Necessary and sufficient condition of the existence of global Hopf bifurcation for Hamiltonian systems

ForH C ² (,R) where 0 R ²ⁿ ,H (0)=0 and detH(0)0, the paper proves that there is a global Hopf bifurcation fromx=0 for Hamiltonian systemx=JH(x) iffJH(0)possesses purely imaginary eigenvalues. The work improves the corresponding result of J.C.Alexander and J. Yorke (Amer. J. Math., 100 (1978), 263–292).     

The use of a premium-payment scheme in a supply chain involving capacity acquisition

We study a practice whereby a downstream firm makes to his supplier a premium-payment for a certain quantity of products. We show that the adoption of this practice can induce the supplier to build bigger capacity. The higher capacity level enables the supplier to satisfy a larger portion of demands from the downstream firm, and this leads to higher payoffs for both parties in the supply chain. With the assistance of an under-capacity penalty imposed on the supplier, this premium-payment scheme can help lure the parties into taking the channel-optimal actions. Our numerical examples help reveal various features of the scheme.     

Riemannian geometry of strong-laser plasma

The optical metric for a strong-laser plasma is derived. The affine connection and curvature related to the optical metric are given and their spatial distributions are studied numerically.     

Synthesis of terpinyl acetate using octadecylamine ethoxylate ionic liquids as catalysts

Terpinyl acetate, an important natural flavor, can be synthesized by esterification of α-pinene with acetic acid under acidic conditions. In this work, seven acidic ionic liquids were first synthesized, using octadecylamine ethoxylates (AC 1810, AC 1815, AC 1820, and AC 1830) as the cations, and characterized by FT-IR, ¹H NMR, and ¹³C NMR spectroscopy. The ionic liquids were then used as catalysts in the synthesis of terpinyl acetate. The effect of preparation conditions on catalyst performance was examined. It was found that the acidic ionic liquid 1-(3-sulfonic acid)propyl-3-poly(ethylene glycol) octadecylamine polyoxyethylene ether tetrafluoroborate ([PAC1815]⁺[BF₄]^?) was an excellent catalyst for synthesis of terpinyl acetate. The effects of the conditions used for preparation of terpinyl acetate were examined in detail, and the optimum preparation conditions were obtained. Under the optimum conditions, the yield of terpinyl acetate reached 35.70 %. When the catalyst was reused for the 5th time, the yield of terpinyl acetate was still 32.00 %. The results showed that effective separation and recycling of catalyst could contribute to developing a new strategy for synthesis of terpinyl acetate.     

新型BrΦnsted-Lewis酸性离子液体的合成及其在松香二聚反应中的应用(英文)

合成、表征了新型 Brφnsted-Lewis 酸性离子液体 1-（3-磺酸）-丙基-3-甲基咪唑氯锌酸盐 （[HO3S-（CH2）3-mim]Cl-ZnCl2）, 并将其用于催化松香二聚反应. 结果表明, [HO3S-（CH2）3-mim]Cl-ZnCl2 （ZnCl2摩尔分数x 〉 0.5）为 Brφnsted 和 Lewis 双酸性, 且以 [HO3S-（CH2）3-mim]Cl-ZnCl2 （x = 0.64） 的催化性能较佳. 在松香 5.0 g, 甲苯15 g, 离子液体质量分数 5%, 反应温度 110℃ 和反应时间 4 h 的较佳实验条件下, 所得产物聚合松香的软化点为 118 ℃. 此外, 该催化剂的使用有利于产物的分离且分离的离子液体催化剂具有良好的重复使用性能.     

A Direct and Rapid Route to Synthesize Pd/Si‐MCM‐41 at Room Temperature

The pure silica mesoporous molecular sieve MCM‐41 was synthesized under hydrothermal conditions. Pd/Si‐MCM‐41 was prepared by the incipient wetness impregnation of pure silica MCM‐41 with mixed solution of PdCl₂, ethanol and CH₂Cl₂. The samples were characterized by x‐ray diffraction (XRD), transmission electron microscopy (TEM), and nitrogen adsorption–desorption isotherms at 77 K. The XRD and TEM results reveal that Pd is actually anchored inside the pores of Si‐MCM‐41 and the Si‐MCM‐41 structure is clearly maintained after impregnation.     

磁性碱木素胺稳定的Ru纳米粒子催化α-蒎烯加氢反应

通过Mannich反应在碱木素结构中引入胺源,再结合共沉淀法制备了包裹Fe₃O₄磁核的稳定金属粒子的碱木素胺载体,并进一步构建了催化可再生资源α-蒎烯加氢反应的Ru纳米粒子催化剂.通过元素分析、粉末X射线衍射、傅里叶变换红外光谱、电感耦合等离子体原子发射光谱、透射电子显微镜、热重分析和X射线光电子能谱等方法对该催化剂进行表征.结果表明,碱木素中的苯环和含氧基团均对金属粒子有稳定作用,但胺源的引入可更加有效地稳定金属粒子.经过对催化剂制备工艺、木质素类型、胺源类型和胺源含量的筛选,得到活性最优的催化剂Fe₃O₄@0.8ALN₁-Ru, Ru负载量为1.92 mmol/g, Ru粒子粒径为(2.1±0.5)nm.该催化剂在n(α-蒎烯)/n(Ru)=65.8, 1 MPa H₂条件下70℃催化1 mLα-蒎烯加氢反应2 h,可获得99.64%的α-蒎烯转化率和96.52%的顺式蒎烷选择性,并表现出良好的重复使用稳定性.     

Robust adaptive sliding mode control of MEMS gyroscope using T–S fuzzy model

In this paper, a multi-input multi-output Takagi–Sugeno (T–S) fuzzy model is proposed to represent the nonlinear model of micro-electro mechanical systems (MEMS) gyroscope and improve the tracking and compensation performance. A robust adaptive sliding mode control with on-line identification for the upper bounds of external disturbances and an adaptive estimator for the model uncertainty parameters are proposed in the Lyapunov framework. The adaptive algorithm of model uncertainty parameters could compensate the error between the optimal T–S model and the designed T–S model, and decrease the chattering of the sliding surface. Based on Lyapunov methods, these adaptive laws can guarantee that the system is asymptotically stable. For the purpose of comparison, the designed controller is also implemented on the nonlinear model of MEMS gyroscope. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme on the T–S model and the nonlinear model.     

偏振光实验方法的改进

用半导体激光电源代替常规的He—Ne激光光源进行偏振光实验,可使偏振光实验精度提高,操作更为简便。