Micellization and gelation of aqueous solutions of star-shaped PEG-PCL block copolymers consisting of branched 4-arm poly(ethylene glycol) and polycaprolactone blocks

Star-shaped block copolymers consisting of non-toxic poly(ethylene glycol) and biodegradable polycaprolactone ((PEG5K-PCL)₄) were synthesized by ring-opening polymerization of the ε-caprolactone monomer with hydroxyl-terminated 4-armed PEG as initiator. These biodegradable, amphiphilic star block copolymers showed micellization and sol-gel transition behaviors in aqueous solution with varying concentration and temperature. In the dilute aqueous solutions of star block copolymers, micellization behavior occurred over specific concentration. The 1,6-diphenyl-1,3,5-hexatriene (DPH) solubilization method was used to determine the critical micellization concentration (CMC) of star block copolymers. The obtained micelle size increased with increasing hydrophobic PCL block length. In high-concentration solutions, the star block copolymers showed temperature-sensitive sol-gel transition behavior. The morphology of the micelle and gel was investigated by atomic force microscopy (AFM). As a result, the micelles showed a core-corona spherical structure at concentration near CMC, while the gel showed a mountain-chain-like morphology picture. It was proposed that with increasing the micelle concentration the worm-like micelle clusters formed firstly and the gel was constructed by the packing of micelle clusters.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

用ATRP法构筑核壳型梯度极性的多羟基多臂星状超支化聚合物及聚合物刷——三层聚合物刷的合成与表征

设计并通过原子转移自由基聚合方法 (ATRP)合成了核壳型具有梯度极性的多羟基多臂星状聚合物刷 .端羟基超支化聚 (3 乙基 3 羟甲基氧杂环丁烷 )与 2 溴 异丁基酰溴反应制得大分子引发剂 (HP Br) ,以Cu(I)Br和N ,N ,N′ ,N′ ,N″ 五甲基二乙基三胺 (PMDETA)为催化体系 ,进行甲基丙烯酸甲酯 (MMA)的ATRP反应 ,得到以甲基丙烯酸甲酯为臂的多臂星状超支化聚合物 (HP g PMMA) .又以HP g PMMA为引发剂 ,进行甲基丙烯酸羟乙酯 (HEMA)的ATRP聚合 ,得到核壳型具有梯度极性的多羟基多臂星状超支化聚合物 (HP g PMMA b PHEMA) ,继续将其羟基官能团溴代化 (与 2 溴 异丁基酰溴反应 ) ,引发HEMA的ATRP溶液聚合 ,得到了多臂星状超支化聚合物刷 .产物的结构用1 H NMR、FTIR、GPC等进行了表征和测试 .     

List star edge coloring of k-degenerate graphs

A star edge coloring of a graph is a proper edge coloring such that every connected 2-colored subgraph is a path with at most 3 edges. Deng et al. and Bezegová et al. independently show that the star chromatic index of a tree with maximum degree $\Delta$ is at most $?\frac{3\Delta }{2}?$, which is tight. In this paper, we study the list star edge coloring of $k$-degenerate graphs. Let $c{h}_{st}^{\prime }\left(G\right)$ be the list star chromatic index of $G$: the minimum $s$ such that for every $s$-list assignment $L$ for the edges, $G$ has a star edge coloring from $L$. By introducing a stronger coloring, we show with a very concise proof that the upper bound on the star chromatic index of trees also holds for list star chromatic index of trees, i.e. $c{h}_{st}^{\prime }\left(T\right)\le ?\frac{3\Delta }{2}?$ for any tree $T$ with maximum degree $\Delta$. And then by applying some orientation technique we present two upper bounds for list star chromatic index of $k$-degenerate graphs.     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

Singular hyperbolicity of star flows on surfaces

In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a consequence, every star flow on the 2-sphere or the projective plane is singular hyperbolic.     

受限于两平行板间的对称星形共聚物Am Bm熔体相行为的格子自洽场理论研究

采用格子自洽场理论计算研究了受限于2个平行板间的对称星形共聚物AmBm(m=1,2,3,4,5)熔体形成的层状相结构.在给定的相互作用下(χNAB不变,χ为Flory-Huggins相互作用参数,NAB=(N?1)/m为单个聚合物分子中一对AB臂的总链节数目),针对平行板间距为体相周期的情况,系统考察了共聚物链长N和单个聚合物分子中A(或B)臂数目m对受限层结构细节及层取向的影响.由计算结果,当N或NAB不变时,受限层的归一化界面宽度随m的增大而减小.受限板为中性时,垂直层结构的单链自由能比平行层结构的低.随着板对共聚物中一种嵌段的选择作用Λ的增大,体系发生垂直层到平行层的转变,该转变为一阶相变.当m不变时,N越小,上述转变出现在越大的Λ值处,体系越容易保持垂直层结构.并且N越小,层状结构周期越小.当N或NAB不变时,m越大体系越容易保持垂直层结构.总之,星形共聚物的链长越短、臂数越多时,垂直层稳定的Λ区间越大、层状结构的界面宽度越小.这些结论可以指导刻蚀应用中对体系参数的选择.     

Synthesis and Rheological Investigation ofModel Symmetric 3-Arm Star Polyethylene简

A variety of linear and 3-arm star polyethylene （PE） model polymers covering a wide range of molecular weight are synthesized by the living polymerization of butadiene and the subsequent hydrogenation. Several rheological parameters of these model linear and 3-arm star PE samples are analyzed for detecting the long chain branching （LCB） structure. It is found that the analyses based on zero shear viscosity, vGP plot and flow activation energy are very sensitive to the 3-arm star PEs. The information on the presence of LCB can be obtained with these methods even for low molecular weight samples, which can not be determined by GPC-MALLS. However the information about the LCB structure can not be obtained by the rheological methods alone.     

区间型多属性群体专家权重的确定方法

针对方案偏好和属性值均为区间数的多属性群决策问题,研究了群体专家权重的确定,并提出了一种新的群决策方法．通过定义区间数向量的内积,计算专家评判的相似度和差异度,进而客观地确定了专家的权重．求解最小化主、客观偏差的目标规划模型,得到了属性的权重,利用方案的群体综合属性值给出排序结果．供应商选择的应用实例验证了方法的可行性和合理性．     

A reduced dimensionality model of torsional vibrations in star molecules

The torsional vibrations of star molecules are studied with a reduced dimensionality model. In this model, the molecule is described by two equivalent sets of lumped inertial cylinders and vibrational frequencies are predicted by solution of the coupled equations of motion. Force constants are determined by including them as free parameters in the model and fitting the computed frequencies to their analogs as determined using full normal coordinate analysis at the HFSCF level of theory. Best agreement between the methods occurs when torsional force constants are included for the first two layers of the molecule. This reveals that non-bonded torsional interactions are important in the vibrational dynamics of these systems. Further insight is afforded by an analysis of why simple harmonic oscillator models are sufficient for modeling some related systems but fail to reproduce the trend in global mode frequencies for saturated aliphatic star molecules. The analysis reveals that the origin of this failure lies in backbone flexibility in these branched polymeric systems.