On the existence theorem of non-trivial periodic solution of periodic systems of high order

In this paper, we consider nonlinear and nonautonomous systems with the trivial solution:dx/dt=f(t, x), x∈R~nwhere f(t+ω,x)+f(t, x), f(t, 0)=0. By using the theory of Brouwer topological degree, we obtainthe existence theorem of nontrivial ω-periodic solution. Finally the applied example of the theoremis cited.     

The consistencies ofMA,SOCA, OCA andISA withKT(ω2)

In this paper, we prove that ifZFC is consistent, then so are the following theories: $$\begin{gathered} ZFC + MA + KT(\omega _2 ) + 2^{\aleph _0 } = \aleph _2 , \hfill \\ ZFC + SOCA + KT(\omega _2 ), \hfill \\ ZFC + SOCA1 + KT(\omega _2 ), \hfill \\ ZFC + OCA + KT(\omega _2 ), \hfill \\ ZFC + ISA + KT(\omega _2 ), \hfill \\ \end{gathered} $$ whereMA denotes Martin's axiom.KT(ω ₂) the statement:“There exists anω ₂-Kurepa tree”, andSOCA, SOCA1,OCA andISA are axioms introduced in [1].     

三硼酸锂晶体的生长形态

用自由生长系统研究了三硼酸锂ＬｉＢ_３Ｏ_５（ＬＢＯ）晶体的实际生长形态。实验表明，它的各晶面簇的重要性的顺序为：｛１１０｝＞｛０１１｝＞｛２０１｝＞｛１１１｝。讨论了ＬＢＯ晶体的生长习性与内部结构之间的关系并应用负离子配位多面体理论模型解释了ＬＢＯ晶体的生长形态。     

高含量钒的钼钒磷杂多化合物的合成和性质研究

本工作改进了文献[4]报导的几种原料同时混合、加热煮沸合成的方法采用分步加入原料,控制反应温度、多次重结晶的方法合成了6、7、8个钒原子取代的钼钒磷杂多酸铵;并以铵盐为原料,用离子交换、冷冻分离和真空抽吸相结合的提纯方法制备了未见文献报导的相应的固体杂多酸;H₅[PMo₅V₇O_37.5]·xH₂O,H₆[PMo₄V₈O_37.5]·xH₂O。通过元素组成分析确定了它们的组成。这些杂多酸在水溶液、非水溶液中的电位滴定表明,杂多阴离子在分解前没有发生自电离、水解等情况,它们在水溶液中是稳定的。酸的碱度分别为5、5、6。通过纸上色谱实验,讨论了杂多酸的分解过程。由热重分析和溶解性实验得到它们的分解温度,本文还讨论了这些化合物的红外、紫外光谱,x光粉末衍射及极谱性质。光谱结果表明,它们可能具有Keggin结构,由导数脉冲极谱得到它们的峰电位。     

New flavonoids from Oxytropis myriophylla

Eight compounds were isolated from Oxytropis myriophylla. On the basis of spectral analyses, their structures were elucidated to be (6R,9R)-roseoside (1), (6R,9S)-roseoside (2), adenosine (3), myriophylloside B (4), myriophylloside C (5), myriophylloside D (6), myriophylloside E (7), and myriophylloside F (8). Five flavonoids (4-8) were new compounds, and the three known compounds were isolated from this plant for the first time.     

明胶包埋黑根霉菌丝体对水中Pb^2＋吸附性能的研究

本文研究了明胶包埋黑根霉菌丝体的包埋条件及包埋后对水中Ｐｂ~（２＋）的吸附作用。结果表明，包埋比例为６／１（Ｗ／Ｗ），交联剂甲醛用量为２５％，凝胶化温度为４０℃，ＰＨ＝１０．０为包埋反应的最佳条件。包埋后的饱和吸附量可达１２１．２ｍｇ／ｇ，比未包埋黑根霉下降１０．８％。吸附平衡时间延长至８００分钟。ｐＨ值对吸附量有较大影响，ＰＨ＝４．０时，吸附最佳。升高温度有利于吸附。流速对动态吸附有很大影响。ＨＮＯ３和ＮａＯＨ可以对吸附剂进行解吸与再生，解吸率在９４％以上。明胶包埋后黑根霉具有较好的物理性能，断裂压缩强度为１２８．１Ｎ／ｃｍ２。