A Preliminary Study of Diastereoselectivity in the PdII‐Catalyzed C(sp3)‐H Alkoxylation of Cyclic Systems

Primary mechanism of a Pd^II‐catalyzed 8‐aminoquinoline‐directed C?H alkoxylation was investigated. It was understood that the Pd^II‐catalyzed C(sp³)?O bond formation proceeded through a concerted reductive elimination from the Pd^IV intermediate in the cyclic system. Deuteration experiments and related computational studies elucidate that intrinsic conformation determined the diastereoselectivity of the Pd^II‐catalyzed C?H alkoxylation of cyclic carboxylic acids.     

变频空调制冷系统流量调节性能分析和实验研究

通过实验分析不同膨胀阀开度和压缩机频率下系统性能。过热度在‘0’点及前后情况下,制冷系统性能及回油状况随膨胀阀开度调节,会出现较大变化。且在过热度为‘0’时系统制冷量和能效比最高。同时对不同频率下系统性能参数变化规律尤其是换热器效率影响进行分析。给出膨胀阀开度和压缩机变转速联合调节在系统性能最优状态下调节策略。     

Generation of grid multi-scroll chaotic attractors via switching piecewise linear controller

In this Letter, a novel method is developed for generating grid multi-scroll chaotic attractors using switching piecewise linear controller. First, a third-order linear system is designed to ensure that its unique equilibrium point belongs to a saddle-focus type with index 2 and the corresponding eigenvalues satisfy Shilnikov conditions. Then, by three different types of switching control strategies, the equilibrium point can be extended along both xy plane and z axis direction, so as to generate grid multi-scroll chaotic attractors. The dynamical behaviors are further analyzed. Moreover, an improved module-based circuit is designed for realizing 5×3 and 4×4 grid scroll chaotic attractors, and the experimental results are also obtained, which is consistent with the numerical simulations.     

Relaxation oscillations and canard explosion in a predator–prey system of Holling and Leslie types

We give a geometric analysis of relaxation oscillations and canard cycles in a singularly perturbed predator–prey system of Holling and Leslie types. We discuss how the canard cycles are found near the Hopf bifurcation points. The transition from small Hopf-type cycles to large relaxation cycles is also discussed. Moreover, we outline one possibility for the global dynamics. Numerical simulations are also carried out to verify the theoretical results.     

New Penta(tetrathiafulvalenyl)[60]fullerenes for Supramolecular Materials

New penta(organo)fullerenes donor–acceptor systems bearing five tetrathiafulvalene recognition units have been synthesized to promote self‐assemblies similar in appearance to shuttlecocks nested into each other thanks to the conical host cavity created around the fullerene together with the π–π and electronic interactions.     

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.     

The multicomponent （2＋1）-dimensional Glachette-Johnson （GJ） equation hierarchy and its super-integrable coupling system

This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.     

A field method for integrating the equations of motion of mechanico--electrical coupling dynamical systems

A field method for integrating the equations of motion for mechanico-electrical coupling dynamical systems is studied. Two examples in mechanico-electrical engineering are given to illustrate this method.     

Perturbation to Mei symmetry and Mei adiabatic invariants for mechanical systems in phase space

For a perturbed mechanical system in phase space, considering d/dt in the structure equation and process of proof including infinitesimal parameter ε obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, an example is given to illustrate the application of the results.     

Equilibrium points and bifurcation control of a chaotic system

Based on the Routh-Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.