Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

上海黄浦江两支流河流甲烷含量研究

甲烷是一种重要的温室气体,虽然目前大气中含量远小于二氧化碳,但排放增长率却大于后者.研究区域为上海市黄浦江支流苏州河和淀浦河,通过实验数据对比城郊春夏的甲烷排放的差异,探讨甲烷产生的机制及其与环境因子的关系,这将有助于研究河流甲烷排放对于环境变化的影响.研究结果认为河流甲烷主要来源于水中沉积物,其产生与水质、温度等因素相关;同时甲烷摩尔浓度与硝酸根离子质量体积比存在负相关性,与铵根离子质量体积比和有机碳质量分数存在正相关性.     

Vertex-disjoint rainbow triangles in edge-colored graphs

Let $G$ be an edge-colored graph of order $n$. The minimum color degree of $G$, denoted by ${\delta }^c\left(G\right)$, is the largest integer $k$ such that for every vertex $v$, there are at least $k$ distinct colors on edges incident to $v$. We say that an edge-colored graph is rainbow if all its edges have different colors. In this paper, we consider vertex-disjoint rainbow triangles in edge-colored graphs. Li (2013) showed that if ${\delta }^c\left(G\right)\ge (n+1)∕2$, then $G$ contains a rainbow triangle and the lower bound is tight. Motivated by this result, we prove that if $n\ge 20$ and ${\delta }^c\left(G\right)\ge (n+2)∕2$, then $G$ contains two vertex-disjoint rainbow triangles. In particular, we conjecture that if ${\delta }^c\left(G\right)\ge (n+k)∕2$, then $G$ contains $k$ vertex-disjoint rainbow triangles. For any integer $k\ge 2$, we show that if $n\ge 16k-12$ and ${\delta }^c\left(G\right)\ge n∕2+k-1$, then $G$ contains $k$ vertex-disjoint rainbow triangles. Moreover, we provide sufficient conditions for the existence of $k$ edge-disjoint rainbow triangles.     

Random copolymerization of macromonomers as a versatile strategy to synthesize mixed-graft block copolymers

The random copolymerization of norbornene-functionalized macromonomers was explored as a method of synthesizing mixed-graft block copolymers (mGBCPs). The copolymerization kinetics of a model system of polystyrene (PS) and poly(lactic acid) (PLA) macromonomers was first analyzed, revealing a gradient composition of side chains along the mGBCP backbone. The phase separation behavior of mGBCPs with PS and PLA side chains of various backbone lengths and side chain molar ratios was investigated, and increasing the backbone length was found to stabilize the phase-separated nanostructures. The graft architecture was also demonstrated to improve the processability of the mGBCP, compared to a linear counterpart. Investigations of mGBCPs comprised of polydimethylsiloxane and poly(ethylene oxide) side chains exemplified the diverse self-assembled morphologies, including a Frank-Kasper A15 phase, that can be obtained with mGBCPs synthesized by random copolymerization of macromonomers. Lastly, a ternary mGBCP was synthesized by the copolymerization of three macromonomers.     

Influence of the Degree of Deacetylation of Chitosan and BMP-2 Concentration on Biocompatibility and Osteogenic Properties of BMP-2/PLA Granule-Loaded Chitosan/β-Glycerophosphate Hydrogels

Compositions based on chitosan/β-glycerophosphate hydrogels with highly porous polylactide granules can be used to obtain moldable bone graft materials that have osteoinductive and osteoconductive properties. To eliminate the influence of such characteristics as chain length, degree of purification, and molecular weight on a designed material, the one-stock chitosan sample was reacetylated to degrees of deacetylation (DD%) of 19.5, 39, 49, 55, and 56. A study of the chitosan/β-glycerophosphate hydrogel with chitosan of a reduced DD% showed that a low degree of deacetylation increased the MSCs (multipotent stromal cells) viability rate in vitro and reduced the leukocyte infiltration in subcutaneous implantation to Wistar rats in vivo. The addition of 12 wt% polylactide granules resulted in optimal composite mechanical and moldable properties, and increased the modulus of elasticity of the hydrogel-based material by approximately 100 times. Excessive filling of the material with PLA (polylactide) granules (more than 20%) led to material destruction at a ~10% strain. Osteoinductive and osteoconductive properties of the chitosan hydrogel-based material with reacetylated chitosan (39 DD%) and highly porous polylactide granules impregnated with BMP-2 (bone morphogenetic protein-2) have been demonstrated in models of orthotopic and ectopic bone formation. When implanted into a critical-size calvarial defect in rats, the optimal concentration of BMP-2 was 10 μg/mL: bone tissue areas filled the entire material’s thickness. Implantation of the material with 50 μg/mL BMP-2 was accompanied with excessive growth of bone tissue and material displacement beyond the defect. Significant osteoinductive and osteoconductive properties of the material with 10 μg/mL of BMP-2 were also shown in subcutaneous implantation.     

Synthesis and Self-Assembly of Mixed-Graft Block Copolymers

Mixed-graft block copolymers (mGBCPs) consist of two or more types of polymeric side chains grafted on a linear backbone in a random, alternating, or pseudo-alternating sequence. They can phase-separate with the backbone serving as the interface of the blocks, and the side chains dominate their self-assembly behavior. mGBCPs are an accessible polymer architecture for exploring the idea of encoding polymer properties through the macromolecular architecture, as there are two distinct structural components that can be tuned: the backbone and the side chains. In this Concept article, the current literature on the synthesis of mGBCPs is reviewed, and the advantages and disadvantages of each synthetic method are noted. The self-assembly of mGBCPs is also discussed where possible. Finally, directions for future research on mGBCP synthesis and self-assembly are suggested.     

Ⅰ级洁净手术室中无影灯直径的确定

采用高雷诺数K-ε二方程模型，从控制污染物的扩散范围和保证工作区乱流度这两个指标出发，对I级洁净手术室内无影灯直径进行了研究，为无影灯直径的选型提供了依据。     

蕴含W5可图序列的最小度和

Gould,Jacobson和Lehel考虑了下述经典Tur偄n型极值问题的变形:对于给定的图H,确定最小的正偶数σ(H,n),使得对于每一个n项可图序列π=(d1,d2,…,dn),当σ(π)=d1+d2+…+dn≥σ(H,n)时,π有一个实现G包含H作为可图的.本文确定了当n≥11时,σ(W5,n)之值,其中Wr是r个顶点的轮图.     

动态规划确定化学反应器序列最小占用时间的方法

通过用动态规划给出化学反应器序列最小占用时间的设计方法,提出了一个过程的最优化输出设计,该设计在输出产品浓度给定的条件下建立问题的基本设计量和数学模型,利用动态规划原则确定各阶段的占用时间,使总的占用时间为最小值,能够合理的确定各阶段反应器的体积以取得较好的经济效应.图3,表1,参8.