Optimal packings of two to four equal circles on any flat torus

We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent vectors. We prove the optimality of the arrangements using techniques from rigidity theory and topological graph theory.     

Protein-Mediated Suppression of Rolling Circle Amplification for Biosensing with an Aptamer-Containing DNA Primer

We report a method to detect proteins via suppression of rolling circle amplification (RCA) by using an appropriate aptamer as the linear primer (denoted as an aptaprimer) to initiate RCA. In the absence of a protein target, the aptaprimer is free to initiate RCA, which can produce long DNA products that are detected via binding of a fluorescent intercalating dye. Introduction of a target causes the primer region within the aptamer to become unavailable for binding to the circular template, inhibiting RCA. Using SYBR Gold or QuantiFluor dyes as fluorescent probes to bind to the RCA reaction product, it is possible to produce a generic protein-modulated RCA assay system that does not require fluorophore- or biotin-modified DNA species, substantially reducing complexity and cost of reagents. Based on this modulation of RCA, we demonstrate the ability to produce both solution and paper-based assays for rapid and quantitative detection of proteins including platelet derived growth factor and thrombin.     

Nucleic acid quantification using nicking–displacement,rolling circle amplification and bio-bar-code mediated triple-amplification

In the present study, an inductively-coupled plasma-mass spectrometry (ICP-MS)-based triple-amplification system, by combination of nicking–displacement, rolling circle amplification (RCA) and bio-bar-code probes, was fabricated for the detection of DNA target. By using this system, hepatitis B virus (HBV) DNA target down to 3.2 × 10⁻¹⁷ M was detected by DNA probes labeled with Au nanoparticles (AuNPs). Single nucleotide polymorphisms in genes can also be effectively discriminated. In addition, we proved that this strategy is capable of detecting the target in complicated biological samples and holds great potential application in biomedical research.     

DNA的滚环扩增合成研究

滚环扩增(RCA)反应作为一种简单高效的等温酶促反应,现已发展为核酸扩增领域的新技术,其产物在组装体搭建和多功能材料的制备方面有着广泛的应用。本文采用琼脂糖凝胶、紫外和透射电镜(TEM)等手段,探究了时间、三磷酸脱氧核糖核苷(dNTPs)、酶以及引物的浓度等因素对脱氧核糖核酸(DNA)滚环扩增产物的影响。结果表明:在反应开始的前30 min,RCA产物的长度受时间的影响比较明显;随着dNTPs浓度的提高,RCA产物的链长增长,浓度也不断提高;酶和引物的浓度对滚环扩增产物的长度没有明显影响,但对RCA产物浓度的影响较大,过量的酶致使RCA产物的含量显著下降。     

Modified classification of non-self-adjoint second-order difference equations

This paper is concerned with the classification of non-self-adjoint second-order difference equations. The relationship between the number of summable solutions of non-self-adjoint difference equations and that of the discrete linear Hamiltonian system is discussed. A classification for non-self-adjoint second-order difference equations is established, which is independent of the choice of the rotated half plane and the fixed point.     

两相流显微PIV/PTV系统的开发

开发了一个能同时测量两相流中两相速度和细颗粒尺寸分布的显微PIV/PTV系统,其硬件系统包括大功率连续激光器、显微镜、高速摄像机;软件系统由改进的球形颗粒图像识别算法、各种图像处理算法和各种先进的PIV/PTV算法组成。其中改进的圆弧识别算法能够进行更准确地进行曲线分割而能对充满噪音并相互重叠的颗粒图像给出较好的识别结果。应用该PIV系统,可以在微秒和微米数量级上捕获细颗粒/气泡图像,并能较准确地同时得到两相速度、颗粒尺寸和浓度分布。对焚香可吸入颗粒物进行了速度和尺寸的同时测量,得到了较满意的结果。     

压电材料椭圆切口的力学分析

在线性压电本构方程框架下，用复势函数方法对椭圆切口模型进行了精确的数值计算。完整地考虑了各向异性力电耦合效应以及切口内不同电介质的介电性质。给出了切口内部不同介电性质对压电材料内部应力的影响。指出了Sosa文章里的一些计算错误。由于现在文献中很少有关于电导通边界条件下理论解的数值结果，所以本文同时提供了不同电边界条件下理论解的数值结果，所以本文同时提供了不同电边界条件下的理论解的数值结果。最后通过最小势能原理建立了8结点有限元模型，对椭圆切口问题进行了计算并与理论解进行了仔细比较。     

龙井水库大坝的渗流和稳定分析

本文以龙井水库大坝为例,运用有限单元法对粘土心墙坝的渗流进行分析计算,同时运用瑞典圆弧滑动法和简化Bishop法对粘土心墙坝的坝体稳定进行分析计算,在此基础上对水库大坝进行了渗流安全评价和稳定性安全评价。