Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

Polypyrrole Shell@3D‐Ni Metal Core Structured Electrodes for High‐Performance Supercapacitors

Three‐dimensional (3D) nanometal films serving as current collectors have attracted much interest recently owing to their promising application in high‐performance supercapacitors. In the process of the electrochemical reaction, the 3D structure can provide a short diffusion path for fast ion transport, and the highly conductive nanometal may serve as a backbone for facile electron transfer. In this work, a novel polypyrrole (PPy) shell@3D‐Ni‐core composite is developed to enhance the electrochemical performance of conventional PPy. With the introduction of a Ni metal core, the as‐prepared material exhibits a high specific capacitance (726 F g^?1 at a charge/discharge rate of 1 A g^?1), good rate capability (a decay of 33 % in C_sp with charge/discharge rates increasing from 1 to 20 A g^?1), and high cycle stability (only a small decrease of 4.2 % in C_sp after 1000 cycles at a scan rate of 100 mV s^?1). Furthermore, an aqueous symmetric supercapacitor device is fabricated by using the as‐prepared composite as electrodes; the device demonstrates a high energy density (≈21.2 Wh kg^?1) and superior long‐term cycle ability (only 4.4 % and 18.6 % loss in C_sp after 2000 and 5000 cycles, respectively).     

用等厚干涉测定液体折射率

介绍一种采用等厚干涉原理测定液体折射率的简单可靠的方法。     

Using multi-exposure of color fringes to measure the beating motion of a moth

A multi-exposure of color fringes method has been developed to improve the capture speed of a conventional color CCD camera. In the method, four groups of projected fringe patterns encoded with different colors and different directions are stored in one CCD frame. Therefore the capture frequency of the conventional CCD can be improved to 200 Hz. It is available to measure the insect wings with low beating frequency, such as dragonfly, moth, or butterfly, whose beating frequency is about 30–40 Hz. We have used the method to measure the beating motion of a moth successfully.     

Electrical properties of neodymium doped CaBi4Ti4O15 ceramics

Neodymium doped bismuth layer structure ferroelectrics (BLSFs) ceramics CaBi_4−xNd_xTi₄O₁₅ (x=0, 0.25, 0.50, 0.75) were prepared by solid-state reaction method. X-ray diffraction pattern showed that single phase was formed when x=0-0.75. The refined lattice parameters showed that a (b) axes decrease at x=0.25 and increase with more Nd³⁺ dopant. The effects of Nd³⁺ doping on the dielectric and ferroelectric properties of CaBi₄Ti₄O₁₅ ceramics are studied. Nd³⁺ dopant decreased the Curie temperature linearly, and the dielectric loss, tan δ, as well. The remnant polarization of Nd³⁺ doped CaBi₄Ti₄O₁₅ ceramics was increased by 80% at x=0.25, while more Nd³⁺ dopant decreased the remnant polarization. CaBi_3.75Nd_0.25Ti₄O₁₅ ceramics had the largest piezoelectric constant d₃₃. The structure and properties of CaBi_4−xNd_xTi₄O₁₅ ceramics showed that Nd³⁺ may occupy different crystal locations when Nd³⁺ content x is less than 0.25 and more than 0.50.     

ITERATIVE APPROXIMATION OF FIXED POINTS OF NON-LIPSCHITZIAN ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS

The purpose of this paper is to investigate the problem of approximating fixed points of non-Lipschitizian asymptotically pseudocontractive mappings in an arbitrary real Banach space by the modified Ishikawa iterative sequences with errors.     

大口径光束波前采样器(孔栅)的研制

应用平面波角谱理论，分析了采样器对光波场采样和分光的基本原理以及对空间采样频率的选择规则，描述了实际研制的大口径采样器的结构设计，并通过数值方法和高能激光大气传输实验研究了高能激光经采样器前／后的远场光斑分布关系。结果表明：利用光束波前采样器能高保真地实现对高能激光束的分光。     

Differential pulse anodic stripping voltammetric determination of traces of copper with a tobramycin-Nafion modified electrode.

A Nafion-modified glassy carbon electrode incorporated with tobramycin for the voltammetric stripping determination of Cu2+ has been explored. The electrode was fabricated by tobramycin containing Nafion on the glassy carbon electrode surface. The modified electrode exhibited a significantly increased sensitivity and selectivity for Cu2+ compared with a bare glassy carbon electrode and the Nafion modified electrode. Cu2+ was accumulated in HAc-NaAc buffer (pH 4.6) at a potential of -0.6 V (vs. SCE) for 300 s and then determined by differential pulse anodic stripping voltammetry. The effects of various parameters, such as the mass of Nafion, the concentration of tobramycin, the pH of the medium, the accumulation potential, the accumulation time and the scan rate, were investigated. Under the optimum conditions, a linear calibration graph was obtained in the concentration range of 1.0 x 10(-9) to 5.0 x 10(-7) mol l(-1) with a correlation coefficient of 0.9971. The relative standard deviations for eight successive determinations were 4.3 and 2.9% for 1.0 x 10(-8) and 2.0 x 10(-7) mol l(-1) Cu2+, respectively. The detection limit (three times signal to noise) was 5.0 x 10(-10) mol l(-1). A study of interfering substances was also performed, and the method was applied to the direct determination of copper in water samples, and also in analytical reagent-grade salts with satisfactory results.     

掺杂偶氮苯聚合物光致异构Z扫描测量及其理论解释

用He_Ne激光对掺有偶氮苯聚合物DR 13的PMMA薄膜样品进行Z扫描研究 ,发现其折射率改变量与光强的关系存在着饱和效应 ,且线偏振光引起的折射率改变明显大于圆偏振光引起的折射率改变 .对于这些现象 ,用光致异构的角烧孔机理进行解释     

A Note on Topological Entropy of Maps

For a given collection of subsets of a compact metric space X which cover X,the entropies,hm(f)and hi(f),are introduced for a continuous map f of X to itseif. Also the concept of shadowing property with same end point (SPSEP for short) is introduced. The main results are,(1)H(f)≤hi(f)+hm(f)and,(2)h(f)=hm(f)whenever f has SPSEP,where h(f) is the topological entropy of f. Moreover,several corollaries are obtained.