一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

Benchmarking of Density Functionals for the Description of Optical Properties of Newly Synthesized π-Conjugated TADF Blue Emitters

Computational modeling of the optical characteristics of organic molecules with potential for thermally activated delayed fluorescence (TADF) may assist markedly the development of more efficient emitting materials for organic light-emitting diodes. Recent theoretical studies in this area employ mostly methods from density functional theory (DFT). In order to obtain accurate predictions within this approach, the choice of a proper functional is crucial. In the current study, we focus on testing the performance of a set of DFT functionals for estimation of the excitation and emission energy and the excited singlet-triplet energy gap of three newly synthesized compounds with capacity for TADF. The emitters are designed specifically to enable charge transfer by π-electron conjugation, at the same time possessing high-energy excited triplet states. The functionals chosen for testing are from various groups ranging from gradient-corrected through global hybrids to range-separated ones. The results show that the monitored optical properties are especially sensitive to how the long-range part of the exchange energy is treated within the functional. The accurate functional should also be able to provide well balanced distribution of the π-electrons among the molecular fragments. Global hybrids with moderate (less than 0.4) share of exact exchange (B3LYP, PBE0) and the meta-GGA HSE06 are outlined as the best performing methods for the systems under study. They can predict all important optical parameters correctly, both qualitatively and quantitatively.