On invariant sets in Lagrangian graphs

In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph.     

拟-Armendariz模

For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm(N)Mm(R) is quasi-Armendariz if and only if Tm(N)Tm(R) is quasi-Armendariz, where Mm(N) and Tm(N) denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.     

Isochronicity Problem of Higher-Order Singular Point for Polynomial Differential Systems

Due to the difficulty, the isochronicity problems with respect to higher-order singular point (or degenerate singular point) of polynomial differential systems are far from being solved. The calculation of period constants is an effective way to find necessary conditions for isochronicity. In this paper, by means of a homeomorphic transformation, higher-order singular point is transferred into the origin. At the same time, a new recursive algorithm to compute period constants at the origin of the transformed system is deduced which is easy to realize with the computer algebraic system such as MATHEMATICA or MAPLE. Finally, to illustrate the effectiveness of our algorithm, the pseudo-isochronous center conditions of higher-order singular point for a class of septic system are investigated. Our work is new in terms of research about the isochronicity problem of higher-order singular point and consists of the existing results related to the origin as a special case when it is an elementary singular point.     

Inverse Coefficient Problems for Elliptic Hemivariational Inequalities

This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.     

Hazard regression with penalized spline: The smoothing parameter choice and asymptotics

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.     

Tearing and Rheological Properties of Fully Biodegradable Poly(Lactic Acid)/Poly(Ethylene Glutaric-Co-Terephthalate) Copolyester Blends

The tearing and rheological properties of poly(lactic acid) (PLA)/poly(ethylene glutaric-co-terephthalate) copolyester (FP) blends were investigated using a wide range of blending ratios. The tearing strength values of PLA/FP were always significantly higher than that of the PLA specimen. The melt flow indexer and capillary rheometer analyses indicated that the viscous flow became difficult and the melt strength of PLA was improved after the addition of FP. The interactions between the molecular chains of PLA and FP adds FP branching and lengthens the macromolecular chains and the degree of macromolecular entanglement increases. The blends with 5 wt% FP reached the maximum melt strength and minimum flow index n, while the tearing strength approached the maximum level. At higher FP contents, the melt flow properties PLA/FP blends increased and the melt strength decreased, the tearing strength of PLA/FP blends also decreased.     

外加直流电场作用下高阶弱非线性复合介质的电势分布

利用同伦分析方法, 研究了一类由柱形杂质随机嵌入基质所形成的、电场和电流密度满足J = σ E + χ |E|²E + η|E|⁴E 形式本构关系的高阶弱非线性复合介质在外加直流电场作用下的电势分布问题. 首先利用模函数展开法, 将本构方程及边界条件化成了一系列非线性常微分方程的边值问题; 再利用同伦分析方法进行求解, 给出了电势在基质和杂质区域的渐近解析解. 关键词： 高阶弱非线性复合介质 模函数展开法 同伦分析方法 电势分布     

大电流碳纳米管场发射阴极研究

报道了在较大发射面积上获得较大场发射电流的碳纳米管场发射阴极。为了加强场发射电流,在丝网印刷浆料中增加一种金属纳米颗粒,金属颗粒增强了碳纳米管发射体和衬底的接触,提高碳纳米管和衬底的粘附作用。利用改进后的丝网印刷方法制备了大电流碳纳米管场发射阴极,测得最大发射电流为68.0 mA,阴极有效发射面积约1.1 mm2,发射电流密度约6.2 A/cm2;并成功将改进方法制备的大电流场发射碳纳米管阴极应用于场发射真空器件原型。实验证明这种具有较大发射电流和较大发射电流密度的场发射能够满足部分大功率电子器件的需求。收稿日期:; 修订日期:     

Nb_3Sn/Cu复合导体分流温度的定量计算

铌三锡是高磁场下实用的一种低温超导材料,分流温度是超导磁体的关键设计参数。文中采用超导体幂指数模型,定量计算了绝热条件下柱状铌三锡复合导体的分流温度,计算结果与现有的分流温度估算公式结果相符;另外还分别讨论了幂指数模型的中的指数n以及磁场对铌三锡复合导体分流温度的影响。结果可以为无液氦直接冷却系统中超导磁体的相关低温技术研究提供一定的数据参考。