Anion-dependent formation of helicates versus mesocates of triple-stranded M2L3 (M = Fe2+, Cu2+) complexes

A series of dinuclear triple-stranded complexes, [Fe(2)L(3)?X]X(6) [X = BF(4)(-) (1), ClO(4)(-) (2)], [Fe(2)L(3)?SO(4)](2)(SO(4))(5) (3), [Fe(2)L(3)?Br](BPh(4))(6) (4), Fe(2)L(3)(NO(3))Br(6) (5), and [Cu(2)L(3)?NO(3)](NO(3))(6) (6), which incorporate a central cavity to encapsulate different anions, have been synthesized via the self-assembly of iron(II) or copper(II) salts with the N,N'-bis[5-(2,2'-bipyridyl)methyl]imidazolium bromide (LBr) ligand. X-ray crystallographic studies (for 1-4 and 6) and elemental analyses confirmed the cagelike triple-stranded structure. The anionic guest is bound in the cage and shows remarkable influence on the outcome of the self-assembly process with regard to the configuration at the metal centers. The mesocates (with different configurations at the two metal centers) have formed in the presence of large tetrahedral anions, while helicates (with the same configuration at both metal centers) were obtained when using the relatively smaller spherical or trigonal-planar anions Br(-) or NO(3)(-).     

Tetraureas versus triureas in sulfate binding

By mimicking the scaffolds of oligopyridine-based ligands, triurea and tetraurea receptors have been developed for sulfate binding. The triureas (L(1), L(2)) show stronger binding of sulfate than tetraureas (L(3), L(4)) in DMSO because of their better conformational complementarity with sulfate, while the tetraureas display better "water tolerance" benefiting from the chelate effect and hydrophobic effect.     

Triple-zero bifurcation in van der Pol’s oscillator with delayed feedback

In this paper, we study a classical van der Pol’s equation with delayed feedback. Triple-zero bifurcation is investigated by using center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the triple-zero bifurcation and show that the model can exhibit transcritical bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and zero-Hopf bifurcation. Some numerical simulations are given to support the analytic results.     

Nonlinear analysis of a novel three-scroll chaotic system

This paper reports the nonlinear dynamics of a novel three-scroll chaotic system. The local stability of hyperbolic equilibrium and non-hyperbolic equilibrium are investigated by using center manifold theorem. Pitchfork bifurcation, degenerate pitchfork bifurcation and Hopf bifurcation are analyzed when the parameters are varied in the space of parameter. For a suitable choice of the parameters, the existence of singularly degenerate heteroclinic cycles and Hopf bifurcation without parameters are also investigated. Some numerical simulations are given to support the analytic results.     

A Colorimetric and Ratiometric Fluorescent Chemosensor for Fluoride Based on Proton Transfer

N-Phenyl-N’-(3-quinolinyl)urea (1) has been developed as a highly selective colorimetric and ratiometric fluorescent chemosensor for fluoride ion based on a proton transfer mechanism. Evidences for the mechanism were provided by UV-vis and fluorescence titration and especially ¹H and ¹⁹F NMR experiments. The sensor gave the largest ratiometric fluorescent response reported so far (R_max/R_min = 2620) to fluoride. Taking H⁺ as the “recovering reagent”, the sensor can be reversibly “used” and “recovered” for several cycles with only a slight decay of the response ability.     

Redox-driven sulfate ion transfer between two tripodal tris(urea) receptors

Two anion receptors with the same tripodal scaffold but different signaling groups are employed to control intermolecular anion transfer via an electrochemical stimulus, which is detected by the change of the fluorescence intensity before and after electrochemical oxidation of the ferrocenyl units.     

Impulsive control and synchronization of nonlinear system with impulse time window

In this paper, the issue on impulsive control and synchronization of nonlinear system with impulse time window are investigated. The considered impulsive effects can be stochastically occurred at a determined time window. Hence, the impulses here can be more general and more applicable than the fixed impulses. Some novel and easy-to-check criteria with impulse time window are obtained to guarantee the impulsive control and synchronization global asymptotical stable. Especially, on the basis of the our analysis, we only choose an efficient impulse time window instead of choosing fixed-impulse sequences. Finally, the simulation results further demonstrate the effectiveness of our theoretical results.     

A phenomenological memristor model for short-term/long-term memory

Memristor is considered to be a natural electrical synapse because of its distinct memory property and nanoscale. In recent years, more and more similar behaviors are observed between memristors and biological synapse, e.g., short-term memory (STM) and long-term memory (LTM). The traditional mathematical models are unable to capture the new emerging behaviors. In this article, an updated phenomenological model based on the model of the Hewlett–Packard (HP) Labs has been proposed to capture such new behaviors. The new dynamical memristor model with an improved ion diffusion term can emulate the synapse behavior with forgetting effect, and exhibit the transformation between the STM and the LTM. Further, this model can be used in building new type of neural networks with forgetting ability like biological systems, and it is verified by our experiment with Hopfield neural network.     

Estimating and enlarging the region of attraction of multi-equilibrium points system by state-dependent edge impulses

Nonlinear Dynamics - When an isolated equilibrium of a nonlinear system is locally attractive, it might be difficult to estimate and then enlarge its Region of Attraction (RA). To solve this...     

竞赛图弧色数的上界

有向图的弧色数指的是对有向图的弧进行着色, 使得所有连贯弧着不同颜色所需要的最少颜色数. 在介绍了一些相关结果的基础上, 通过确定顶点数较少的竞赛图弧色数的最大值, 说明了已有弧色数的上界虽然对一般有向图是紧的, 对竞赛图却是可以改进的.