多元微积分中的线性代数

在处理多元微积分的很多问题时,我们可以将该函数局部地看作一次式,也就是局部看作它的微分式,而用线性代数的观点来处理,会给理解和记忆带来很大便利.这样给出的证明简单明了,不失严谨,它本质上是微积分"以直代曲"的表现.本文给出几个常见的困扰教学问题的简单证明.     

Designing anticancer combretastatin A-4 analogues with aggregation-induced emission characteristics

Science China Chemistry - Herein a series of combretastatin A-4 (CA-4) analogues with aggregation-induced emission characteristics (compounds a1–a19) were rationally designed and synthesized....     

Cu2SnTe3 Nanoparticles for Chemodynamic/Photodynamic /Photothermal Combination Tumor Therapy

Cancer is a serious threat to human life. However, the effect of single treatment method is limited at present. Here, a Cu₂SnTe₃ (CST) nano-reagent which can provide a strong synergetic effect in tumor therapy is successfully constructed. CST nanoparticles can not only convert endogenous H₂O₂ into ∙OH through surface-catalyzed reactions, but also generate ¹O₂ based on light irradiation-induced electron pair separation, leading to excessive oxidative stress accumulation in tumor cells. Interestingly, CST nanoparticles are also found to possess catalase-like activity, which enhances the level of O₂ within hypoxic tumors, further improving the production efficiency of ¹O₂ by photodynamic therapy (PDT). In addition, the CST nanoparticles exhibit good photothermal conversion, which facilitates to promote more ^∙OH production by chemodynamic therapy (CDT). The results of in vitro and in vivo anti-tumor experiments both demonstrate that CST nanoparticles can effectively inhibit the growth of tumor with minimal side effects. To sum up, CST nanoparticles have great potential in tumor treatment for efficient synergetic CDT/PDT/photothermal therapy.     

双噁唑啉对聚碳酸1,2-环己二酯的扩链研究

采用马来酸酐封端聚碳酸1,2-环己二酯(PCHC),使其末端羟基转变为端羧基(MA-PCHC),并以2,2'-双-(2-噁唑啉)(BOZ)为扩链剂进行扩链反应.研究发现,BOZ与MA-PCHC中的羧基等摩尔情况下,扩链效果最佳.扩链后的PCHC的数均分子量从扩链前的5.6×104增长到12.4×104.扩链后的PCHC...     

特殊Lorentz变换的一种新的导出方法

利用光速不变原理，在尽可能少的条件下，导出了特殊Ｌｏｒｅｎｔｚ变换公式，避开了在以往的特殊Ｌｏｒｅｎｔｚ变换公式的推导中所添加的那些除光速不变原理以外的种种限制，简化推导步骤，以利于扩大其应用领域．     

孔洞厚度对高功率微波脉冲耦合的影响

通过数值模拟研究了高功率微波脉冲与有限厚度孔洞的耦合过程，得出了孔洞厚度对高功率微波脉冲耦合的一些有用结果。     

角度重叠模型的应用 Ⅰ.计算过渡金属配合物电子光谱的微机程序

按照角度重叠模型,用FORTRAN语言编写了计算过渡金属配合物电子光谱的微机程序。     

人工神经网络方法用于PC/ABS材料定量分析

采用人工神经网络(ANN)算法建立了不同共混比的ABS/PC样品的近红外光谱数据与共混比的定量校正模型,并对校正模型的准确性进行了验证。实验分析结果表明,该方法适合于高分子材料共混比的测定。     

配位场弱场方案的酉群方法(dN离子)

本文用酉群方法(UGA)处理d壳层的弱配位场方案, 着重讨论了如何构成与群链U(5)>SU(5)>SO(3)>G匹配的对称函数。这些函数是用Lie代数方法构成,并且用U(5)群的Gelfand态表示。     

Extraction of Am(III) and Eu(III) with dialkyldi (or mono) thiophosphinic (or phosphoric) acids

Extraction of Am(III) and Ln(III) from NaClO₄ medium with di(2-ethylhexyl)dithiophosphoric acid (DEHDTP), di(2-ethylhexyl)monothiophosphoric acid (DEHMTP), di(2-ethylhexyl)monothiophosphinic acid (DEHMTPI), dihexyldithiophosphinic acid (DHXDTPI), diheptyldithiophosphinic acid (DHPDTPI), dioctyldithiophosphinic acids (DODTPI), dinonyldithiophosphinic acid (DNDTPI), di(1-methylheptyl)dithiophosphinic acid (DMHDTPI) and di(2-ethylhexyl)dithiophosphinic acid (DEHDTPI) in xylene has been investigated. The order of the extraction selectivity for Am(III) is DEHDTPI > DEHDTP > DEHMTPI > DEHMTP, DHPDTPI > DODTPI > DHXDTPI > DNDTPI, DMHDTPI > DEHDTPI > DODTPI, for extractants with 2-ethylhexyl alkyl, straight chain alkyl, branch chain alkyl, respectively. Using 0.1 mol/l NaClO₄ solution as aqueous phase, the slope values of the logD-pH and logD-logC curves are not integers, and the slope values for Am(III) are slightly higher than those for Eu(III), for all extractants. The relationship between the slope value and extraction conditions can be described as: logS = alg(C _HA/C _M ^S/4)+b. In the presence of macro Eu(ClO₄)₃, the formula, logSF _Am/Ln = B-2log(C _HL-D _Ln/(D _Ln + 1)C _Eu), can well describe the relationship between separation factor and the extraction condition. A high separation factor (SF _Am/Eu = 2500) is obtained by solvent extraction with 0.5 mol/1 DEHDTPI in toluene from 1 mol/l NaNO₃ solution.