由藜芦醛合成娃儿藤碱

以藜芦醛(1)、3,4-二甲氧基苯乙酸(2)、(S)-L-脯氨酸(6)等为原料,经8步反应,合成了一种抗肿瘤活性(s)-( )-娃儿藤碱。先由化合物1和2在乙酸酐/三乙胺催化下反应得到3,4-二甲氧基一反式-α-(3′, 4′-二甲氧基苯基)．肉桂酸(3),在0℃、三氟乙酸存在下用VOF_3对其关环成2,3,6,7-四甲氧基-9-羧基菲(4),然后用喹啉作介质,在230℃、无水CuSO_4催化下脱去羧基,得到2,3,6,7-四甲氧基菲(5),再和(S)-N- (三氟乙酰)-L-脯氨酰氯(6b)傅-克反应得到(S)-N-(三氟乙酰基)-2,3,6,7-四甲氧基-9-L-脯氨酰基菲(7),并对产物进行了柱纯化,所得产物在三氟化硼乙醚存在下用三乙基硅烷还原羰基,然后脱去三氟乙酰保护基,最后在盐酸存在下用甲醛闭环得到目标产物(10)。用NMR和MS表征了中间体和目标产物的结构。该合成反应条件温和,总收率为3．5％,产品纯度98．5％(HPLC)。     

Fractal metal nanoparticle aggregates morphology formation mediated by polyelectrolyte/surfactant complex films at interfaces

In this work, the gold nanoparticle self-assembly behavior of mica-surface-confined polyelectrolyte/surfactant complex films was investigated. First, modified partially hydrated polyacrylamide (MHPAM)/hexadecyltrimethylammonium bromide (CTAB) complex films were deposited on the mica surface using Langmuir–Blodgett technique. Then, the preadsorbed MHPAM/CTAB complex film mica plate was dipped into the gold aqueous solution and the interesting fractal nanostructured gold network was formed. In addition, the effect of dipping time on gold nanoparticle self-assembly morphology was studied. The mechanism of formation process is briefly proposed.     

载体γ-Al2O3和钐对非晶态NiB合金热稳定性的影响

用化学还原法制备了NiB、NiB/Al2O3和NiBSm/Al2O3三种催化剂，它们都呈非晶结构.用等离子耦合发射光谱仪(ICP)对催化剂组分进行了分析，采用差示扫描量热法（DSC）对三种催化剂进行了热稳定性分析.结果表明，载体的引入使非晶态NiB合金的体相组成中B的含量降低.将非晶态NiB合金负载到γ-Al2O3上,可以明显改善非晶态合金的热稳定性，少量Sm可以进一步提高晶化温度.晶化激活能数据亦表明了载体和Sm对非晶结构具有良好的稳定作用.载体和Sm可能通过不同的作用提高了非晶态合金的热稳定性.     

约束刻蚀剂层技术对金属铝的微结构加工研究

采用约束刻蚀剂层技术, 以亚硝酸钠为先驱物, 通过电化学氧化产生刻蚀剂(硝酸)刻蚀铝, 并以NaOH为捕捉剂, 在电极模板上形成约束刻蚀剂层. 在金属铝表面加工出梯型槽微结构, 加工分辨率约为500 nm. 通过测量表面氢离子浓度, 对捕捉剂的约束效果进行了分析.     

固相萃取-液质联用法同时测定饮用水中双酚A和邻苯二甲酸二丁酯

建立了饮用水中痕量双酚A和邻苯二甲酸二丁酯同时测定的LC/MS-MS快速分析方法.水样中双酚A和邻苯二甲酸二丁酯经HLB固相萃取小柱富集,以V(乙腈)∶V(水)＝90∶10为流动相,选择双酚A m/z 227/212、邻苯二甲酸二丁酯m/z 301/228为检测离子对,利用多反应监测(MRM)和扫描时间分段检测技术实现正、负离子不同扫描模式一次完成.该方法对水样体积为250 mL时双酚A和邻苯二甲酸二丁酯的线性范围为0.4～40 ng/L,检出限分别为0.16和0.10 ng/L,低中高3个不同水平的加标平均回收率均在90%以上.应用于5种不同来源的饮用水及原水中双酚A和邻苯二甲酸二丁酯的测定.     

Cartan’s Second Main Theorem and Mason’s Theorem for Jackson Difference Operator

Let f : C → Pⁿ be a holomorphic curve of order zero. The authors establish a Jackson difference analogue of Cartan’s second main theorem for the Jackson q-Casorati determinant and introduce a truncated second main theorem of Jackson difference operator for holomorphic curves. In addition, a Jackson difference Mason’s theorem is proved by using a Jackson difference radical of a polynomial. Furthermore, they extend the Mason’s theorem for m + 1 polynomials. Some examples are constructed to show that their results are accurate.     

Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection

In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|^α|?u|^p?2?u) + λ 1/|x|^β |?u|^p?2?u · x = |x|^γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|^α|?u|^p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? R^N(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection.     

求解二维Fisher-KPP方程的一类保正保界差分格式及其Richardson外推法

本文研究求解二维Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP)方程的一类保正保界差分格式.运用能量分析法证明了当网格比满足$R_{x}+R_{y}+[b\tau (p-1)]/2\leq\frac{1}{2}$时差分解具有一系列数学性质,包括保正性、保界性和单调性,且在无穷范数意义下有$O (\tau+h_{x}^{2}+h_{y}^{2})$的收敛阶.然后通过发展Richardson外推法得到收敛阶为$O (\tau^{2}+h_{x}^{4}+h_{y}^{4})$的外推解.最后数值实验表明数值结果与理论结果相吻合.值得提及的是在运用本文构造的Richardson外推法时对时空网格比没有增加更严格的条件.     

A Multi-Scale Method for Distributed Convex Optimization with Constraints

Journal of Optimization Theory and Applications - This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using...     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.