Codimension 2 bifurcations of double homoclinic loops

In this work, the double-homoclinic-loop bifurcations in four dimensional vector fields are investigated by setting up local coordinates near the double homoclinic loops. We get the existence, uniqueness and incoexistence of the large 1-hom and large 1-per orbit, and their corresponding existence regions are located. Furthermore, the inexistence of the large 2-hom and large 2-per orbit are also demonstrated.     

Synthesis, characterization and quantum chemistry study of 3,6-bis(1H-1,2,3,4-tetrazol-5-yl-amino)-1,2,4,5-tetrazine

3,6-bis(1H-1,2,3,4-tetrazol-5-yl-amino)- 1,2,4,5-tetrazine (BTATz) was synthesized by the condensation of triaminoguanidinium nitrate with 2,4-pentanedione, followed by oxidation and substitution reaction. The product was characterized by elemental analysis, IR, NMR spectrometry and DSC analysis. Instead of nitrogen dioxide/N-methylpyrrolidone, acetic acid/sodium nitrite was used as the oxidizer during the oxidation. Thus, the cost was reduced and the process was simplified. The theoretical properties of BTATz were estimated by a B3LYP method based on a 6-31G(d,p) basis set, and the stable geometric configuration and bond order were obtained. The vibrational frequencies, IR spectrum and thermodynamic properties under different temperatures were obtained from vibrational analysis and the relationship between temperature and thermodynamics properties was deduced. Pyrolysis mechanism of BTATz was discussedand the transition state and activation energy of ring opening reaction of the tetrazole were deduced. __________ Translated from Chinese Journal of Organic Chemistry, 2008, 28(3) (in Chinese)     

空间刚性杆——弹簧组合结构轨道、姿态耦合动力学分析

以空间太阳帆塔在轨运行中遇到的强耦合动力学问题为研究背景,建立了空间刚性杆-- 弹簧组合结构轨道与姿态耦合 问题的动力学模型,采用辛 (几何) 算法研究了其轨道与姿态耦合的动力学行为,研究结果可以从系统的能量保持情况间接得到验 证. 首先,基于变分原理,通过引入对偶变量将描述空间刚性杆-- 弹簧组合结构动力学行为的拉格朗日方程导入哈 密尔顿体系,建立简化模型的正则控制方程;随后,采用辛龙格库塔方法模拟分析了地球非球摄动对轨道、姿态的影响及系统能 量的数值偏差问题. 数值模拟结果显示:随着初始姿态角速度增大,轨道半径的扰动 增大,轨道与姿态之间的耦合效应加剧; 带谐摄动对空间刚性杆-- 弹簧组合结构模型的轨道、姿态产生的影响比田谐摄动要高出至少两个数量级;同时辛龙格库塔方法能更好 地快速模拟地球非球摄动影响下空间刚性杆-- 弹簧组合结构的动力学行为,并能够长时间保持系统的总能量,有望为 超大空间结构实时反馈控制提供实时动力学响应结果.      

Bifurcation analysis of an SIRS epidemic model with standard incidence rate and saturated treatment function

An epidemic model with standard incidence rate and saturated treatment function of infectious individuals is proposed to understand the effect of the capacity for treatment of infective individuals on the disease spread. The treatment function in this paper is a continuous and differential function which exhibits the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. It is proved that the existence and stability of the disease-free and endemic equilibria for the model are not only related to the basic reproduction number but also to the capacity for treatment of infective individuals. And a backward bifurcation is found when the capacity is not enough. By computing the first Lyapunov coefficient, we can determine the type of Hopf bifurcation, i.e., subcritical Hopf bifurcation or supercritical Hopf bifurcation. We also show that under some conditions the model undergoes Bogdanov-Takens bifurcation. Finally, numerical simulations are given to support some of the theoretical results.     

Visible‐Light Photoredox‐Catalyzed C−H Difluoroalkylation of Hydrazones through an Aminyl Radical/Polar Mechanism

An unprecedented visible‐light‐induced direct C?H bond difluoroalkylation of aldehyde‐derived hydrazones was developed. This reaction represents a new way to synthesize substituted hydrazones. The salient features of this reaction include difluorinated hydrazone synthesis rather than classical amine synthesis, extremely mild reaction conditions, high efficiency, wide substrate scope, ease in further transformations of the products, and one‐pot syntheses. Mechanistic analyses and theoretical calculations indicate that this reaction is enabled by a novel aminyl radical/polar crossover mechanism, with the aminyl radical being oxidized into the corresponding aminyl cation through a single electron transfer (SET) process.     

Dinuclear Gold-Catalyzed para-Selective C−H Arylation of Undirected Arenes by Noncovalent Interactions

The regioselectivity of C−H functionalization is commonly achieved by directing groups, electronic factors, or steric hindrance, which facilitate the identification of reaction sites. However, such strategies are less effective for reactants such as simple monofluoroarenes due to their relatively low reactivity and the modest steric demands of the fluorine atom. Herein, we present an undirected gold-catalyzed para-C−H arylation of a wide array of monofluoroarenes using air-stable aryl silanes and germanes at room temperature. A high para-regioselectivity (up to 98 : 2) can be realized by utilizing a dinuclear dppm(AuOTs)₂ (dppm=bis(diphenylphosphino)methane) as the catalyst and hexafluorobenzene as the solvent. This provides a general and practical protocol for the concise construction of structurally diverse para-arylated monofluoroarenes through C−H activation manner. It features excellent functional group tolerance and a broad substrate scope (>80 examples). Besides, this strategy is also robust for other simple monosubstituted arenes and heteroarenes. Our mechanistic studies and theoretical calculations suggest that para-C−H selectivity arises from highly electrophilic and structurally flexible dinuclear Ar−Au(III)−Au(I) species, coupled with noncovalent interaction induced by hexafluorobenzene.     

Unlocking Migratory Insertion in Gold Redox Catalysis

Exploration of elementary reactions in organometallic catalysis is an important method with which to discover new reactions. In this article, we report a gold(I)-catalyzed iodo-alkynylation of benzyne involving the merging of challenging migratory insertion and an oxidative addition process in gold catalytic cycle. A wide range of structurally diverse alkynyl iodides are good coupling partners in this iodo-alkynylation transformation. Both aliphatic and aromatic alkynyl iodides can react with benzynes smoothly to afford highly functionalized 1,2-disubstituted aromatics in moderate to good yields. Its good functional group compatibility and late-stage application of complex molecules demonstrate its synthetic robustness. Studies of the mechanism reveals the feasibility of oxidative addition and the DFT calculations demonstrate the possible migratory insertion of benzyne into Au^III-carbon bonds in the Au^I/Au^III redox catalytic cycle, representing an important step towards an elementary reaction in gold chemistry research.     

Hendecanuclear [Cu_6Gd_5] magnetic cooler with high molecular symmetry of D_(3h)

A new family of isostructural 3 d-4 f polymetallic complexes,formulated as [Cu_6Ln_5(μ_3OH)_9(C_4H_8O_2N)_6(C_5H_4ON)_6(H_2O)_9]·(ClO_4)_6·(H_2O)_(22)(Ln=Pr,1;Nd,2;Sm,3;Eu,4;Gd,5),was successfully isolated through the simple hydrolysis reaction of 2-aminoisobutyric acid,2-hydroxypyridine,Cu(CH_3COO)_2·H_2O,and Ln(ClO_4)_3·6 H_2O.Notably,the [Cu_6Ln_5] clusters with high molecular symmetry ofD_(3 h) are rare examples of2-aminoisobutyric acid-based 3 d-4 f clusters.The successful theoretical modeling of 5 yielded that the Gd-Gd exchange is of order 0.2 K,whereas the Gd-Cu exchange is an order of magnitude larger.Magnetization data collected for comp lex 5 yield a magnetic entropy change(-ΔSm) of 19.6 J kg ~1 K~11 at 3 K and 7 T,which may be attributed to the weak magnetic interactions between the component metal ions.     

Preparation of nano-sized Al2O3–2SiO2 powder by sol–gel plus azeotropic distillation method

Nano-sized amorphous Al₂O₃–2SiO₂ powder was prepared by a sol–gel method coupled with azeotropic distillation. The structure of the powder was investigated by DTS, BET, TEM, FT-IR, TG-DTA and XRD, showing that n-butanol azeotropic distillation could effectively remove water from the aluminosilicate gels and prevent the formation of hard agglomerates in the drying process. The average particle diameter of the powder was about 70 nm. The largest BET specific surface area of the powder was 669 m²/g. To examine the alkali-activation reactivity of the powder, alkali-activation tests were performed with the powder reacting with sodium silicate solution. The synthetic powder was found to be highly reactive.