论基础数学工具的创新运用

在建立叶轮机三元流面理论时,吴仲华巧妙地、创造性地提出了全导数型的沿流面方向偏导数的概念和表达式,导出了两类流面气动力学数学模型,不但数学形式简洁,而且具有明晰的物理意义,有利于分析和求解。在吴氏流面理论的启示下,作者不断致力于基础数学工具和概念的推广和创新运用,挖掘并发挥其潜在功能。本文将通过流体力学、传热学以及最优控制论方面的一些实例来综合介绍个人的心得和体会。     

基于当地笛卡尔架构的无网格方法

提出了一种新的无网格方法,该方法是自动地在每一样点建立一个局部笛卡尔架构并选取相应的邻近点,然后运用全导数公式构造该样点的所有导数,它不需要任何网格单元,所以是彻底的无网格方法．数值算例表明,该方法具有很高的精度．     

A design of novel type superconducting magnet for super—high field functional magnetic resonance imaging by using the harmonic analysis method of magnetic vector potentials

The approach of expanding the magnetic scalar potential in a series of Legendre polynomials is suitable for designing a conventional superconducting magnetic resonance imaging magnet of distributed solenoidal configuration. Whereas the approach of expanding the magnetic vector potential in associated Legendre harmonics is suitable for designing a single-solenoid magnet that has multiple tiers, in which each tier may have multiple layers with different winding lengths. A set of three equations to suppress some of the lowest higher-order harmonics is found. As an example, a 4T single-solenoid magnetic resonance imaging magnet with 4×6 layers of superconducting wires is designed. The degree of homogeneity in the 0.5m diameter sphere volume is better than 5.8 ppm. The same degree of homogeneity is retained after optimal integralization of turns in each correction layer. The ratio B_m/B₀ in the single-solenoid magnet is 30% lower than that in the conventional six-solenoid magnet. This tolerates higher rated superconducting current in the coil. The Lorentz force of the coil in the single-solenoid system is also much lower than in the six-solenoid system. This novel type of magnet possesses significant advantage over conventional magnets, especially when used as a super-high field functional magnetic resonance imaging magnet.     

Aerodynamic design method of cascade profiles based on load and blade thickness distribution

A cascade profile design method was proposed using the aerodynamic load and blade thickness distribution as the design constraints, which were correspondent to the demands from the aerodynamic characteristics and the blade strength. These constraints,together with all the other boundary conditions , were involved in the stationary conditions ofa variational principle , in which the angle-function was employed as the unknown function.The angle-function ( i. e. , the circumferential angular coordinate) was defined in the image plane composed of the stream function coordinate ( circumferential direction ) and streamline coordinate. The solution domain, i.e., the blade-to-blade passage, was transformed into a square in the image plane, while the blade contour was projected to a straight line ; thus, the difficulty of the unknown blade geometry was avoided. The finite element method was employed to establish the calculation code. Applications show that this method can satisfy the design requests on the blade     

解变分不等式的一种二次投影算法

该文研究一种新的解变分不等式的二次投影算法.通过构造一类新的严格分离当前迭代和变分不等式解集的超平面,进而建立了解决伪单调变分不等式投影算法的一种新的框架.通过改进已有结果的证明方法,证明了该算法生成的无穷序列是全局收敛的,并且在局部误差和Lipschitz条件下给出了收敛率分析.     

磁性Fe_3O_4@SiO_2@ZrO_2对水中磷酸盐的吸附研究

合成了以Fe3O4为核,以SiO2为壳的磁性纳米微粒(Fe3O4@Si O2),并采用沉淀沉积法将ZrO2包覆到材料表面。通过XRD、TEM、VSM、ζ电位、XPS和N2吸附/脱附等手段对材料进行表征,结果表明材料Fe3O4@SiO2@ZrO2上沉积了氧化锆纳米颗粒,具有超顺磁性,可在外加磁场作用下实现从水中快速分离。同时系统研究了材料对水中磷酸盐的吸附行为,结果表明沉积Zr O2使得材料对磷酸盐表现出良好的吸附性能,并且随着沉积量的增大吸附量增加。吸附等温线符合Freundlich方程。吸附动力学可用拟二级动力学模型描述,吸附速率随磷酸盐初始浓度增加而减小。磷酸盐吸附量随溶液p H值的增大而减小,但几乎不受离子强度影响。     

离子液体催化CO2与环氧化物合成环状碳酸酯

综述了离子液体催化CO2与环氧化物的环加成反应制备环状碳酸酯的研究进展。目前报道的离子液体主要包括咪唑盐、季铵盐、季鏻盐等。对比了传统离子液体与功能化离子液体对CO2环加成反应的催化活性、选择性以及催化作用机制。与传统的离子液体相比,功能化离子液体的羟基或羧基等官能团与卤素离子等Lewis碱之间存在协同效应,使得其对CO2与环氧化物的环加成反应具有更好的催化活性;将功能化离子液体固载于无机材料(SiO2,SBA-15,MCM-41等)或聚合物所得的多相催化剂不仅保持了官能团与阴离子之间的协同效应,而且载体与离子液体活性组分之间也显示出协同效应,使得该类催化剂具有很好的催化活性,稳定性好,可以多次重复使用,具有较好的工业化前景,是值得深入研发的一类催化材料。此外,离子液体对于手性环状碳酸酯的合成也具有较好的催化活性和立体选择性。     

磁性Fe3O4@SiO2@ZrO2对水中磷酸盐的吸附研究

合成了以Fe₃O₄为核,以SiO₂为壳的磁性纳米微粒（Fe₃O₄@SiO₂）,并采用沉淀沉积法将ZrO₂包覆到材料表面。通过XRD、TEM、XPS和N₂吸附/脱附等手段对材料进行表征,结果表明材料Fe₃O₄@SiO₂@ZrO₂上沉积了氧化锆纳米颗粒,具有超顺磁性,可在外加磁场作用下实现从水中快速分离。同时系统研究了材料对水中磷酸盐的吸附行为,结果表明沉积ZrO₂使得材料对磷酸盐表现出良好的吸附性能,并且随着沉积量的增大吸附量增加。吸附等温线可用Freundlich方程拟合。吸附动力学可用拟二级动力学模型拟合,吸附速率随初始浓度增加而减缓。磷酸盐吸附量随溶液pH值的增大而减小,但几乎不受离子强度影响。     

Ti-MWW催化烯丙基氯环氧化高效合成环氧氯丙烷

 研究了具有MWW结构的新一代钛硅分子筛Ti-MWW催化剂对烯丙基氯液相环氧化高效合成环氧氯丙烷的催化性能. 结果表明, Ti-MWW的催化活性以及产物选择性均优于传统的钛硅分子筛TS-1. 对于Ti-MWW,合适的溶剂为非质子性溶剂丙酮和乙腈,在该溶剂中环氧化物不易发生溶剂化开环反应; 而对于TS-1,合适的溶剂是质子性溶剂甲醇,但甲醇可导致醇醚副产物的生成. 在Ti-MWW催化剂上烯丙基氯的转化率和环氧氯丙烷的选择性都能达到99%以上.     

去甲氯胺酮半抗原及其全抗原的合成与鉴定

在低温条件下,去甲氯胺酮与琥珀醛酸反应,合成了半抗原羧基-去甲氯胺酮,电喷雾质谱鉴定结果表明,目标半抗原合成成功;通过碳二亚胺法将半抗原与载体蛋白偶联制备人工抗原,红外光谱法鉴定结果表明,人工抗原合成成功,基质辅助激光解析电离飞行时间质谱鉴定表明去甲氯胺酮半抗原与牛血清白蛋白的偶联比为11:1。经动物免疫,获得高效价特异性多克隆抗体,抗血清效价可达5.12×104。