2022年全国高中数学联合竞赛中一道染色题的推广

先给出2022年全国高中数学联合竞赛一试(A卷)填空题第8题的一种学生容易理解的常规解法,再将试题推广到更一般的情况.     

Neighbor sum distinguishing total colorings of graphs with bounded maximum average degree

A proper [h]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [h]={1,2,...,h}.Letw(u) denote the sum of the color on a vertex u and colors on all the edges incident to u.For each edge uv∈E(G),if w(u)≠w(v),then we say the coloring c distinguishes adjacent vertices by sum and call it a neighbor sum distinguishing [h]-total coloring of G.By tndi(G),we denote the smallest value h in such a coloring of G.In this paper,we obtain that G is a graph with at least two vertices,if mad(G)3,then tndi∑(G)≤k+2 where k=max{Δ(G),5}.It partially con?rms the conjecture proposed by Pil′sniak and Wozniak.     

由均匀染色导出的强Chernoff界（英文）

本文研究了相关变量的Chernoff问题.利用相关变量构造图的方法,利用均匀染色的结果,获得了更强的Chernoff界,推广了Chernoff不等式在相关随机变量的不等式下的界.     

酸性染料用于木材染色的研究

选择酸性染料对低质阔叶材单板进行染色研究，发现此类染料对滇杨木，滇桤木，西南桦有较好的易染性，通过试验得到几例常见木材颜色的染料配比，并对染色工艺进行了初步探讨，结果表明温度在70-80℃，pH=4及助染剂量1.5(wt)%时，染色效果最佳。     

酸性媒介深黄GG稀土染料的制备、表征及染色性能

制备并提纯了酸性媒介深黄GG稀土(La, Nd, Y)染料, 稀土及元素分析测得其稀土与酸性媒介深黄GG染料物质的量的比为1∶2, 红外光谱、紫外-可见光谱分析表明, 在酸性媒介深黄GG稀土染料的结构中, 稀土离子(La3+, Nd3+, Y3+)与配体染料分子中的羧基、羟基产生配位作用, 并与磺酸基作用;所有样品的羊毛布料染色实验及其各项牢度测试结果表明 酸性媒介深黄GG稀土染料羊毛染色比相应配体酸性媒介深黄GG染料和相应的铬络合染料染色颜色鲜艳, 酸性媒介深黄GG稀土染料的多项羊毛染色牢度比相应的配体酸性媒介深黄GG染料好, 但比相应的铬络合染料差.     

新型侧基含磷共聚酯的合成、表征及性能

以精制对苯二甲酸（TPA）、乙二醇（EG）和含磷反应型阻燃剂9,10-二氢-9-氧杂-10-[2,3-二（2-羟基乙氧基）羰基丙基]-10-磷杂菲-10-氧化物为原料,利用熔融缩聚法合成了含磷量分别为0．35％、0．65％的阻燃聚酯。通过熔融纺丝法将聚酯制成纤维及织物,研究了纤维的染色性能,并通过极限氧指数法和垂直燃烧法研究了织物的阻燃性能。FT-IR和NMR研究结果表明：阻燃共聚酯含磷量为0．35％时,其氧指数（LOI）达31．5％,并无熔滴、烟雾产生,具有优异的阻燃性能和抗熔滴性能。DSC、TG和XPS的研究结果表明：侧基舍磷单元的引入降低了聚酯的Tg和Tm,较低的Tm将有利于材料加工性能的改善;阻燃聚酯侧基上的P-C、P-O键易断裂并挥发至气相中,从而降低了聚酯热稳定性,阻燃聚酯可能以气相阻燃机理为主发挥阻燃作用。此外,含磷共聚酯纤维具有较优异的染色性能。     

常压低氧下Wistar大鼠脑组织中HIF-1α表达与脑损伤

研究了常压低氧条件下Wistar大鼠脑组织中HIF-1α表达及脑损伤。设计了短期和长期低氧两种模式。短期急性低氧模式中,成年Wistar大鼠被随机分为4组:6%、8%、10%低氧组和常压常氧组。各组在上述氧气浓度条件下暴露2h;长期急性低氧在6%氧气浓度下每天低氧2h、连续低氧暴露10d。使用免疫组织化学和蛋白质印迹方法对低氧诱导因子HIF-1α在模型鼠脑组织内表达进行了表征,考察了低氧暴露强度、抗体稀释度对低氧诱导因子HIF-1α表达的影响;并应用HE染色法对脑组织的病理损伤进行了研究。实验结果证实,HIF-1α属于对低氧环境敏感的、低丰度的DNA结合蛋白,表达于脑组织核蛋白提取液中。高的低氧暴露强度和较低的一抗稀释度有利于HIF-1α表征。HE染色表明经6%急性低氧暴露2h处理后,模型鼠脑组织有损伤,海马神经细胞出现散在性单个坏死现象。     

聚合色素的研究：Ⅺ.蒽醌型聚酯色素的合成与可加工性

用熔融缩聚法合成蒽醌型聚酯色素，研究了色素用量，反应温度和反应时间等对反应的影响，对用所合成聚合色素着色的聚酯的可加工性能作了初步的研究。     

Change Color Effect and Spectral Properties of Gold Nanoparticle-cationic Surfactants System

The change color effect of gold nanoparticle solutions was studied by means of resonance scattering and absorption spectrometry and scan electron microscopy. The red Au nanoparticles with a size of 10 nm exhibit a resonance absorption peak and a resonance scattering peak all at 525 nm. After some inorganic electrolyte was added to a red Au nanoparticles solution, the color of the solution became blue and the absorbance at 600-700 nm was significantly increased. The ratio of the concentration of rnonovalent cations, at which the resonance scattering of the system at 525 nm is maximal to that of divalent cations, is in the range of 100 : 1--100 ; 1. 8. It is in good agreement with the Schulze-Hardy rule of the coagulation value of electrolyte. After adding some cationic surfactants to the above solution, the color of the solution is in deep blue, with two resonance absorption peaks at 550 and 680 nm, and a greatly enhanced resonance scattering peak at 525 nm. The experiments demonstrate that the stronger the hydrophobicity of the cationic surfactant is, the stronger the change color effect of the Au nanoparticle solution promoted by cationic surfactant is. The change color effect of Au nanoparticle solution is resulted from the increased diameter of Au nanoparticles, and the changes of resonance absorotion DeaR and resonance scattering.