Subword complexity of the Fibonacci–Thue–Morse sequence: The proof of Dekking’s conjecture

Recently F. M. Dekking conjectured the form of the subword complexity function for the Fibonacci–Thue–Morse sequence. In this note we prove his conjecture by purely computational means, using the free software Walnut.     

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.     

On amenability of two-generator groups

A discrete group G is amenable if there exists a finitely additive probability measure on G which is invariant under left translations and is defined on all subsets of G. It is proved that if the group is generated by two elements and is amenable then there are words being relators whose most of the consecutive pairs of the letters belong to a certain four-element set of pairs. This fact is applied to reproving non-amenability of a braid group. The same group provides an example showing that such type of condition is not su?cient for amenabilty.     

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.     

Protection‐Group‐Free Synthesis of Sequence‐Defined Macromolecules via Precision λ‐Orthogonal Photochemistry

An advanced light‐induced avenue to monodisperse sequence‐defined linear macromolecules via a unique photochemical protocol is presented that does not require any protection‐group chemistry. Starting from a symmetrical core unit, precision macromolecules with molecular weights up to 6257.10 g mol^?1 are obtained via a two‐monomer system: a monomer unit carrying a pyrene functionalized visible light responsive tetrazole and a photo‐caged UV responsive diene, enabling an iterative approach for chain growth; and a monomer unit equipped with a carboxylic acid and a fumarate. Both light‐induced chain growth reactions are carried out in a λ‐orthogonal fashion, exciting the respective photosensitive group selectively and thus avoiding protecting chemistry. Characterization of each sequence‐defined chain (size‐exclusion chromatography (SEC), high‐resolution electrospray ionization mass spectrometry (ESI‐MS), and NMR spectroscopy), confirms the precision nature of the macromolecules.     

基于回波平移序列的快速三维磁共振温度成像方法

高强度聚焦超声（HIFU）是一种无创的热消融疗法，为保证其安全性和有效性，需要一种精度高、速度快的测温方法在其治疗过程中对温度进行监控.基于质子共振频率位移（PRFS）的磁共振温度成像（MRT）对温度具有较高的灵敏度，且与温度具有良好的线性关系，因此常被用于引导HIFU治疗.然而在实际应用中，HIFU治疗的最大隐患在于可能造成表皮灼伤，并且灼伤区域可能与焦点区域相隔较远.因此MRT的监控范围十分重要.本文基于三维回波平移成像序列，结合可控混叠的空间并行成像技术，实现了时间分辨率为3 s的快速三维温度成像.为了验证该方法的精度，本文首先设计了仿体降温实验，利用光纤温度计验证回波平移序列测温的准确度和精确度.然后在室温条件下扫描离体猪肉组织，对比加速前后的MRT的测温精确度.在HIFU加热条件下扫描离体猪肉组织，对比加速前后的MRT的测温准确度.结果显示，本文提出的方法可以在3 s内完成三维温度精准测量，对于HIFU治疗的安全监控具有重要意义.     

一种刺松藻来源的硫酸阿拉伯聚糖的制备及特征结构表征

刺松藻(Codium fragile)经水提-醇沉获得粗多糖, 进一步将刺松藻粗多糖(CFP) 通过Q-Sepharose Fast Flow(QFF) 阴离子交换柱纯化得到6个多糖组分CFP1CFP6, 其中, 在CFP6中发现纯度较高的阿拉伯聚糖. 采用高效凝胶渗透色谱与十八角激光散射仪联用法和1-苯基-3-甲基-5-吡唑啉酮(PMP)柱前衍生高效液相色谱法对CFP6的分子量及单糖组成进行了分析. 结果表明, CFP6是一种分子量为79290的多糖, 由阿拉伯糖(Ara)和半乳糖(Gal)组成, 二者摩尔比为14.8:1.0. 通过多维核磁共振波谱、 液相色谱-质谱联用及二级质谱等方法对CFP6的糖苷键连接方式及其寡糖序列结构进行表征, 进一步阐明了该复杂多糖的特征结构. 经判断, CFP6主链由Ara组成, 通过 β-(1→3)糖苷键连接, 在Ara的C2位存在分支结构, 硫酸基位于Ara的C4或C2位.