Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

Connectivity keeping stars or double-stars in 2-connected graphs

In Mader (2010), Mader conjectured that for every positive integer $k$ and every finite tree $T$ with order $m$, every $k$-connected, finite graph $G$ with $\delta \left(G\right)\ge ?\frac{3}{2}k?+m?1$ contains a subtree $T^{\prime }$ isomorphic to $T$ such that $G?V\left(T^{\prime }\right)$ is $k$-connected. In the same paper, Mader proved that the conjecture is true when $T$ is a path. Diwan and Tholiya (2009) verified the conjecture when $k=1$. In this paper, we will prove that Mader’s conjecture is true when $T$ is a star or double-star and $k=2$.     

Crystallization behavior and electroactive properties of PVDF,P(VDF-TrFE) and their blend films

PVDF, poly(vinylidene fluoride), as a semi-crystalline polymer, has interesting electroactive properties but usual melt and solution processing techniques result in its thermodynamically favored non-polar α-phase. By comparison, poly(vinylidene fluoride-trifluoroethylene) P(VDF-TrFE), PT for short, directly crystallizes in the polar β-phase under the same conditions as PVDF. In this study, blend thin films comprising PVDF and P(VDF-TrFE) were prepared by solvent casting method. The difference in the crystallization behavior is comprehensively investigated between the polymers: PVDF, P(VDF-TrFE), and the resulting blend films. It is found that replacement of the fluoride atom in TrFE monomer induces a strong steric hindrance that may alter the crystallization process to become more favorable for nucleation of the PVDF β-phase. To figure out the effect of TrFE content on the crystallization behavior and electroactive properties, films with different blend ratios of PVDF and P(VDF-TrFE) were prepared. We found that the PVDF films exhibit higher crystallization activation energy (ΔE) as PT content increases. The atomic force microscopy (AFM) in the piezoresponse force microscopy (PFM) mode illustrated that P5T5 films with equal contents of PVDF and P(VDF-TrFE) induced the highest d₃₃ values.     

Threshold dynamics of a nonlinear multi‐group epidemic model with two infinite distributed delays

The global stability of equilibria is investigated for a nonlinear multi‐group epidemic model with latency and relapses described by two distributed delays. The results show that the global dynamics are completely determined by the basic reproduction number under certain reasonable conditions on the nonlinear incidence rate. Moreover, compared with the results in Michael Y. Li and Zhisheng Shuai, Journal Differential Equations 248 (2010) 1–20, it is found that the two distributed delays have no impact on the global behaviour of the model. Our study improves and extends some known results in recent literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterizations of the BMO and Lipschitz Spaces via Commutators on Weak Lebesgue and Morrey Spaces

Acta Mathematicae Applicatae Sinica, English Series - We prove that the weak Morrey space WM is contained in the Morrey space $$M_{{q_1}}^p$$ for 1 ≤ q1 < q ≤ p < ∞....     

Generalized synchronization of discrete systems

Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.