On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

Polyhydroxyalkanoates (PHAs) are considered promising “green” alternatives to synthetic polymers because they are bio-derived, biodegradable and biocompatible. The properties of bacterial PHA copolymers depend on their microstructures, which can be modified with the use of different fermentation processes and feed materials. Thus, it is desirable to have an improved testing method for the determination of PHA microstructures. In this work, a detailed NMR analysis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) microstructure was made. Previously only two of the hydroxyvalerate ¹³C NMR peaks have been assigned at the triad level. In this work, three of the ¹³C hydroxyvalerate peaks and two of the hydroxybutyrate peaks were found to be split into four peaks each due to comonomer sequence effects. Using eight copolymer samples with a wide compositional range, we were able to assign all these peaks to B-centered and V-centered triad sequences. Through curve deconvolution, the triad intensities were determined. These triad sequence intensities can then be analyzed via both the first-order Markovian and two-component Bernoullian models to obtain more in-depth information on copolymer composition and comonomer reactivities.     

An Arbitrarily Regulated Monomer Sequence in Multi-Block Copolymer Synthesis by Frustrated Lewis Pairs

Rapid access to sequence-controlled multi-block copolymers (multi-BCPs) remains as a challenging task in the polymer synthesis. Here we employ a Lewis pair (LP) composed of organophosphorus superbase and bulky organoaluminum to effectively copolymerize the mixture of methacrylate, cyclic acrylate, and two acrylates, into well-defined di-, tri-, tetra- and even a hepta-BCP in one-pot one-step manner. The combined livingness, dual-initiation and CSC feature of Lewis pair polymerization enable us to achieve not only a trihexaconta-BCP with the highest record in 8 steps by using four-component monomer mixture as building blocks, but also the arbitrarily-regulated monomer sequence in multi-BCP, simply by changing the composition and adding order of the monomer mixtures, thus demonstrating the powerful capability of our strategy in improving the efficiency and enriching the composition of multi-BCP synthesis.     

含N-乙酰化肝素寡糖的制备及序列分析

建立了含N-乙酰化肝素寡糖的分离提纯及其序列结构分析方法.首先应用肝素酶Ⅰ深度酶解低分子量肝素来富集含N-乙酰化结构寡糖,通过Bio-Gel P10凝胶色谱法分离制备了包括二糖至十四糖的系列肝素寡糖粗样品,ProPac PA-1强阴离子高效液相色谱(SAX-HPLC)等方法对粗样品进一步分离,提纯得到4种六糖和3种八糖片段.其次应用肝素酶Ⅰ,Ⅱ和Ⅲ复合酶解与HPLC法分析各纯化寡糖的二糖组分,并结合肝素酶Ⅰ底物特异性,初步推断4种六糖和3种八糖的序列结构.在寡糖的糖链两端均含有N-硫酸化二糖,而N-乙酰化二糖分布在糖链当中.应用电喷雾离子阱-飞行时间质谱(ESI-IT-TOF-MS)在负离子模式下进一步表征寡糖并分析其裂解规律.结果表明,各寡糖中均出现大量因SO32-丢失形成的碎片离子峰,六糖中主要有双电荷和三电荷碎片离子峰;在八糖中出现了一系列从双电荷至五电荷的离子峰.各寡糖的双电荷离子峰质荷比进一步确定了上述寡糖的序列结构.六糖的裂解规律表明,裂解主要存在于糖苷键,N-乙酰葡糖胺和糖醛酸上的裂解方式分别为0,2X和0,2Z.本研究提供了切实有效的分离、分析未知结构肝素寡糖序列的新方法.     

电喷雾质谱在寡糖序列分析中的应用

选取具有不同结构特征的N-糖链、硫酸软骨素寡糖、人乳寡糖以及海洋来源的壳寡糖、褐藻胶寡糖、卡拉胶寡糖和硫酸岩藻寡糖等,对电喷雾质谱在寡糖的主链序列、分支位点、硫酸基取代位置确定、单糖组成和聚合度分析等方面的应用技术及碎片离子的断裂规律进行了总结.根据相邻同类碎片离子之间的质荷比差值可初步判断寡糖的单糖组成类型;通过与色谱分离技术联用或衍生化方法可提高寡糖的分辨率和离子化效率,并测得寡糖的分子量及聚合度;借助串联质谱及对寡糖还原端的特异性标记,可获得寡糖的还原端残基和部分序列信息;根据寡糖产生的特征碎片离子及其丰度大小可判断残基的特定位置和类型.另外,寡糖的分支通常作为一个整体发生糖苷键断裂或产生D离子,据此可判断分支点的位置;根据硫酸寡糖产生的特异性跨环断裂碎片,可以确定硫酸基的连接位置.这些规律和方法的总结为未知寡糖的结构和序列的分析提供了启发和指导.     

Systematic investigation of sequence and structural motifs that recognize ATP

Interaction between ATP, a multifunctional and ubiquitous nucleotide, and proteins initializes phosphorylation, polypeptide synthesis and ATP hydrolysis which supplies energy for metabolism. However, current knowledge concerning the mechanisms through which ATP is recognized by proteins is incomplete, scattered, and inaccurate. We systemically investigate sequence and structural motifs of proteins that recognize ATP. We identified three novel motifs and refined the known p-loop and class II aminoacyl-tRNA synthetase motifs. The five motifs define five distinct ATP–protein interaction modes which concern over 5% of known protein structures. We demonstrate that although these motifs share a common GXG tripeptide they recognize ATP through different functional groups. The p-loop motif recognizes ATP through phosphates, class II aminoacyl-tRNA synthetase motif targets adenosine and the other three motifs recognize both phosphates and adenosine. We show that some motifs are shared by different enzyme types. Statistical tests demonstrate that the five sequence motifs are significantly associated with the nucleotide binding proteins. Large-scale test on PDB reveals that about 98% of proteins that include one of the structural motifs are confirmed to bind ATP.     

纳米自组装γ-Al_2O_3孔隙结构的核磁共振表征

纳米自组装γ-Al_2O_3具有两种纳米级孔道,可作为适合于大分子扩散的催化剂载体,也可用于页岩气藏模型。表征纳米材料孔隙结构的方法有扫描电镜、氮吸附法及压汞法等,各有局限。本文利用核磁共振弛豫测量对纳米自组装γ-Al_2O_3孔隙结构进行研究和定量表征,并通过核磁共振实验和数值模拟对纳米自组装γ-Al_2O_3表面弛豫强度及孔径分布进行探索。结果表明,数值模拟核磁弛豫表征的纳米自组装γ-Al_2O_3的主体孔径为5-7 nm和30-42 nm,核磁弛豫实验通过误差函数法表征的主体孔径为5-9 nm和29-47 nm。相比于氮吸附仅表征微孔介孔及部分大孔,不能表征大于100 nm孔径,压汞法描述小于10 nm孔径相对不准确等问题,核磁弛豫能够全面表征2.8-315 nm纳米自组装γ-Al_2O_3的双峰孔隙系统。三个样品S-1、S-2、S-3的横向弛豫时间T_2谱小孔大孔波峰的信号幅度比0.603、1.15、1.84直接反映各自的化学小孔大孔氧化铝投料比0.85、1.38、1.7的变化。建立的表征方法可以应用于页岩气微观结构和机理研究中,前景广阔。     

On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems

Shape gradient flows are widely used in numerical shape optimization algorithms. We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems. We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative. Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.     

A deep neural network-based method for solving obstacle problems

In this paper, we propose a method based on deep neural networks to solve obstacle problems. By introducing penalty terms, we reformulate the obstacle problem as a minimization optimization problem and utilize a deep neural network to approximate its solution. The convergence analysis is established by decomposing the error into three parts: approximation error, statistical error and optimization error. The approximate error is bounded by the depth and width of the network, the statistical error is estimated by the number of samples, and the optimization error is reflected in the empirical loss term. Due to its unsupervised and meshless advantages, the proposed method has wide applicability. Numerical experiments illustrate the effectiveness and robustness of the proposed method and verify the theoretical proof.