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.     

THE DETERMINATION OF THE COMPUTATIONAL DEGREES OF FREEDOM OF BAR SYSTEMS1)

为了简化和统一结构力学教材中杆件体系计算自由度$W$的算法,本文提出了“直接法”。该方法以相邻节点间的杆件和结点为分析对象,对于含$m$根杆件、$g$ 个单刚结点和$h$个单铰结点的平面杆件体系,直接法给出计算自由度公式$W=3m-(3g+2h$)。相比于已有方法,直接法研究对象清晰,数学运算统一,适合于编程计算,便于初学者准确而快速计算复杂体系的$W$;也为结构超静定次数的确定提供了一种简单有效的数值算法。     

一种基于自适应单元删除率的BESO方法

在ESO中采用动态删除率能有效地提高优化效率和稳定性，但现有的动态删除率策略都含有经验参数，确定删除率的过程较为复杂。本文提出了一种用于BESO的无经验参数自适应单元删除率确定方法。通过分析单元删除率对优化稳定性的影响，得到了结构优化过程中单元删除率的理想变化规律和单元灵敏度均匀化信息对删除率的影响情况，并据此分析了经验参数引入的原因，从而构造了评价单迭代步的单元灵敏度均匀化程度指标。然后，基于单迭代步的单元灵敏度均匀化程度指标，构造了全部迭代步信息下的单元灵敏度均匀化程度相对指标，结合单元删除率的推荐范围值，给出了一种自适应于结构优化进程的单元删除率自适应函数。最后，给出了基于自适应单元删除率的BESO方法实现流程。经典算例的结果对比说明，本文方法在保证优化质量相近的情况下，具有更好的优化效率和稳定性。     

Erratum: The average degree of an edge-chromatic critical graph II

In the article “The average degree of an edge-chromatic critical graph II” by Douglas R. Woodall (J. Graph Theory 56 (2007), 194-218), it was claimed that the average degree of an edge-chromatic critical graph with maximum degree $\mathrm{\Delta }$ is at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+1\right)$ if $\mathrm{\Delta }⩾2$, at least $\text{◂+▸}\frac{2}{3}\mathrm{\Delta }+1$ if $\mathrm{\Delta }⩾8$, and at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+2\right)$ if $\mathrm{\Delta }⩾15$. Unfortunately there were mistakes in the proof of the last two of these results, which are now proved only if $\mathrm{\Delta }⩾18$ and $\mathrm{\Delta }⩾30$, respectively.     

Radical polymerization in the presence of peroxide and reducing agent monomer for branched polymers

In this article, we report the radical polymerization in the presence of peroxide and commercially available or designed reducing agent monomer (RAM) for the preparation of branched poly(methyl methacrylate)s (PMMAs). The reaction behavior of the RAM was studied by NMR. Triple‐detection SEC (TD‐SEC) analysis was used to confirm the branching structure of the prepared PMMAs and to investigate the influence of peroxide concentration and RAM concentration on molecular weight and branched structure. The obtained branched PMMAs exhibited high molecular weights and relatively narrow polydispersities at high conversion of MMA. Interestingly, a significant increase in molecular weight and degree of branching of the obtained polymers are observed in higher BPO concentration, these results are quite different from that reported in the literature. The unique radical polymerization mechanism in the RAM/BPO redox‐initiated radical polymerization system resulted in branched PMMAs with high molecular weights at relatively high RAM and BPO concentrations. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 833–840