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.     

Tensor method for optimal control problems constrained by fractional three-dimensional elliptic operator with variable coefficients

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional two- (2D) and three-dimensional (3D) elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D $n\times n\times n$ spacial grids. Using the diagonalization of the arising matrix-valued functions in the eigenbasis of the one-dimensional Sturm–Liouville operators, we construct the rank-structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor structured format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an $\epsilon$-threshold. This method reduces the numerical cost for solving the control problem to $O(n\log n)$ (plus the quadratic term $O(n^2)$ with a small weight), which outperforms traditional approaches with $O(n^3\log n)$ complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by $O(n\log n)$. This essentially outperforms the traditional methods operating with fully populated $n^3\times n^3$ matrices and vectors in ${?}^{n^3}$. Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated preconditioned conjugate gradient iteration in the univariate grid size n.     

Modeling and character analyzing of multiple fractional-order memcapacitors in parallel connection

Recently,the memory elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behaviors.Thus,the modeling and characterizing of the mem-elements become essential.In this paper,the analysis of the multiple fractional-order voltage-controlled memcapacitors model in parallel connection is studied.Firstly,two fractional-order memcapacitors are connected in parallel,the equivalent model is derived,and the characteristic of the equivalent memcapacitor is analyzed in positive or negative connection.Then a new understanding manner according to different rate factor K and fractional orderαis derived to explain the equivalent modeling structure conveniently.Additionally,the negative order appears,which is a consequence of the combination of memcapacitors in different directions.Meanwhile,the equivalent parallel memcapacitance has been drawn to determine that multiple fractional-order memcapacitors could be calculated as one composite memcapacitor.Thus,an arbitrary fractional-order equivalent memcapacitor could be constructed by multiple fractional-order memcapacitors.     

A novel lipid droplets-targeting fluorescent probe based on dicyanisophorone and carbazole for Cu2+ and its application

A novel fluorescent probe, LCH , based on dicyanisophorone and carbazole, was prepared for the visual detection of Cu²⁺. The probe LCH could recognize Cu²⁺ by fluorescence quenching in EtOH/H₂O (1/4, v/v) solution, which could be easily identified under the 365 nm UV lamp, and the detection limit was as low as 0.785 μM. The recognition mechanism of probe LCH with Cu²⁺ was determined by combining ¹H NMR titration, MS, and theoretical calculations. Practical application experiments showed that probe LCH could be used to detect Cu²⁺ in the test strip experiments. Cell imaging experiments showed that the probe LCH owned good cell permeability and could be applied to the imaging of Cu²⁺ in HepG2 cells. In addition, fluorescence colocalization experiments showed that LCH could target lipid droplets. These results indicate that the probe LCH will have a good application prospect in environmental detection and clinical medicine.     

新型N-杂环取代查尔酮衍生物的合成

以4-二甲氨基苯甲醛与4'-氟苯乙酮为原料,经羟醛缩合反应制得4-二甲氨基-4'-氟查尔酮(1);1分别与咪唑、哌嗪等含氮杂环化合物经取代反应合成了6个新型的N-杂环取代查尔酮衍生物,其结构经1H NMR,13C NMR和IR表征。     

2,2-二甲基-1-[5-二茂铁基-3-(三氟甲基)-1H-吡唑-1-基]丙-1-酮的合成及其电化学性质

以乙酰基二茂铁为原料,经3步反应合成了一个新型的二茂铁衍生物——2,2-二甲基-1-[5-二茂铁基-3-(三氟甲基)-1H-吡唑-1-基]丙-1-酮(4),其结构经1H NMR,ESI-MS,元素分析和X-射线单晶衍射表征。4属单斜晶系,P2(1)/c空间群,晶胞参数a=7.805 6(4),b=20.906 1(11),c=11.124 6(6),β=93.820(2)°,V=1 811.33(17)3,Z=4,Dc=1.482 g·cm-3,μ=0.872 mm-1,R1=0.034 8,wR2=0.089 2。采用循环伏安法研究了4的电化学性质。结果表明:4有一对可逆的氧化还原峰,Epa=0.640 V,Epc=0.482 V,ΔE=153 m V。     

双官能单萜氧杂二环二醇乙酸酯类衍生物的合成及其除草活性

以(3R,4R)-4,7,7-三甲基-6-氧杂二环[3,2,1]辛烷-3,4-二醇(1)和乙酰氯(2)为原料,经"一锅法"制得混合物Ⅰ;Ⅰ经分离纯化得4个新型的双官能单萜氧杂二环二醇乙酸酯类衍生物(3a~3d),其结构经1H NMR,13C NMR,FT-IR和HR-MS表征。考察了物料比r[n(2)∶n(1)]和反应时间对3a~3d相对浓度的影响。结果表明,在反应条件[1 5 mmol,r=7,回流反应7 h]下,3a~3d的相对浓度分别为21.6%,15.6%,37.9%和24.9%;在反应条件[1 5 mmol,r=4,回流反应7 h]下,3a~3d的相对浓度分别为50.7%,36.6%,7.84%和4.86%。用培养皿法测试了1和3a~3d的除草活性。实验结果表明,1和3a~3d均能显著抑制一年生黑麦草胚根与胚芽生长;在用药浓度为5 mmol·L-1时,1和3a~3d对根长抑制率分别为55.1%,86.0%,84.2%,91.3%和97.5%;对芽长抑制率分别为55.1%,76.5%,92.8%,94.8%和98.4%。     

不同产地黄芪的红外光谱鉴别研究

采用红外光谱、二阶导数红外光谱和二维相关红外光谱,对四种不同产地的黄芪原药材进行了鉴别研究。结果表明:不同产地黄芪的红外光谱和二阶导数红外谱具有一定的相似度,与淀粉的红外谱图比对,4个不同产地的黄芪均含有淀粉,其中陕西绥德产黄芪的淀粉含量比其它3个产地黄芪的都要高。山西浑源和山西天镇产黄芪谱图的1 510、1 425cm-1木质素特征峰比内蒙古固阳和陕西绥德产黄芪的更为明显,说明前二者产黄芪中木质素含量高于后二者产黄芪。在二维相关红外谱图上,根据4个产地黄芪的相对峰强度的差异,可进行产地的鉴别。研究结果表明对于不同产地黄芪的鉴别,红外三级鉴定法是一种快速有效的新方法。     

供/吸电子基团共轭桥联的双BODIPY衍生物的合成及性能

设计合成了4种对称的以不同供/吸电子基团为共轭桥、两端连接meso位苯或噻吩取代的新型氟化硼二吡咯甲川(BODIPY)衍生物;通过1H NMR,13C NMR和MS等手段对其进行了结构表征;并采用紫外吸收光谱、荧光发射光谱及循环伏安(CV)等方法研究了其光电性能.紫外光谱数据表明,BODIPY结构具有明显的特征吸收,中间的桥联基团无论是强供电子的苯并二噻吩(BDT)还是强吸电子的苯并噻二唑(BT)均不能使整个分子产生明显的分子内电子迁移(ICT).另一方面,meso位的取代基可与BODIPY核产生微弱的ICT,且meso位噻吩取代的分子比meso位苯环取代的分子表现出更强的ICT.紫外光谱数据和电化学测试结果表明,meso位噻吩取代的分子比meso位苯环取代的分子具有更低的氧化电位和更窄的能隙.     

二苯胺取代吖啶衍生物发光材料的合成、表征及电致发光性能

设计合成了2个苯胺取代吖啶衍生物N3,N3,N6,N6-四苯基吖啶基-3,6-二胺(1)和N3,N3,N6,N6-四对甲苯基吖啶基-3,6-二胺(2),通过化学修饰在吖啶核的两端引入二苯胺取代基可以调节化合物的能级和堆积结构等性质,从而使这些吖啶衍生物具有良好的发光性能,可用于制备电致发光器件.基于吖啶衍生物为掺杂发光材料制备的电致发光器件均呈现绿光发射,器件开启电压较低(2.4 V),以化合物1和2制备的器件最高功率效率分别为4.9和8.2 lm/W.考察了其光物理、电化学、热学和荧光量子效率等性能.结果表明,化合物1和2具有较高的量子效率及匹配的能级结构,这是获得较高电致发光效率的基础.