Generalized indices of operators inB(H)

A generalized dimension is further developed. Here subtraction and addition of two generalized dimensions are defined, so that the operations: ∞ ± n = ∞, ∞ + ∞ = ∞, which used to play an inflexible role, are refined and moreover, ∞ - ∞, which used to be meaningless, is done in sense. Then generalized index for semi-Fred-holm operators is developed to wholeB(H), i.e. all of bounded linear operators in Hilbert spaceH. Theorem 2.2 is proved with an example, which is in contradiction to a known proposition for semi-Fredholm operators in form, practically a refined result of the known proposition. Then, it is proved thatB(H) is the union of countably many disjoint arewise connected sets over all the generalized dimensions ofB(H). Project supported by the National Natural Science Foundation of China     

Electrically forced microthreading of highly viscous dielectric liquids

The behaviour of three high viscosity (4875, 12 125 and 58 560 mPa s), dielectric liquids was investigated at flow rates of 10⁻¹⁰, 10⁻¹² and 10⁻¹⁴ m³ s⁻¹ and the applied voltage range 6–15 kV. In these experiments, due to the low electrical conductivity of the liquids (10⁻¹³ S m⁻¹) and therefore the ensuing high electrical relaxation time, classical electrohydrodynamic atomization conditions are not satisfied. Only dripping and unstable jetting were observed at 4875 mPa s. A transition from no jetting to stable microthreading was observed for the 12 125 and 58 560 mPa s samples. The relics accompanying the transition were found to change from discrete droplets to a continuous filament. Stable microthreading, which generates uniform filaments, was obtained for the 12 125 mPa s sample at flow rates 10⁻¹⁰ and 10⁻¹² m³ s⁻¹ and in the case of the 58 560 mPa s sample at all the flow rates investigated. The high viscosity assisted stable microthreading with the filament diameter decreasing with increasing applied voltage and more dramatically decreasing with reducing flow rate.     

用13CNMR研究聚甲基丙烯酸锡酯的立构序列分布

本文测定了自由基型溶液聚合的聚甲基丙烯酸三甲基锡酯(PTMTM),聚甲基丙烯酸三乙基锡酯(PTETM)和聚甲基丙烯酸三丁基锡酯(PTBTM)的¹³C-NMR谱,对其C-2谱扩展分峰,计算立构序列,从定量数据表明,聚合物样品的空间立构富于或稍富于间规立构,随取代基的体积增大而趋于无规分布,作者认为受空间位阻效应和分子内或分子间形成配位键的影响。     

Solutions of dynamic problems for incompressible and slightly compressible helically orthotropic non-uniform thick-walled cylinders

Exact analytic solutions are obtained of the one-dimensional dynamic problem for an incompressible elastic radially non-uniform helically orthotropic thick-walled cylinder under plane-strain conditions, loaded with a time-dependent pressure from inside and/or outside. The necessary and sufficient conditions for solutions to exist and to be unique are established. The convergence of the wave solutions for slightly compressible cylinders to the analytic relations obtained for incompressible cylinders is investigated.     

Topological Properties of Urban Public Traffic Networks in Chinese Top-Ten Biggest Cities

We investigate the topological characteristics of complex networks as exemplified by the urban public traffic network （UPTN） in Chinese top-ten biggest cities. It is found that the UPTNs have small world behaviour, by the examination of their topological parameters. The quantitative analysis of the transport efficiency of the UPTNs reveals their higher local efficiency El and lower global efficiency Eg, which coincide well with the status quo of those Chinese cities still at their developing stage. Furthermore, the topological properties of efficiency in the UPTNs are also examined, and the findings indicate that, on the one hand, the UPTNs show robustness to random attacks and frangibility to malicious attacks on a global scale; on the other hand, the interrelation between UPTN efficiency and network motifs deserves our attention. The motifs which interrelate the UPTN efficiency are always triangular-formed patterns, e.g. motifs ID 238, ID 174 and ID 102, etc.     

Electroluminescence of a Multi-Layered Organic Light-Emitting Diode Utilizing Trans-4-[p-[N-methyl-N-(hydroxymethyl)amino]styryl]-N-Methylphridinium Tetraphenylborate as the Active Layer

Employing an organic dye salt of trans-4-[p-[N-methyl-N-(hydroxymethyl)amino]styryl]-N-methylphridinium tetra\-phenylborate (ASPT) as the active layer, 8-hydrocyquinoline aluminium (Alq₃) as the electron transporting layer and N,N’-diphenyl-N,N’-bis(3-methylphenyl)-[1,1’-biphenyl]-4,4’-diamine (TPD) as the hole transporting layer, respectively, we fabricate a multi-layered organic light-emitting diode and observe the colour tunable electroluminescence (EL). The dependence of the EL spectra on the applied voltage is investigated in detail, and the recombination mechanism is discussed by considering the variation of the hole-electron recombination region.     

Validation of an optimization procedure to improve low frequency characteristics of rooms

A set of experiments was carried out to validate an optimization procedure based on finite element method (FEM). The idea of the procedure, fully presented in previous edition of this journal [Zhu X, Zhu Z, Cheng J. Using optimized surface modifications to improve low frequency response in a room. Appl Acoust 2004;65:841-60], is to produce an optimal geometry modification on the wall for improving low frequency sound uniformity in small rooms. Four experimental models were set up with a scale of 1:5. One was modified according to the optimized result and the others were treated with no optimization consideration. Measured frequency responses of four rooms were compared with numerical results calculated by FEM models. The transient responses in these rooms were also measured and analyzed. The agreements between calculation and measurement are satisfactory though the discrepancies due to the uncertainty of acoustic behavior of the room boundaries remain. The optimization procedure has been supported by the results that the optimized room produces the flattest frequency response and also the most smooth energy decay within the frequency range studied. The reductions of response fluctuation have reached 4.3 dB for prediction and 2.6 dB for measurement, respectively.     

Polaron effects on third-harmonic generation in cylindrical quantum-well wires

Polaron effects on third-harmonic generation (THG) in cylindrical quantum wires with a finite confining potential are investigated. The THG coefficient is obtained by using the compact-density-matrix approach and an iterative method, and the numerical results are presented for GaAs/AlAs cylindrical quantum wires. The results show that the THG coefficient is greatly enhanced and the peak shift to the aspect of high energy when considering the influence of electron-phonon interaction.     

POSITIVE SOLUTION FOR NONLINEAR SINGULAR BOUNDARY VALUE PROBLEMS

Under suitable conditions on f(·,u), it is shown that the two-point boundaryvalue problem((u'))' + λq(t)f(u) = 0in (0, 1),u(0) = u(1) = 0,has two positive solution or at least one positive solution for λ in a compatibleinterval.     

Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays

A delay-differential equation modelling a bidirectional associative memory (BAM) neural network with three neurons is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold reduction. Numerical simulation results are given to support the theoretical predictions.