一类平面七次多项式系统赤道环的稳定性与极限环分支

本文研究一类平面七次多项式系统赤道环的稳定性和极限环分支，给出了系统的前12个奇点量公式，可积性条件及在赤道附近存在3个极限环的条件，较为精细地指出了极限环的存在位置。     

Measurements of edge-uncolorability

Cubic bridgeless graphs with chromatic index four are called uncolorable. We introduce parameters measuring the uncolorability of those graphs and relate them to each other. For k=2,3, let c_k be the maximum size of a k-colorable subgraph of a cubic graph G=(V,E). We consider r₃=|E|−c₃ and . We show that on one side r₃ and r₂ bound each other, but on the other side that the difference between them can be arbitrarily large. We also compare them to the oddness ω of G, the smallest possible number of odd circuits in a 2-factor of G. We construct cyclically 5-edge connected cubic graphs where r₃ and ω are arbitrarily far apart, and show that for each 1c<2 there is a cubic graph such that ωcr₃. For k=2,3, let ζ_k denote the largest fraction of edges that can be k-colored. We give best possible bounds for these parameters, and relate them to each other.     

Synthesis and crystal structures of extremely crowded oligophenylenes as model precursors to ‘cubic graphite’

By using drastic conditions for a Diels-Alder cycloaddition reaction, it was possible to synthesize an oligophenylene with an extremely dense packing of the benzene rings. Crystallographic data could be obtained and a projection of the structure on the plane of the central phenyl ring reveals that the molecule retained its theoretical threefold symmetry with only minor deviations. Due to its dense packing of interlocked benzene rings, this oligophenylene could be furthermore used as a suitable precursor for constructing a subunit of ‘cubic graphite’.     

进一步改进边界元方法以克服振动声辐射计算中解的非唯一性

章利用基于三次B样条插值的边界元方法，对振动体外部声辐射问题进行了研究，对CHIEF法及其改进方法作了进一步的改进，提出在加权余量意义下，通过把内部Helmholtz积分方程与其对内点坐标取导后的方程式作线性叠加，在域外构作的一个小体积块上进行积分以形成补充方程，经与表面Helmholtz积分方程相结合，来求解任意频率下的声辐射问题，并以脉动球和摆动球作为算例，说明本提出的方法能够有效地克服在特殊频率处解的非唯一性问题。     

Volumetric properties of ethanol–water mixtures under high temperatures and pressures

The densities of ethanol and ethanol–water mixtures were measured with a vibrating tube densimeter at 25.0, 50.0 and 75.0 °C in the pressure range from 0.10 to 40.00 MPa. Densities were correlated using an empirical model. Partial molar volumes, excess molar volumes, isothermal compressibilities, cubic expansion coefficients and internal pressures were calculated from obtained densities. This study reports the dependence of densities, partial molar volumes, excess molar volumes, isothermal compressibilities, cubic expansion coefficients and internal pressures on composition, temperature and pressure.     

Synthesis and characterization of LiCo<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript>2−<Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>4</Subscript> powder by a novel CAM microwave-assisted sol–gel method for Li ion battery

LiMn₂O₄-based spinels are of great interest as positive electrode materials for lithium ion batteries. LiCo _x Mn_2−x O₄ (x = 0.0, 0.1, 0.2, 0.3, and 0.4) spinel phases have been synthesized by novel citric acid-modified microwave-assisted sol–gel method. The structural properties of the synthesized products have been investigated by X-ray powder diffraction and scanning electron microscopy. To improve the recharge capacity of Li/LiCo _x Mn_2−x O₄ cells, the electrochemical features of LiCo _x Mn_2−x O₄ compounds have been evaluated as positive electrode materials. The structural properties of Co-doped oxides are very similar to LiMn₂O₄ electrode. Techniques like cyclic voltammetry, charge–discharge and cycle life are also used to characterize the LiCo _x Mn_2−x O₄ (x = 0.0, 0.1, 0.2, 0.3, and 0.4) electrodes.     

Facile synthesis and characterization of monocrystalline cubic ZrO2 nanoparticles

Crystalline ZrO₂ nanoparticles were prepared from zirconium isopropoxide by slow hydrolysis and subsequent hydrothermal treatment of solutions containing various amounts of sodium hydroxide at 180 °C. Whereas moderately basic solutions lead to the formation of nanoparticles of monoclinic ZrO₂ with plate-like morphology, and nanoparticles of the cubic ZrO₂ high-temperature polymorph with diameters of approx. 5 nm were obtained from strongly basic solutions. The morphology, structure and properties of as-synthesized nanoparticles were characterized using HRTEM, XRD, Raman spectroscopy, UV–vis, PL spectroscopy and BET measurements. The formation of both, the monoclinic and the cubic polymorph, was confirmed by electron microscopy and Raman spectroscopy. The crystallinity and morphology of the resulting ZrO₂ nanoparticles can be adjusted by the choice of the reaction conditions. The cubic ZrO₂ nanoparticles have a high surface area (300 m²/g) and exhibit a strong photoluminescence in the UV region.     

Nonlinear dynamics of imperfectly-supported pipes conveying fluid

In this paper, the nonlinear dynamics of a pipe imperfectly supported at the upstream end and free at the other and conveying fluid is investigated. The imperfect support is modelled via cubic translational and rotational springs. The equation of motion is obtained via Hamilton’s principle for an open system, and the Galerkin method is used for discretizing the resulting partial differential equation. The dynamics of a system with either strong rotational or strong translational stiffness is examined in details. Numerical results show that similarly to a cantilevered pipe, the system undergoes a supercritical Hopf bifurcation leading to period-1 limit cycle oscillations. The Hopf bifurcation may, however, occur at a much lower flow velocity compared to the perfect system. At higher flow velocities, quasi-periodic and chaotic-like motions may be observed. The amplitude of transverse displacement is generally much higher than that for a cantilevered pipe, mainly due to large-amplitude rigid-body motion. In addition, effects of the mass ratio, internal dissipation, hardening- or softening-type nonlinearity, as well as concentrated- or distributed-type nonlinearity on the dynamics of the system are examined.     

A categorical invariant for cubic threefolds

We prove a categorical version of the Torelli theorem for cubic threefolds. More precisely, we show that the non-trivial part of a semi-orthogonal decomposition of the derived category of a cubic threefold characterizes its isomorphism class.