THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

1IntroductionThispaperisconcernedwithpositivesolutionOfthesemilinearheatequationswithlocalizedreactionssubjecttoeitherinitialconditions(Cauchyproblem)ortheinitialandboundary-value(DirichletorNeumanntype)conditionswherenisaboundeddomaininRe,icEO.Equations(1.1)canbethoughtofasamodeltodescribesomephysicalphenomena(heatpropagation,chemicalreaction)inwhichthenonlinearreactionsinadynndcalsystemtakesplaceonlyatasinglesite.InthesequelforconvenienceweshallsamplycalltheCauchy,initial-Direchlet,orini…     

凸集的广义Reuleaux三角形

常宽凸集的面积最小者为Reulaux三角形，而非常宽凸集的面积最小者为何呢？它就是本文将给出的广义Reuleaux三角形△R。     

EXPONENTIAL STABILITY AND PERIODIC SOLUTION OF HYBRID BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DISCRETE DELAYS

In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1,2, …, n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.     

Assembly and Photophysics of Ternary Luminescent Lanthanide Molecular Complex Systems

In this paper, according to the molecular fragment principle, a series of eight ternary luminescent lanthanide complex systems were assembled, and whose compositions were determined with elemental analysis and infrared spectrum: Ln(MA)₃(L)·H₂O, where Ln = Sm, Eu, Tb, Dy; HMA = α‐methylacrylic acid; L = 1,10‐phenanthroline (phen), 2,2′‐bipyridine (bipy). The photophysical properties of these functional molecular systems were studied with ultraviolet‐visible absorption spectrum, and fluorescence excitation and emission spectrum. It was found that the heterocylic compounds (phen and bipy) act as the main energy donor and luminescence sensitizer for their suitable energy match and effective energy transfer to the emission energy level of Ln³⁺ ions. MMA ligand was only used as the terminal structural ligand to influence the luminescence. Especially terbium complex systems show the strongest luminescence for the optimum energy match and transfer between phen (bipy) and Tb³⁺ ion.     

Clustering study in Eu(DBM)3Phen-doped polymer optical fibers by optical properties and near-field scanning microscopy

The clusters of Eu3+ ion in Eu(DBM)3Phen-doped polymethyl methacrylate (PMMA) have been studied by three means. The relative fluorescence intensity ratio of the 5D0 → 7F2 to 5D0 → 7F1 transitions with different concentrations of Eu3+ in Eu(DBM)3Phen-doped PMMA and metastable-state (5D0) lifetime dependence on Eu3+ concentration are analyzed. The analysis indicates that there are no clustering effects in Eu3+ ions of Eu(DBM)3Phen-doped PMMA when the Eu3+ doping concentration is up to 1.0 wt.-%. At the same time, the clustering effect has not been observed by the scanning near-field optical microscopy (SNOM) in Eu(DBM)3Phen-doped PMMA with 1.0 wt.-% of Eu3+ ions. The analysis reveals that a high concentration of Eu3+ can be incorporated into polymer optical fiber (POF) without clustering effect.OCIS codes: 180.5810, 300.6280, 250.5460, 160.5690.     

一种基于代价函数和模糊熵的图像分割方法

提出了一种基于代价函数和模糊熵的图像分割方法.该方法先用代价函数最小化法对退化的图像作预处理,之后,利用模糊熵作进一步的处理.实验结果表明:新方法和一般的阈值分割方法相比,不但分割图像的错分率较小,而且图像的视觉效果也有较大的改善.     

L-fuzzifying topology

A new topology in terms of order on fuzzy sets, revealing better the relationship between smooth topology and Chang’s fuzzy topology, is presented in the paper. Some basic properties are discussed.     

最小费用k度限制树对策

本在Glover—Klingman算法及最小费用支撑树对策的基础上，讨论了最小费用k度限制树对策问题．利用威胁、旁支付理论制订了两种规则，并利用优超、策略等价理论分别给出了在这两种规则下最小费用k度限制树对策核心中的解，从而证明了在这两种规则下其核心非空．     

CO_2 Reforming of CH_4 over Ni/CeO_2-ZrO_2-Al_2O_3 Prepared by Hydrothermal Synthesis Method

The Ni/CeO2-ZrO2-Al2O3 catalyst with different Al2O3 and NiO contents were prepared by hydrothermal synthesis method. The catalytic performance for CO2 reforming of CH4 reaction, the interaction among components and the relation between Ni content and catalyst surface basicity were investigated. Results show that the interaction between NiO and Al2O3 is stronger than that between NiO and CeO2-ZrO2.The addition of Al2O3 can prevent the formation of large metallic Ni ensembles, increase the dispersion of Ni, and improve catalytic activity, but excess Al2O3 causes the catalyst to deactivate easily. The interaction between NiO and CeO2 results in more facile reduction of surface CeO2. The existence of a small amount of metallic Ni can increase the number of basic sites. As metallic Ni may preferentially reside on the strong basic sites, increasing Ni content can weaken the catalyst basicity.