On the numerical solution of ill‐conditioned linear systems by regularization and iteration

We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning.     

Dynamical analysis,circuit realization,and application in pseudorandom number generators of a fractional-order laser chaotic system

A new five-dimensional fractional-order laser chaotic system (FOLCS) is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system. Dynamical behavior of the system, circuit realization and application in pseudorandom number generators are studied. Many types of multi-stable states are discovered in the system. Interestingly, there are two types of state transition phenomena in the system, one is the chaotic state degenerates to a periodical state, and the other is the intermittent chaotic oscillation. In addition, the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm. Moreover, a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit. Finally, a pseudo-random sequence generator is designed using the FOLCS, and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22. This study enriches the research on the dynamics and applications of FOLCS.     

Rational Design of a Near-infrared Fluorescent Material with High Solid-state Efficiency,Aggregation-induced Emission and Live Cell Imaging Property

Near-infrared(NIR) fluorescent materials with high photoluminescent quantum yields(PLQYs) have wide application prospects. Therefore, we design and synthesize a D-A type NIR organic molecule, TPATHCNE, in which triphenylamine and thiophene are utilized as the donors and fumaronitrile is applied as the acceptor. We systematically investigate its molecular structure and photophysical property. TPATHCNE shows high T_gof 110℃ and T_d of 385℃ and displays an aggregation-induced emission(AIE) property. A narrow optical bandgap of 1.65 eV is obtained. The non-doped film of TPATHCNE exhibits a high PLQY of 40.3% with an emission peak at 732 nm, which is among the best values of NIR emitters. When TPATHCNE is applied in organic light-emitting diode(OLED), the electroluminescent peak is located at 716 nm with a maximum external quantum efficiency of 0.83%. With the potential in cell imaging, the polystyrene maleic anhydride(PMSA) modified TPATHCNE nanoparticles(NPs) emit strong fluorescence when labeling HeLa cancer cells, suggesting that TPATHCNE can be used as a fluorescent carrier for specific staining or drug delivery for cellular imaging. TPATHCNE NPs fabricated by bovine serum protein(BSA) are cultivated with mononuclear yeast cells, and the intense intracellular red fluorescence indicates that it can be adopted as a specific stain for imaging.     

Yb:CaF2–YF3 transparent ceramics ultrafast laser at dual gain lines

Yb³⁺:CaF₂-YF₃ transparent ceramics with excellent optical quality was successfully fabricated by hot-pressed method. Pulsed laser properties of this ceramics were investigated for the first time. Laser diode (LD) was applied as the pump source to generate a dual-wavelength mode-locked (ML) laser. The maximum average output power was 310 mW, which represents the highest output power of ultrafast calcium fluoride ceramic laser. The spectrum separated at 1048.9 nm and 1049.7 nm with a total pulse duration of 8.9 ps. The interval period between the beating signals was about 4.3 ps, corresponding to a 0.23 THz beat pulse repetition rate. These results demonstrate its potential in producing dual-wavelength ultrashort pulses. These Yb³⁺:CaF₂-YF₃ ceramics with low-cost and short-preparation period are ideal candidate materials for ultrafast lasers.     

Linear independence of a finite set of time-frequency shifts

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L² function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.     

阳离子交换皂石黏土在基质辅助激光解吸电离飞行时间质谱分析中的应用

将一种人工合成的无机聚合物——蒙脱石皂石黏土（smectite，Sm）应用于基质辅助激光解吸电离飞行时间质谱分析（matrix-assisted laser desorption/ionization time of flight mass spectrometry, MALDI-TOF-MS），以检测糖类化合物。 将传统的有机基质2，4，6-三羟基苯乙酮（trihydroxyacetophenone, THAP）与阳离子交换后的皂石黏土混合制备成新型复合基质，应用于糖类化合物的检测。通过比较不同的制样方法，测定不同分子直径的糖类化合物，发现由于受复合基质晶面间距的限制，只有小分子糖类化合物能进入晶面间隙充分接触有机基质并被离子化，从而实现对小分子糖类化合物的选择性检测。