A necessary condition for the minimum of a quadratic form under rearrangements

A necessary condition is derived for a quadratic form p^tGp to be minimal among all permutations of the nonnegative nontrivial vector p. The quadratic form arises from the stability problem of a fixed-fixed taut string loaded with masses at equidistant points.     

Repetition rate multipliers for efficient implementation of multiphoton and pump-probe fluorescence microscopy

With the advances in pulsed laser systems, microscopic imaging techniques such as multiphoton and pump-probe fluorescence microscopy have developed into effective tools for investigating intensity and time-resolved phenomena inside biological systems. However, pulsed lasers used in these techniques usually are commercial systems with repetition frequencies of around 80 MHz. While these systems have proven to be adequate for multiphoton and pump-probe microscopic imaging applications, the temporal separation of the laser pulse train (around 12.5 ns) is long compared to the fluorescence lifetimes of many common fluorescence species. In this work, we present the designs of repetition rate multipliers based on passive optical components that can be used to increase the efficiency in multiphoton and pump-probe fluorescence microscopy. Depending on the lifetime of fluorescence molecules under investigation, the passive repetition rate multiplier can increase the duty cycle of multiphoton or pump-probe microscopy up to fourfold.     

对数凸模糊映射

利用模糊数的表示定理,本文证明了对数凸模糊映射一些基本性质,并纠正了S.N anda和K.K ar对数凸模糊映射定义的不合理性和其证明中的错误。     

Effects of oxygen vacancy location on the electronic structure and spin density of Co-doped rutile TiO₂ dilute magnetic semiconductors

According to density functional theory (DFT) using the plane wave base and pseudo-potential, we investigate the effects of the specific location of oxygen vacancy (VO) in a (Ti,Co)O 6 distorted octahedron on the spin density and magnetic properties of Co-doped rutile TiO2 dilute magnetic semiconductors. Our calculations suggest that the V O location has a significant influence on the magnetic moment of individual Co cations. In the case where two Co atoms are separated far away from each other, when the V O is located at the equatorial site of a Co-contained octahedron, the ground state of the two Co cations is d6 (t3 2g ↑, t 3 2g ↓) without any magnetic moment. However, if the V O is located at the apical site, these two Co sites have different ground states and magnetic moments. The spin densities are also observed to be modified by the exchange coupling between the Co cations and the location of V O . Some positive spin polarization is induced around the adjacent O ions.     

Preparation of non-oriented silicon steel with high magnetic induction using columnar grains

Columnar grains can lead to detrimental surface ridging and an inhomogeneous microstructure, although their {1 0 0}〈0 v w〉 texture is considered desirable due to their good magnetic properties in non-oriented silicon steel. Based on the hereditary tendency of {1 0 0}〈0 v w〉 texture, the effects of lubrication and heating rate on texture and on final magnetic properties were investigated using a cast slab containing 100% columnar grains. Hot rolling with lubrication, normalization at low heating rate, two-stage cold rolling, and final annealing at 1000 °C helped achieve high performance. As a result, a new non-oriented silicon steel with high magnetic induction (B₅₀=1.82 T) and low core loss (P_1.5=2.35 W/kg) was prepared. The possibility of further performance optimization was also discussed.     

Characterization of Pinched Ricci Curvature by Functional Inequalities

In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature, along with gradient estimates, \(L^p\)-inequalities and log-Sobolev inequalities. These results are further extended to differential manifolds carrying geometric flows. As application, it is shown that they can be used in particular to characterize general geometric flow and Ricci flow by functional inequalities.     

A mathematical model of Schmidt corrector plate with defocus in variable for quick F ratio and large aperture systems

To make it easier for designing Schmidt optical systems, based on wavefront aberration functions, a mathematical model of the corrector plate aspheric surfaces varies as a function of defocusing amount is established. It corrects not only the third-order spherical aberration, but also the 5th-order spherical aberration for the system. A series of Schmidt optical systems were designed as examples to evaluate the mathematical model of the aspherics. Results show that the mathematical model is precisely in fitting the needed shape of the corrector, and can be used for the systems for quick F ratio and large aperture. A mathematical model for reflective correctors shape is also established.     

Studies on the interaction between scopoletin and two serum albumins by spectroscopic methods

The interactions of scopoletin to bovine serum albumin (BSA) and human serum albumin (HSA) have been investigated by spectroscopic methods. The fluorescence tests indicated that the formation mechanism of scopoletin–BSA/HSA complexes belonged to the static quenching. The displacement experiments suggested that scopoletin primarily bound to tryptophan residues of BSA/HSA within site I (subdomain IIA). The binding distance of scopoletin to BSA/HSA was 2.38/2.34 nm. The thermodynamic parameters (ΔG, ΔH and ΔS) calculated on the basis of different temperatures revealed that the binding of BSA–scopoletin was mainly depended on van der Waals interaction and hydrogen bond, and yet the binding of HSA–scopoletin was strongly relied on the hydrophobic interaction and electrostatic interaction. The results of synchronous fluorescence, 3D fluorescence, UV–vis absorption, and FT-IR spectra showed that the conformations of BSA and HSA altered with the addition of scopoletin. In addition, the effects of some common ions on the binding constants of scopoletin to proteins were also investigated.     

季铵盐型双子表面活性剂16-4-16聚集状态的NMR研究

核磁共振弛豫，自扩散以及2D NOESY谱研究结果表明：双子表面活性剂16-4-16溶液在形成胶束的过程中，联结基团及其邻近的碳氢链质子形成胶束的壳层，而距离离子头较远的疏水质子位于胶束的内部. 与对应的单链的表面活性剂CTAB相比，其分子运动更受限制. 2D NOESY谱显示联接基团及临近的碳氢链的质子间有较强的交叉峰，表明形成胶束时，分子在联结基团附近堆积的较为紧密. 由2D NOESY谱计算得到的质子间距与HYPERCHEM模拟值有偏差，表明这些强交叉峰是分子间相互作用的结果，并且对应质子对在双子表面活性剂16-4-16分子中位于邻近的区域. 因此我们推测，双子表面活性剂16-4-16分子在球形胶束中形成特殊的排列方式.     

ps级脉冲光纤放大器和压缩器

 对掺镱双包层脉冲光纤放大器进行实验研究。当用入纤功率为1.9 W的半导体激光器激光泵浦0.5 m长的双包层掺镱光纤时,把平均功率为7 mW、重复频率25.4 MHz的激光放大到505 mW,相应的单脉冲能量为19.8 nJ,经过光栅对压缩后,得到2.7 ps的脉冲激光。