nano-sized polymer balls can be reduced to 810 nm, and the developed film exhibits high transmission (98.49%) without sacrificing the high haze (91.77%). This paper demonstrates that UV click reaction is an economical approach to fabricate optical diffusers in a controllable manner.     

关于不定方程x3-1=749y2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x³-1=749y²仅有整数解(x,y)=(1,0).     

G-Frame and Riesz Sequences in Hilbert Spaces

G-frames generalize frames in Hilbert spaces. The literatures show that g-frames and frames share many similar properties, while they behave differently in redundancy and perturbation properties. Interestingly, g-frames have been extensively studied, but g-frame sequences have not. This problem is nontrivial since a g-frame and a frame both involve all vectors in the same Hilbert space, while a g-frame sequence and a frame sequence do not. They involve different linear spans. Using the synthesis and Gram matrix methods, we in this paper characterize g-frame sequences and g-Riesz sequences; obtain the Pythagorean theorem for g-orthonormal systems. These results recover several known results and lead to some new results on g-frames.     

On Applications of Quasi-Monotone Sequences and Quasi Power Increasing Sequences

In this article, we prove a general theorem dealing with an application of quasi-f-power increasing sequences and δ-quasi monotone sequences. This theorem also includes some known and new results.