Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

核-壳型聚丙烯酸酯复合乳液

简述了核-壳型聚丙烯酸酯复合乳液的合成方法、形态及其影响因素与判断方法、结构与性能等方面的研究进展;认为核-壳型复合乳液膜机械性能优良的原因是:核、壳两相间存在的过渡区适当地抑制了二者的相分离。     

Effects of monomer structure on the morphology of polymer networks and the electro-optical properties of polymer-dispersed liquid crystal films

Polymer-dispersed liquid crystal (PDLC) films were prepared by photochemical polymerisation with a series of (meth)acrylate monomers. The effects of monomer structure on the morphology of polymer networks in the PDLC films were studied. The acrylate monomers without sidegroup chain formed uniform polymer networks. The methacrylate monomers with methyl as their sidegroup chains formed lace-like networks. The size of the LC droplets increased with increasing the length of the flexible chain of both methacrylate and acrylate monomers. Meanwhile, the effects of the morphology of the polymer network on the electro-optical properties of PDLC films were also investigated.     

Low volatile monofunctional reactive diluents for radiation curable formulations

In the last decades the importance of UV curable formulations has increased continuously. Their fast curing speed, solvent-free polymerization conditions, and the formation of hard and highly crosslinked photopolymer networks represent major benefits. Commercial UV resins generally consist of multi-functional vinyl oligomers, photoinitiators, additives, and reactive diluents. Mono- and multi-functional reactive diluents serve as thinners to lower the overall resin viscosity and to improve processability. However, many monofunctional reactive diluents like isobornyl (meth)acrylate or benzyl (meth)acrylate exhibit high volatility, often already at room temperature. This causes adverse effects such as unpleasant odor, potential health risks, and changing resin composition during processing. A new group of monomers that show high potential for replacing traditional highly volatile reactive diluents are salicylate (meth)acrylates. In this work, salicylate-based thinners are synthesized, polymerized, and characterized with respect to their viscosity, volatility, thermal stability, photoreactivity, and thermomechanical properties of their homopolymers. Additionally, a first example of their diluting effect in a highly viscous difunctional polyester urethane methacrylate is demonstrated with 30 wt% of a cycloaliphatically and an aromatically substituted salicylate methacrylate. The polymers of the diluted resin exhibit similarly high glass transition temperatures of 110 and 126 °C, which are in the range of the polymers of the undiluted resin.     

Controlled grafting of cellulose esters using SET‐LRP process

Here, we present the first example of application of single‐electron transfer living radical polymerization (SET‐LRP) process to a controlled grafting of cellulose esters, cellulose diacetate (CDA), and cellulose acetate butyrate (CAB). The cellulose ester macroinitiators with various functionality densities have been prepared by acylation of the backbones with 2‐bromoisobutyryl (BrIB) and dichloroacetyl (DCA) groups, respectively. Methacrylate monomers were polymerized using DCA‐functionalized macroinitiators in the presence of pentamethyldiethylene triamine as a ligand. At 30 °C, the reaction is rather slow, reaching about 10% conversion after 3 to 6 h of polymerization, whereas the higher temperature (60 °C) perceptibly speeds up the polymerization so that methyl methacrylate (MMA) conversion is ～30% after 5 h. Graft copolymers with random‐type and diblock‐type grafts having amphiphilic character were also synthesized. For acrylate grafting (BuA and t‐BuA), BrIB‐functionalized macroinitiators are more convenient in a combination with a low concentration of Cu(0) and Me₆TREN as a ligand and polymerization is detectably faster even at the lower temperature than that of MMA. Kinetic studies show “living” character of both the graftings. Important advantages of SET‐LRP, compared with classic ATRP, are (i) higher polymerization rate, (ii) lower extent of recombination of the growing grafts and (iii) negligible coloration of the products with catalytic residua, so that the prepared polymers do not require additional careful purification. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

PISO算法在求解方柱绕流非定常尾迹中的应用

应用PISO算法及非交错斜交网格技术,编制了求解二维定常、非定常流动的通用程序。计算分析了定常不可压缩Couette流动以及水平通道内方柱绕流尾迹的非定常流动,并详细分析了不同时刻方柱后尾迹的旋涡结构及发展过程,得到了合理的结果。验证了非迭代PISO算法及非交错斜交网格在分析非定常流动中的有效性,为进一步开展非定常流动的数值分析奠定了基础．     

侧链含查尔酮基团的聚(甲基)丙烯酸酯的光交联特性

采用红外光谱、热重分析、紫外光谱和荧光光谱对侧链含查尔酮基团的聚（4-甲基丙烯酰氧基-4'-二甲氨基查尔酮）（PMADMAC）和聚（4-丙烯酰氧基查尔酮）（PAC）的光交联特性进行了研究。随着光照时间的增加,PMADMAC和PAC聚合物光致环加成反应迅速进行,波长短的紫外线更易使得聚合物发生[2+2]环加成反应。与溶液状态相比,固体薄膜状态下的光交联反应速率较慢。PMADMAC聚合物更容易发生光致环加成反应,其光交联速率要比PAC聚合物快,环加成反应也更彻底。采用荧光光谱研究了聚合物的发光特性,发现PAC聚合物无荧光,而PMADMAC聚合物具有溶剂极性敏感的荧光特性。在PMADMAC聚合物的稀溶液中,随着365 nm紫外光照时间的增加,荧光强度迅速降低,其荧光特征波长在紫外光照射后发生蓝移。 PMADMAC和PAC聚合物的热稳定性较好,光交联后形成热不稳定的环丁烷结构,其热稳定性有所降低。     

基团转移聚合合成PMMA—PEA—PAN嵌段共聚物的研究

丙烯酸系橡胶的综合性能仅次于氟橡胶,成本较低,若制成可重复加工的热塑性弹性体则更有价值。前人曾用阴离子聚合法进行过合成试验,均因副反应太多等原因而未能获得满意的结果。基团转移聚合(GTP)是八十年代建立的合成高分子新方法,在室温下进行“活性聚合”是其重要特征。本文利用GTP方法、单官能团引发剂,仅通过适当控制加料次序和时机就合成了软段居中的三元共聚物,为合成全丙烯酸系热塑弹性体奠定了基础。     

物距-像距法测凹透镜焦距实验中透镜的选择

本文根据对物距－像距法测凹透镜焦距存在的系统误差分析,指出实验安排上应选择长焦距、对称的双凹透镜．     

Photochemical activities of polymers with aurone fragment

ABSTRACT

In this work we report preliminary results obtained for methacrylic polymers incorporating aurone side-group as photochemical active molecule. The aurone polymers were obtained by a three-step synthetic approach: (2Z)-6-hydroxy-2-(4-R-benzyliden)-1-benzofuran-3(2H)-ones were synthesized by using condensation reation of 6-hydroxybenzofuran-3-one with benzaldehydes; then methacrylate monomers were synthesized by reaction the alcohols with methacryloyl chloride; and the polymers were synthesized by free radical polymerization. Polymers were characterized by ¹HNMR spectroscopy and DSC techniques. Their physicochemical properties are determined by absorption, fluorescence excitation and emission spectroscopies.