Synthesis of novel copper compounds containing isonicotinic acid and/or 2,6-pyridinedicarboxylic acid: third-order nonlinear optical properties

Two novel compounds, [Cu₂(pydc)₂(inta)₂(H₂O)₂]·3H₂O 1 (pydc?=?2,6-pyridinedicarboxylic acid, inta?= isonicotinic acid) and [Cu(pydc)₂][Cu(H₂O)₅]·2H₂O 2, have been synthesized in aqueous solution and characterized by single-crystal X-ray diffraction, elemental analyses and IR spectra. Compound 1 exhibits reverse saturable absorption and self-defocusing. X-ray structural analysis reveals that Compounds 1 and 2 both possess π–π stacking and hydrogen-bonding interactions forming three-dimensional (3D) networks. Crystal data for 1: a?=?7.2345(14), b?=?12.219(2), c?=?17.069(3)?Å, α?=?90.44(3), β?=?91.82(3), γ?=?93.56(3)°, Z?=?1, R1?=?0.0435, wR2?=?0.1216. Crystal data for 2: a?=?8.3708(17), b?=?27.386(6), c?=?9.6170(19)?Å, α?=?90.00, β?=?98.14(3), γ?=?90.00°, Z?=?3, R1?=?0.0742, wR2?=?0.2160.     

Specific Features of Strain Dependences of Loss Modulus in Highly Stretched Elastomers

The loss modulus E″ in elastomer strips stretched by a factor of λ is studied theoretically. A small oscillating deformation is applied to these strips in the transition frequency zone between the glassy and rubbery states. The range of λ under study ranges up to ultimate extensions close to fracture. A model of E″/λ dependence in the transition frequency zone is suggested that considers the possible distortion in the local chain structure in the ultimate extension range. It is found that E″ in the range of moderate and high λ increases owing to the finite extensibility of the chains. However, upon further extension up to ultimate values, E″ decreases and a maximum appears on the E″/λ curves. These features are also confirmed experimentally.

     

Stochastic exponential synchronization of jumping chaotic neural networks with mixed delays

This paper deals with the exponential synchronization problem for a class of stochastic jumping chaotic neural networks with mixed delays and sector bounded nonlinearities. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time delays. By applying the Finsler’s Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent feedback controllers with sector nonlinearities are developed to achieve the synchronization in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve no free weighting matrices, the computational burden is largely reduced. One numerical example is provided to demonstrate the effectiveness of the theoretical results.     

Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion

Separate studies have been published on the stability of fuzzy cellular neural networks with time delay in the leakage term and synchronization issue of coupled chaotic neural networks with stochastic perturbation and reaction-diffusion effects. However, there have not been studies that integrate the two fields. Motivated by the achievements from both fields, this paper considers the exponential synchronization problem of coupled chaotic fuzzy cellular neural networks with stochastic noise perturbation, time delay in the leakage term and reaction-diffusion effects using linear feedback control. Lyapunov stability theory combining with stochastic analysis approaches are employed to derive sufficient criteria ensuring the coupled chaotic fuzzy neural networks to be exponentially synchronized. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.     

Continuous and discontinuous opinion dynamics with bounded confidence

In this paper, we study a continuous-time version of the Hegselmann-Krause opinion dynamics, which models bounded confidence by a discontinuous interaction. Intending solutions in the sense of Krasovskii, we provide results of existence, completeness and convergence to clusters of agents sharing a common opinion. For a deeper understanding of the role of the mentioned discontinuity, we study a class of continuous approximating systems, and their convergence to the original one. Our results indicate that their qualitative behavior is similar, and we argue that discontinuity is not an essential feature in bounded confidence opinion dynamics.     

Global analysis of an SIS model with an infective vector on complex networks

In this paper, a modified SIS model with an infective vector on complex networks is proposed and analyzed, which incorporates some infectious diseases that are not only transmitted by a vector, but also spread by direct contacts between human beings. We treat direct human contacts as a social network and assume spatially homogeneous mixing between vector and human populations. By mathematical analysis, we obtain the basic reproduction number R₀ and study the effects of various immunization schemes. For the network model, we prove that if R₀<1, the disease-free equilibrium is globally asymptotically stable, otherwise there exists an unique endemic equilibrium such that it is globally attractive. Our theoretical results are confirmed by numerical simulations and suggest a promising way for the control of infectious diseases.     

Ultimate boundedness and an attractor for stochastic Hopfield neural networks with time-varying delays

This paper investigates ultimate boundedness and a weak attractor for stochastic Hopfield neural networks (HNN) with time-varying delays. By employing the Lyapunov method and the matrix technique, some novel results and criteria on ultimate boundedness and an attractor for stochastic HNN with time-varying delays are derived. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.     

Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

<正>The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper.Based on Lyapunov stability theory and Barbalat’s lemma,generalized matrix projective lag synchronization criteria are derived by using the adaptive control method.Furthermore,each network can be undirected or directed,connected or disconnected,and nodes in either network may have identical or different dynamics.The proposed strategy is applicable to almost all kinds of complex networks.In addition,numerical simulation results are presented to illustrate the effectiveness of this method,showing that the synchronization speed is sensitively influenced by the adaptive law strength,the network size,and the network topological structure.     

Time‐resolved reconstruction of defect creation sequences in diode lasers

The propagation of defect networks in failed 980 nm emitting high‐power diode lasers is analyzed. This is accomplished ex post facto by electron‐beam based techniques applied without device preparation and in situ by thermographic microscopy with 1 µs time resolution. Moreover, an iterative model is established, which allows for describing both the shape of the observed defect networks as well as the kinetics of their spread. This concerted approach allows the clear assignment of starting points of extended defect systems as well as analysis of their evolution kinetics. Eventually this knowledge may help in making devices more resistive against defect creation and extension.     

Markov chain-based analysis of a modified Cooper-Frieze model

From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the exis- tence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.