聚丙烯酰胺固定化糖化酶特性的研究

本研究以丙烯酰胺单体通过反向悬浮聚合技术合成聚丙烯酰胺作为载体材料，采用包埋—交联法固定化葡萄糖淀粉酶，并对其特性进行了研究．结果表明，该固定化酶最适pH值为5．0，最适温度为55～58℃，而且具有较好的贮存稳定性和操作稳定性，8个月后该固定化酶的残余活力仍保持在94％左右，可重复使用43批次，此固定化酶酶活回收率达到56％．实验表明丙烯酰胺悬浮聚合固定化糖化酶的方法是简便可行的．     

基于Labview的一级环形倒立摆逆系统轨迹法自动摆起控制

利用求解非线性方程两点边值问题,得到逆系统参考轨迹;通过设计逆系统前馈控制及LQR反馈控制器,对参考轨迹实时跟踪。基于QNET 2.0旋转倒立摆实验平台,采用Labview编程软件,实现了一级环形倒立摆的自动摆起与稳定的实物控制。实验结果证明控制算法的有效性,可以使一级环形倒立摆在一个摆周期内自动摆起,并保持稳定状态。与能量法自动起摆实验比较,逆系统算法具有较好的快速性和稳定性。     

The use of inverse gas chromatography to study surface thermal oxidation of polypropylene

Thermo-oxidative effects on the surface energy of polypropylene were measured by inverse gas chromatography as a function of exposure time and temperature. Unaltered polypropylene had a surface energy of 33 mJ/m². Oxidized polypropylene, after exposure to air at temperatures of 100 °C and 110 °C, had a range of maximum surface energies from 38 to 41 mJ/m². Comparisons between FTIR carbonyl peak growth and the surface energy showed that both methods detect oxidation, though the increase in surface energy is detected before the carbonyl peak growth is noticeable. The work of adhesion predicted by the surface free energies obtained in this work between a coated calcium carbonate and polypropylene changes by 10% due to the oxidation of the polymer at 110 °C.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Utilization of inverse approach in the design of materials over nano‐ to macro‐scale

In the light of recent developments in computer technology, a promising and efficient way to design a material with a desired property would be to solve the inverse problem: use a physical property to predict structure. Here, we discuss the basic idea and mathematical foundation of the inverse approach, and proposed strategies for its utilization in the design of materials over nano‐ to macro‐scales. At the nano‐scale, analyzed strategies include scanning of a high‐dimensional space of chemical compounds for those compounds that have a targeted property, and identification of correlations in large databases of materials. However, unlike utilization of inverse approach at nano‐scale where full structural information ‐ atoms and their positions‐ is linked to targeted properties, at the meso‐ and macro‐scale, only partial structural information, manifested via structural motifs or representative volume elements, is available. We discuss the role of partial structural information in the inverse approach to the design of materials at those scales. Risks and limitations of the inverse approach are analyzed and dependence of the approach on factors such as structure parametrization, approximations in theoretical models, and feedback from structural characterization, is addressed.

     

Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin inverse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.     

Phase unwrapping by accumulation of residual maps

We present a path independent (global) algorithm for phase unwrapping based on the minimisation of a robust cost function. The algorithm incorporates an outlier rejection mechanism making it robust to large inconsistencies and discontinuities. The proposal consists on an iterative incremental scheme that unwraps a sub-estimation of the residual phase at each iteration. The sub-estimation degree is controlled by an algorithm׳s parameter. We present an efficiently computational multigrid implementation based on a nested strategy: the process is iterated by using multiple resolutions. The proposal׳s performance is demonstrated by experiments with synthetic and real data, and successfully compared with algorithms of the state of the art.     

Nonlinear Schrödinger equation in a semi-strip: Evolution of the Weyl–Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions

Rectangular matrix solutions of the defocusing nonlinear Schrödinger equation (dNLS) are studied in quarter-plane and semi-strip. Evolution of the corresponding Weyl–Titchmarsh (Weyl) function is described in terms of the initial Weyl function and boundary conditions. In the next step, the initial Weyl function is recovered (for the quarter-plane case) from the long-time asymptotics of the wave function considered at the boundary. Thus, it is shown that the evolution of the Weyl function is uniquely defined by the boundary conditions. Moreover, a procedure to recover solutions of dNLS (uniquely defined by the boundary conditions) is given. In a somewhat different way, the same boundary value problem is also dealt with in a semi-strip (for the case of a quasi-analytic initial condition).