基于相移偏折法的高反射表面面形测量技术

利用单相机所采集的图像实现了对光滑高反射表面面形的直接检测.首先利用相机获取参考平面在标准平面镜中的镜像,然后通过参考平面上的点与归一化成像平面上图像点之间的密集折返对应关系,求得待测镜面的深度距离,从而实现对高反射表面面形的测量.通过光线追迹将该测量过程转化为求解物空间中关于两对应光线束之间的相交问题.以相位为载体获取面形梯度分布,求得该表面的法向量场,并求解相应的反射光线束.通过光线追迹对该光线束与相应入射光线束求“交点”检测高反射表面.对标准平面镜进行实验检测,测量得到的面形平面度为0.19 mm.采用传统方法与本文所提方法对汽车后视镜进行检测,所得检测结果对应点之间的平均距离为0.15 mm,验证了本文方法检测镜面面形的有效性.     

Approximation of Functions by the Szász-Mirakjan-Kantorovich Operator

We characterize the approximation of functions in the L_p-norm by the Szász-Mirakjan-Kantorovich operator. We prove a direct and a strong converse inequality of type B in terms of an appropriate K-functional.     

Iodine/persulfate-promoted site-selective direct thiolation of quinolones and uracils

A simple and general method for direct thiolation of 4-quinolones with disulfides or thiols under I₂/K₂S₂O₈ system has been developed. Under the optimal conditions, the C–S bond coupling can take place effectively with good to decent yields and excellent regioselectivity of the S-linked products. The established metal-free site-selective approach was also applicable to transform a range of uracil substrates to the thio-substituted products under mild conditions. Further transformation to the sulfone derivatives can be conveniently performed in one-pot. These easy-to-handle protocols represent a useful and interesting synthetic alternative with good substrate scope and functional group compatibility.     

Kaplansky’s “infinite abelian groups” and its two test problems

Abstract

Kaplansky’s Infinite Abelian Groups, originally published in 1954, has recently been republished. In recognition of its continuing significance after 65?years, the authors illustrate some important ideas and techniques described in the book. In particular, a class of groups is defined for which there are affirmative answers to the author’s two famous “Test Problems.”     

Direct synthesis of Poly(Ԑ-Caprolactone)-block-poly (glycidyl methacrylate) copolymer and its usage as a potential nano micelles carrier for hydrophobic drugs

Ring-opening (ROP) and enzymatic copolymerization (ECP) are among the most widely used approaches for synthesizing copolymers of polycaprolactone (PCL). It involves multiple-step reactions and the utilization of enzymes that make the process a lot more complicated, time consuming, and expensive. Atom transfer radical polymerization (ATRP) has been adopted to synthesize a novel amphiphilic copolymer in our study. The study presents a method to eliminate the ROP/ECP multiple steps in monomer polymerization thus making the process simpler and smoother. The synthesis of cationic polymer micelles copolymer of PCL-PGMA (polycaprolactone grafted poly glycidyl methacrylate) was carried out using direct functionalization of hydroxy group in crude PCL to achieve a higher degree of functionalization, i.e., 12.8% for macroinitiator. FTIR and ¹H-NMR confirmed the successful synthesis of the copolymer with better control over the molecular weight with a PDI (1.84). DSC and XRD results showed the reduction of crystallinity by 86.81%, making copolymer more compatible for drug delivery application. The synthesized copolymer was further converted to nano-micelles drug carrier having an average size of 96.08 ± 21.22 nm. The drug encapsulation efficiency achieved was 60.0 ± 1.7%, and nano-micelles rendered a slow and controlled release of naproxen with long-term storage stability.     

DMA-80测汞仪的应用探讨

本文的主要实验目的是利用DMA-80测汞仪直接测定固体样品中的汞并证明其方法可靠。采用升温加热直接进行热分解、金汞齐反应,采用长、短双检测池,可直接测定固体、液体样品,汞含量在0.n×10-9～600.0×10-9范围内的样品都能被很准确地测定,每个样品测定时间约为5min。 测试结果证明其方法具可靠性。     

Blow‐up phenomena for a semilinear parabolic equation with weighted inner absorption under nonlinear boundary flux

Blow‐up phenomena for a nonlinear divergence form parabolic equation with weighted inner absorption term are investigated under nonlinear boundary flux in a bounded star‐shaped region. We assume some conditions on weight function and nonlinearities to guarantee that the solution exists globally or blows up at finite time. Moreover, by virtue of the modified differential inequality, upper and lower bounds for the blow‐up time of the solution are derived in higher dimensional spaces. Three examples are presented to illustrate applications of our results. Copyright © 2016 John Wiley & Sons, Ltd.     

Blow‐up of the smooth solutions to the compressible Navier–Stokes equations

In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981–3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio γ. Then we prove the blow‐up of smooth solution of compressible Navier–Stokes equations in half space with Navier‐slip boundary. The main ideal is constructing the differential inequality. Copyright © 2017 John Wiley & Sons, Ltd.     

Blow‐up for the b‐family of equations

In this paper, we consider the b‐family of equations on the torus u _t ?u _{t x x} +(b + 1)u u _x =b u _x u _{x x} +u u _{x x x} , which for appropriate values of b reduces to well‐known models, such as the Camassa–Holm equation or the Degasperis–Procesi equation. We establish a local‐in‐space blow‐up criterion. Copyright © 2016 John Wiley & Sons, Ltd.     

On the decay and blow‐up of solution for coupled nonlinear wave equations with nonlinear damping and source terms

In this work, we consider a nonlinear coupled wave equations with initial‐boundary value conditions and nonlinear damping and source terms. Under suitable assumptions on the damping terms and source terms and initial data in the stable set, we obtain that the decay estimates of the energy function is exponential or polynomial by using Nakao's method. By using the energy method, we obtain the blow‐up result of solution with some positive or nonpositive initial energy. Copyright © 2016 John Wiley & Sons, Ltd.