二次四元数系统正定解的迭代法

二次四元数系统XAX-BX=P是离散型Lyapunov方程正定解反问题的推广形式.本文在四元数体上讨论它的正定解存在性及迭代求解方法.利用等价二次方程的系数矩阵的极大极小特征值,获得其正定解的存在区间,并针对系数矩阵的不同情况构建出三种收敛的迭代格式.同时根据每种迭代的特点,给出了迭代初始矩阵的选取方法.最后通过四元数...     

动态固定化方法制备微酶反应器研究初探

以固定化人工膜为固定相,胰蛋白酶为固定靶蛋白,利用生物功能化色谱的方法,制备固定化微酶反应器,并与HPLC-MS/MS技术联用,检测目标蛋白牛血清白蛋白、肌红蛋白和细胞色素C的酶解效率.实验初步证明,所制备的新型微柱酶解器具有活性高、稳定性高、催化效率高、酶活性持久、快速再生及操作简单等优点.     

Interactions between heavy quarks and tilted QGP fireballs in 200 A GeV Au+Au collisions

Heavy quark observables are applied to probe the initial energy density distribution with violation of longitudinal boost invariance produced in relativistic heavy-ion collisions. Using an improved Langevin model coupled to a (3+1)-dimensional viscous hydrodynamic model, we study the nuclear modification factor (\begin{document}$R_{AA}$\end{document}) and directed flow (\begin{document}$ v_1 $\end{document}) and elliptic flow (\begin{document}$ v_2 $\end{document}) coefficients of heavy mesons and their decayed electrons at an RHIC energy. We find that the counter-clockwise tilt of nuclear matter in the reaction plane results in a positive (negative) heavy flavor \begin{document}$ v_1 $\end{document} in the backward (forward) rapidity region, whose magnitude increases with the heavy quark transverse momentum. The difference in the heavy flavor \begin{document}$R_{AA}$\end{document} between different angular regions is also proposed as a complementary tool to characterize the asymmetry of the medium profile. Our model results are consistent with currently available data at the RHIC and provide predictions that can be tested by future measurements.     

Stereoselective Assembly of Hydrogen-Bonded Anionic Cages Dictated by Organophosphate-Based Chiral Nodes

Inspired by the signal transduction function of organophosphates in biological systems, bioactive organophosphates were utilized for the first time as chiral nodes to dictate the stereoselective assembly of hydrogen-bonded anionic cages. Phosphonomycin (antibiotics), tenofovir (antivirals), adenosine monophosphate (natural product, AMP) and clindamycin phosphate (antibiotics) were assembled with an achiral bis-monourea ligand, thereby leading to the stereoselective formation of quadruple or triple helicates. The extent of the stereoselectivity could be enhanced by either lowering the temperature or adding stronger-binding cations as templates. With the chiral anionic cages as the host, some enantioselectivity was achieved when binding chiral quaternary ammonium cations.     

C−H Functionalization of Aldehydes and Ketones with Transient Directing Groups: Recent Developments

In order to directly functionalize C−H bonds of complex molecules and, in particular, to control the regioselectivity of the reaction, a wide range of directing groups has been used. However, these directing groups need to be installed and removed for further applications, which may limit the use of C−H activation in synthesis. Concerning aldehydes and ketones, a transient directing group strategy has recently emerged to overcome this drawback. The addition of an additive, in general an amine, allowed the in situ formation of the real directing group to achieve C−H activation. This review presents the latest developments in the field over the period 2020–2023.     

Metal-Free and Mild Synthesis of 2,4-Diarylquinolines

We have developed a useful method to synthesize quinoline derivatives, which required no transition metals, no peroxides, and no high temperatures. This method provides a novel and gentle synthetic route for various multifunctional 2,4-diarylquinolines with good yields.     

Melnikov Functions for a Class of Piecewise Hamiltonian Systems

This paper is concerned with the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. By constructing a Poincar\''{e} map, we obtain explicit expressions of the first, second and third order Melnikov functions. In addition, we apply their expressions to give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.     

非线性随机分数阶延迟积分微分方程Euler-Maruyama方法的强收敛性

本文研究了一类新的模型问题:非线性随机分数阶延迟积分微分方程.当方程中的漂移项和扩散项满足全局Lipschitz条件和线性增长条件时,基于压缩映射原理给出了该方程解存在唯一的充分条件.由于理论求解的困难,构造了一种数值方法(Euler-Maruyama方法),并证得强收敛阶为α-1/2,α∈(1/2,1].最后通过数值试验,验证了这一理论结果.