Finite determinacy and polynomial normal forms for diffeomorphisms near a strongly 1-resonant fixed point

In this paper we study polynomial normal forms and smooth (C^∞$C^{\infty }$) classification of one kind of diffeomorphisms which have infinite many resonant relations but are finitely determined. We derive a complete list of normal forms of all such germs with arbitrary degeneracy of their nonlinear parts.     

双循环半群上的同余关系

从双循环半群的同余关系出发,讨论了幂等元所在的同余类,证明了双循环半群上的一类同余ρd(d∈N)与其逆子半群之间的相互唯一确定关系,并对这种同余做成的集合进行了刻画,证明了这种同余做成的格与自然数集在某种偏序下做成的格同构,得到了一些有意义的结果.     

两类图的符号控制数

图G的符号控制数γs(G)有着许多重要的应用背景,因而确定其精确值有重要意义.Cm表示m个顶点的圈,n-Cm和n·Cm分别表示恰有一条公共边或一个公共顶点的n个Cm的拷贝.给出了n-Cm和n·Cm的符号控制数.     

Dynamics of non-autonomous parabolic problems with subcritical and critical nonlinearities

This is a subsequent work of our previous one in [25]. Let the nonlinear terms of non-autonomous parabolic problems with singular initial data satisfy subcritical and critical growth conditions. We first establish the existence of uniform attractors in W^1,r(Ω)$W^{1,r}(\Omega )$, 1<r<N$1<r<N$, for the family of processes corresponding to the equations with external forces being translation bounded but not translation compact. Then, we prove the existence of pullback attractors in L^r(Ω)$L^r(\Omega )$ and W^1,r(Ω)$W^{1,r}(\Omega )$, respectively, for the process corresponding to the equation with the weaker assumption on the external force than previous one. Finally, we investigate the robust of attractors and establish the existence of pullback exponential attractors for the process acting in L^r(Ω)$L^r(\Omega )$ and W^1,r(Ω)$W^{1,r}(\Omega )$, respectively.     

New sets of frequency-hopping sequences with optimal Hamming correlation

Frequency-hopping spread spectrum and direct-sequence spread spectrum are two main spread coding technologies in communication systems. Frequency-hopping sequences are needed in FH-CDMA systems. In this paper, a construction of optimal sets of frequency-hopping sequences using cyclotomy and the Chinese remainder theorem is introduced. It generalizes some earlier constructions, and produces new optimal sets of frequency-hopping sequences.     

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015     

β-Cyclodextrin carbon-based nanoparticles with a core-shell-shell structure for efficient adsorption of crystal violet and bisphenol A

Textile wastewater contains highly toxic,nondegradable,carcinogenic organic pollutants,causing severe damage to the ecological environment.In this work,β-cyclod...     

Growth and scintillation properties of the Na2W2O7 crystal

The growth and scintillation properties of the Na₂W₂O₇ crystal are reported. The solid reaction between Na₂CO₃ and WO₃ is used to synthesise the Na₂W₂O₇ material. The Na₂W₂O₇ single crystal has been grown by the Bridgman method. And the Na₂W₂O₇ single crystal with sizes 14×7×6 mm³ has been achieved. The transmission spectra, the Ultraviolet fluorescence spectra and the X-ray excited luminescence spectra of the Na₂W₂O₇ crystal are measured. The measurement results show that the Na₂W₂O₇ crystal is a promising intrinsic scintillator.     

Synthesis,characterization and anticancer activity of new palladacycles derived from chiral α‐diimines

Optically pure α‐diimines quantitatively obtained in solvent‐free conditions starting from 2,3‐butanedione and (S)‐(?)‐1‐phenylethylamine and (S)‐(?)‐1‐(4‐methylphenyl)ethylamine, respectively, yielded the new chiral mono‐Pd complexes 2a–b, which have been partly characterized by IR, ¹H‐ and ¹³C‐NMR spectroscopies along with MS‐FAB⁺ spectrometry. The crystal and molecular structure for palladacycle 2a has been fully confirmed by single‐crystal X‐ray studies. Studies in vitro of 2a–b have displayed growth inhibition against different classes of cancer: leukemia (K‐562 CML), colon cancer (HCT‐15), breast cancer (MCF‐7), central nervous system (U‐251 Glio) and prostate cancer (PC‐3) cell lines. Copyright © 2009 John Wiley & Sons, Ltd.