Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.     

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.     

Novel low-dielectric constant and soluble polyimides from diamines containing fluorene and pyridine unit

Polyimides (PI's) with low-dielectric constant and excellent organic solubility have broad application prospects in the electronic field. Herein, this study designed a series of novel, low dielectric, organic soluble PI films by creatively introducing fluorene and pyridine ring into diamine monomers. Because of the noncoplanar structure of fluorenyl and the polarization of pyridine ring, PI films achieved a low-dielectric constant (2.22–3.09 at 10 MHz) and excellent organic solubility. Even in some organic solvents with low-boiling points, these PI films still exhibited outstanding solubility. In addition, all the films possessed high-tensile strength (≈120 MPa) and excellent optical transparency (>70%, 450 nm). It was worth noting that the glass transition temperature of films was all above 280°C and 5% weight loss temperature (T_5%) was at 486–553°C. In general, the novel high-performance low-dielectric PI films are expected to be used in the field of microelectronics.     

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

光栅衍射实验中测量光栅常数的两种辅助方法

衍射光栅可以将不同波长的光在空间上分离开,在光谱分析领域中有广泛应用.利用光栅的衍射来测量光栅常数是大学物理实验中的一个典型实验,而本文介绍的正是光栅衍射实验中的两个有趣现象:一是旋转光栅时,谱线的偏转角存在一个最小值;二是光栅旋转到一定角度时,衍射光斑会逐渐消失在视野中.论文从理论上分析解释这两种现象,并设计出两种测量光栅常数的方法,在实验上进行验证.与传统的用最小偏转角测光栅常数的方法相比,本文重点分析了由判定最小偏转角位置偏差所带来的影响,并提出了对称旋转测量的方法来进一步减小误差.     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化，研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板，采用层合板表面连续变化的速度环量来模拟空气对其的作用，速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性，分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明，通过纤维的变角度铺设，可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．     

Fast Cysteine Bioconjugation Chemistry

Cysteine bioconjugation serves as a powerful tool in biological research and has been widely used for chemical modification of proteins, constructing antibody-drug conjugates, and enabling cell imaging studies. Cysteine conjugation reactions with fast kinetics and exquisite selectivity have been under heavy pursuit as they would allow clean protein modification with just stoichiometric amounts of reagents, which minimizes side reactions, simplifies purification and broadens functional group tolerance. In this concept, we summarize the recent advances in fast cysteine bioconjugation, and discuss the mechanism and chemical principles that underlie the high efficiencies of the newly developed cysteine reactive reagents.     

基于正弦控制因子的Lateral变异鲨鱼优化算法

针对传统鲨鱼优化算法在求解高维目标函数时,易早熟收敛,陷入局部最优的缺陷.提出一种基于正弦控制因子的Lateral变异鲨鱼优化算法.通过正弦曲线的特性和自适应惯性权重,改善了传统鲨鱼优化算法中由于随机选取控制因子数值大小可能导致算法在迭代后期全局搜索能力降低的问题,提高了算法在迭代后期的全局收敛能力,并对最佳鲨鱼位置引入Lateral变异策略,加强了算法跳出局部最优的可能性.改进后的算法对多个shifted单峰,多峰以及固定维测试函数进行求解,实验结果表明,对比多种不同优化算法而言,本文所提LSSO算法具有更高的收敛精度和搜索速度.