On Properties of Rectangular Hyperbolas

This paper improves an old theorem about a rectangular hyperbola : its centre lies on the pedal circle of any point on with respect to any triangle inscribed in . We also prove that an analogous result holds for Cevian circles. These results are used to obtain new characterisations of the Feuerbach, Jarabek, and Kiepert hyperbolas of a triangle.     

Two-level Atom in an Electromagnetic Wave of Circle Polarization

We study a two-level atom interacting with an electromagnetic wave of circle polarization, and work out the wave functions, the energy values and momentum values of the atom. PACS: 32.80.-t, 03.65.Ge     

数值积分求解均匀带电圆环平面上的电场分布

本文用数值积分的方法计算椭圆积分，求出在均匀带电圆环平面上的场强与电势．     

A novel electrochemical sensing strategy for rapid and ultrasensitive detection of Salmonella by rolling circle amplification and DNA–AuNPs probe

A novel electrochemical sensing strategy was developed for ultrasensitive and rapid detection of Salmonella by combining the rolling circle amplification with DNA–AuNPs probe. The target DNA could be specifically captured by probe 1 on the sensing interface. Then the circularization mixture was added to form a typical sandwich structure. In the presence of dNTPs and phi29 DNA polymerase, the RCA was initiated to produce micrometer-long single-strand DNA. Finally, the detection probe (DNA–AuNPs) could recognize RCA product to produce enzymatic electrochemical signal. Under optimal conditions, the calibration curve of synthetic target DNA had good linearity from 10 aM to 10 pM with a detection limit of 6.76 aM (S/N = 3). The developed method had been successfully applied to detect Salmonella as low as 6 CFU mL⁻¹ in real milk sample. This proposed strategy showed great potential for clinical diagnosis, food safety and environmental monitoring.     

基于传播圆补偿像散的被动锁模激光器谐振腔设计方法

由于超短脉冲激光器的谐振腔大都采用多镜折叠的形式,像散已成为影响锁模激光器性能优劣的重要问题.本文提出了一种基于传播圆补偿像散的被动锁模激光器谐振腔设计方法,该方法简单、直观、高效,容易找到补偿像散的最佳位置.理论研究表明,当SESAM位于子午和弧矢传播圆交汇处附近时,SESAM处的子午光斑和弧矢光斑大小几乎相等,像散得到补偿.该谐振腔对外界干扰引起的腔镜振动和热透镜焦距的变化均不敏感,谐振腔的抗干扰性很强.实验研究表明,当SESAM位于子午和弧矢传播圆交汇处附近时,锁模激光器可获得稳定连续的锁模激光脉冲,且激光器的抗干扰性很强.本文的理论研究与实验结果相一致.     

极限圆型Hamilton算子乘积的自伴性

本文讨论了极限圆型Hamilton算子乘积的自伴性,利用Calkin方法及奇异Hamilton系统自伴扩张的一般构造理论,给出了在极限圆型时判定Hamilton算子乘积自伴的一个充要条件.     

圆内零级亚纯函数的充满圆及应用

本文研究了圆内零级亚纯函数的充满圆序列,获得了在关于型函数的Borel点附近存在充满圆序列,从而得到了Hayman点的存在性.     

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.     

Estimate for exponential sums and its applications

In this paper, we establish a new estimate on exponential sums by using the Bombieri-type theorem and the modified Huxley-Hooley contour. We also generalize the famous Goldbach-Vinogradov theorem, via different argument from that of Vinogradov. In particular, our major arcs are quite large and these enlarged major arcs are treated by the estimate we have established.